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<b>Student’s</b>

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<b>Verifier’s</b>

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<b>Contents </b>

<b>I.Introduc on ... 5</b>

<b>II.The sta s cal methods used business planning for quality, inventory, and capacity management in... 5</b>

<b>2.1 Measuring the variability business processes quality management. inor... 5</b>

<b>2.1.1.The Range ... 6</b>

<b>2.1.2 Variance ... 7</b>

<b>2.1.3.Standard Devia on ... 8</b>

<b>2.1.4.The Coe cient Varia on of... 8</b>

<b>2.2. Probability distribu ons and applica on to business opera ons and processes ... 10</b>

<b>2.2.1. Discrete Probability Distribu on ... 10</b>

<b>2.2.2.Con nuous probability distribu ons ... 12</b>

<b>2.5.1.One sample T-test: Es ma on and Hypotheses tes ng ... 20</b>

<b>2.5.2.Two sample T-test: Es ma on and Hypotheses tes ng ... 23</b>

<b>2.5.3.Measuring the associa on between two variables (from the dataset) regression technique. by... 27</b>

<b>III.Create/draw di erent types of visual representa ons for variables in the dataset. Explain the advantages and disadvantages of each visual representa on. ... 28</b>

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<b>Figure </b>

<b>Figure 1: Mean, mode, median, range and standard devia on of ROE ... 6 </b>

<b>Figure 2: The correla on between the variables ... 9 </b>

<b>Figure 3: Categorical ROE ... 10 </b>

<b>Figure 4: Bell-shaped distribu on ... 12 </b>

<b>Figure 5: Example of Empirical rules ...14 </b>

<b>Figure 6: Linear regression model of predicted variable (ROA) is a ected by variables SAGR, FIXED, LEV, DAR 27Figure 7: Simple tables of my data set ...29 </b>

<b>Figure 8: Frequency of ROE ... 30 </b>

<b>Figure 9: Histogram of ROE ... 31 </b>

<b>Figure 10: Bar chart of Return On Equity ... 32 </b>

<b>Figure 11: Sca er plot shows the correla on between SIZE and DAR ... 33 </b>

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<b>I. Introduc on </b>

<b>1. Background and the reasons why you choose the topic </b>

Title: Analysis of factors a ec ng telecommunica ons enterprises Vietnam. in

<b>2. Objec ves, scope, and meaning of the study </b>

Objec ve: The objec ve of this study is to nd out the factors affec ng the business performance of enterprises in the telecommunica ons sector Vietnam and expand in to the scale busine ac vi es with of sse cient use of capital.

The study in scope: All telecommunica ons companies opera ng in Vietnam listed on HNX, HOSE, and Upcom in the period 2014-2021.

Meaning: The meaning of this research paper is to provide recommenda ons for telecommunica ons businesses that they can o er methods help businesses improve and improve business performance or so tocapital e ciency in the following business periods help the business operate be er. to

<b>3. Methodology (changed) </b>

Using quan ta ve analysis, nancial ra o comparison, and descrip ve research, we looked into the rela onship between nancial ratios and the nancial performance of Vietnamese telecom rms. Vietnam as determined by the regression formula. The applica on and interpreta on of statis cs is known as descrip ve analysis. Unlike inferen al or induc ve sta s cs, which aim to make conclusions about the popula on the sample is supposed to represent, descrip ve sta s cs focus on summarising a sample. This usually means that descrip ve sta s cs are non-parametric sta s cs, in contrast to inferen al sta s cs, which are based on probability theory. Even in cases where inferen al sta s cs are u lized to derive meaningful inferences from data analysis, descrip ve sta s cs are typically presented.

<b>4. Structure of the report </b>

I will rst employ a variety of sta s cal techniques used in business planning for capacity, inventory, and quality management in my ASME ar cle. A er that, I'll measure the variability in inferen al sta s cs,

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q y g y , y ,probability distribu ons and their applica on to business opera ons and procedures, and quality management. Subsequently, I use inferen al sta s cs to show how the popula on and sample di er based on various sampling strategies and tac cs. I'll be working on one sample T-test and two sample T-tests in it, using the regression technique to measure the rela onship between two variables (from the dataset). provide an explana on of regression and its use in the dataset (Stata), and construct or draw various visual representa ons for the variables in the dataset, such as frequency tables, basic tables, pie charts, and histograms. I'll be studying those sec ons in my ASM.

<b>II. The sta s cal methods used business planning f quality, inventory, and capacity management inor</b>

<b>2.1.Measuring the variability in business processes quality management.or</b>

According to Bhandari, A(2023), variability describes how far apart data points lie from each other and from

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the center of a distribu on. Along with measures of central tendency, measures of variability give you descrip ve sta s cs that summarize your data. Variability is also referred to as spread, sca er or dispersion. It is most commonly measured with the following:

Range: the di erence between the highest and lowest values Standard devia on: average distance from the mean Variance: average of squared distances from the mean

Coe cient Varia on: a sta s cal measure the dispersion data points around the mean of of ofWhile the central tendency, or average, tells where most of the points lie, variability summarizes how far apart they are. This is important because the amount of variability determines how well can generalize results from the sample to the popula on.

Low variability is ideal because it means that can be er predict informa on about the popula on based onsample data. High variability means that the values are less consistent, so it’s harder make predic ons. toData sets can have the same central tendency but di erent levels of variability or vice versa. If know only the central tendency or the variability, you can’t say anything about the other aspect. Both of them together give a complete picture your dataset. of

<b>2.1.1.The Range </b>

According to Frost, A(2017), the range is the most straigh orward measure of variability to calculate and the simplest to understand. The range a dataset is of the di erence between the largest and smallest values in that dataset. While the range is easy to understand, it is based on only the two most extreme values in the dataset, which makes it very suscep ble to outliers. If one of those numbers is unusually high or low, it a ects the en re range even if is atypical. it

Formularies: Range = Highest value The lowest value –

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Figure 1: Mean, mode, median, range and standard devia on of ROE

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For example: In the dataset of Figure 1 above, the dataset of ROE Variable has a range of -8.687789 to 0.5592108, which means ROE has Min= -8.687789 and Max=0.5592108 or that means the total sta s cs of368 observa ons of ROE show that the enterprise with the lowest ROE index is approximately -868.78% and enterprises have the highest ROE of index is approximately 55.92%. the range is 55.92%-(-868,78%) So= 924,7%

<b>2.1.2. Variance </b>

Although the range and interquar le range measure the spread of data, both measures take into account only two of the data values. We need a measure that would average the total (Σ) distan ce between each of the data values and the mean. But for all data sets, this sum will always equal zero because the mean is the center of the data. If the data value is less than the mean, the di erence between the data value and the mean would be nega ve (and distance is not nega ve). If each of these di erences is squared, then each observa on (both above and below the mean) contributes to the sum of the squared terms. The average of the sum of squared terms is called the variance. A measure of variability using all the data is called variance. It is based on the discrepancy between the mean ( for a sample, m for a popula on) and each observa on's 𝑥 value (xi). When comparing the variability of two or more variables, the variance is helpful. The average of the squared variances between each data value and the mean is the variance (Frost, 2023).

Formular: With respect to variance, the population variance, σ2 , is the sum of the squared differences between each observa on and the popula on mean divided by the popula on size, N

<small>𝟐</small>: Popula on variance

: Ith observa on in the popula on

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: Popula on mean

: Number of observa ons in popula on

The sample variance, s2, is the sum of the squared di erences between each observa on and the sample mean divided by the sample size, n, minus 1:

<small>𝟐</small>: Sample variance

: Ith observa on in the sample : Sample mean

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: Number of observa ons in a sample Example:

I’ll work through an example prac ce in Stata for a sample on my dataset with 368 observa ons in Figure 1. The total sta s cs 368 observa ons of of ROE show that the Variance is 0.2217484 or 22,17%

<b>2.1.3. Standard Devia on </b>

The standard devia on is the standard typical di erence between each data point and the mean. When the orvalues in a dataset are grouped closer together, you have a smaller standard devia on. On the other hand, when the values are spread out more, the standard devia on is larger because the standard distance is greater. Conveniently, the standard devia on uses the original units of the data, which makes interpreta on easier. Consequently, the standard devia on is the most widely used measure variability. The standard devia on is ofjust the square root of the variance. Recall that the variance is in squared units. Hence, the square root returns the value to the natural units. The symbol for the standard devia on as a population parameter is σ while s represents it as a sample es mate. To calculate the standard devia on, calculate the variance as shown above, and then take the square root of it (Frost, 2023).

Formularies:

The sample standard devia on 𝒔: Sample standard devia on The popula on standard devia on

𝝈 = √𝝈<small>𝟐</small>

𝝈: Popula on standard devia on

Example: In the variance sec on, the total statis cs 368 observa ons ROE show that the Variance of of is0.2217484 or 22,17%, from that the standard devia on is the square root of the variance equal to 0.4709017

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or 47,09%. This is clearly shown in Figure 1 above. Standard Devia on is 47.09% shows an unequal distribu on in the observed samples. That is, businesses in the telecommunica ons sector are having a disparity in opera ng ability and pro tability.

The coe cient of varia on (rela ve standard devia on) is a sta s cal measure of the dispersion of data points around the mean. The metric is commonly used to compare the data dispersion between dis nct series of data. Unlike the standard devia on that must always considered be in the context of the mean of the data, the coe cient of varia on provides a rela vely simple and quick tool to compare di erent data series. In nance, the coe cient of varia on is important in investment selec on. From a nancial perspec ve, the

nancial metric represents the risk- -reward ra o where the vola lity shows to the risk of an investment and themean indicates e reward th of an investment.

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By determining the coe cient of varia on of di erent securi es, an investor iden es the risk- -reward ra o toof each security and develops an investment decision. Generally, an investor seeks a security with a lower coe cient (of varia on) because it provides the most op mal risk- -reward ratio with low volatility but high toreturns. However, the low coe cient is not favorable when the average expected return is below zero ( Sebas an Taylor, 2023).

<b>Formular of coe cient variance: </b>

The popula on coe cient of varia on is:

σ – the standard devia on

μ – the mean

The sample coe cient of varia on is:

<b>Example: </b>

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Ge ng signi cant at 5% means a con dence level of 95%. Comparing the correlation rela onship between SIZE and DAR variables, we see that these two variables have a correla on value with a signi cant value is

<b>Figure 2: The correla on between the variables </b>

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0.00 (< 0.05) with a correla on coe cient of 0.2249. SIZE increases by 1, and DAR will increase to 0.2249. Larger enterprises tend to expand, loosen trade credit policies, are less able to manage receivables, and slower the recovery rate receivables. of

<b>2.2. Probability distribu ons and applica on to business opera ons and processes </b>

De ni on: Probability is a quan ta ve representa on of the likelihood of an event happening, expressed on a scale from 0 to 1. A probability close to 0 suggests a low likelihood, signifying that the event is improbable, while a probability near 1 indicates a high likelihood, implying that the event is highly probable or almost certain to occur (Turney, 2023).

For example: Coin Toss:

Experiment: Tossing a fair coin. Possible Outcomes: Head (H) or Tail (T).

Probability Assignment: Each outcome has a probability of 1/2. So, P(H) = 1/2 and P(T) = 1/2.

There are two types of probability distribu on which are used for di erent purposes and various types of data genera on processes.

Discrete Probability Distribu on Con nuous Probability Distribu on

<b>2.2.1. Discrete Probability Distribu on </b>

Discrete Probability distribu ons are applied for discrete random variables. Discrete distribu ons represent data with a countable number outcomes, meaning that of the poten al outcomes can put into bea list and then graphed. The list may be nite in nite oung, 2023). or (Y

The required condi ons for a discrete probability func on are: (𝑥) ≥ 0 𝑎𝑛𝑑 ∑ (𝑥) = 1

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For example, when determining the probability distribu on of a die with six numbered sides, the list is 1, 2, 3,4, 5, 6. If you're rolling two dice, the chances rolling two sixes (12) of or two ones (two) are much less than other combina ons; on a graph, you'd see the probabili es of the two represented by the smallest bars onthe chart. Or in My dataset, is : it

<b>Figure 3 Categorical ROE : </b>

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In there:

1. ROE -0.2022917 0 percen les –2. ROE - 0.0587492 percen les 0 3. ROE 0.0587493- 0.1246682 percen les 4. ROE 0.1246683 0.4530335 percen les –

Several discrete probability distribu ons speci ed by formulas are the discrete-uniform, binomial, Poisson, a ndhypergeometric distribu ons. We only study Poison distribu on.

<b>Poison: </b>

De ni on: A Poisson-distributed random variable is o en useful in es ma ng the number of occurrences over a speci ed interval of me or space. It is a discrete random variable that may assume an in nite sequence of values (x = 0, 1, 2, . . . ).

We can use the Poisson distribu on to determine the probability of each of these random variables, which are characterized as the number of occurrences or successes of a certain event in a given con nuous interval (such as me, surface area, or length). A Poisson distribu on is modeled according to certain assump ons. The Poisson distribu on is a discrete probability distribu on signifying the average likelihood of successful event occurrences within a given me frame. In its rst condi on, the probability of two variables being iden cal within the same me interval is considered. In the second condi on, the presence or absence of one variable is en rely independent of the other (Poisson_dist, 2008). The core trait of the Poisson distribu on revolves around the frequency of occurrences.

Poisson distribu on formula:

Where:

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X= the number of occurrences in an interval (fx) = the probability of x occurrences in an interval

μ = mean number of occurrences in an interval e= 2.71828

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F(x)= = 0.916082

<b>2.2.2.Con nuous probability distribu ons </b>

De ni on: A con nuous probability distribu on is a probability distribu on for con nuous random variables. When it comes to con nuous random variables, we cannot determine the probability for a par cular value. Therefore, to determine probability, we determine the probability of occurrence of a certain range of values (amsi.org.au, n.d.).

For example: Height of Individuals:

Random Variable: The height of a randomly selected individual from a popula on.

Interval: The height can take any real value within a con nuous range, such as [4 feet, 7 inches] to [7 feet, 2 inches].

In nite Values: There are infinitely many possible heights within the given interval, as height is a continuous measurement.

Examples of con nuous probability distribu on, probability distribu ons can be con nuous or discrete. On the other hand, a person’s height or blood pressure levels can take any value in a continuum of outcomes, so in this case, data are said to follow a con nuous probability distribu on.

A) Normal distribution

A normal distribu on, also known as a Gaussian distribu on or bell curve, is a sta s cal distribu on that is symmetric and bell-shaped. It is characterized by the probability density func on, which describes the likelihood of observing a par cular value within the distribu on. The shape of the curve is determined by two parameters: the mean (μ), which rep resents the center of the distribution, and the standard deviation (σ), which measures the spread or dispersion of the values.

For instance, the heights of people within a popula on tend to follow a normal distribu on. Most people fall near the average height, with fewer individuals at signi cantly shorter or taller heights. IQ scores,

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measurement errors in scien c experiments, and test scores of a large popula on.

The normal distribu on is a hypothe cal symmetrical distribu on used to make comparisons among scores or to make other kinds of sta s cal decisions. The shape of this distribu on is o en referred to as "bell-shaped" or colloquially called the "bell curve”.

<b> Figure 4 Bell-shaped distribu on : </b>

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The bell is tall and narrow for small standard devia ons and short, and wide for large standard devia ons. In which, the func on F(x) is popular to determine the area of this graph.

The normal distribu on closely approximates the probability distribu ons of a wide range of random variables. For example, the dimensions of parts and the weights of food packages often follow a normal distribu on.

The normal probability distribu on represents a large family of distribu ons, each with a unique speci ca on for the parameters μ and σ. These parameters have a very convenient interpretation.

The density func on of a normal probability distribu on is bell-shaped and symmetrical about the mean. The normal probability distribu on was introduced by the French mathema cian Abraham de Moivre in 1733. He used it to approximate probabili es associated with binomial random variables when n is large.

The probability density func on for a normally distributed random variable is: Normal Probability Density Func on:

Where:

μ=mean

σ = standard deviation π = 3.14159

e = 2.71828 For example:

For those who buy products from HYN Bag Store, the average purchase amount per customer is 15,015 USD. Let's say the standard devia on is $3540.

• a.One what is the probability that a customer has a purchase amount greater than $18,000? • b. What is the probability that a customer's purchase amount is less than $10,000?

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μ = 15,015

σ = 3540

1-0.800447= 0.199553

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B) Empirical rules

<b> Figure 5 Example of Empirical rules : </b>

The empirical rule, also some mes called the three-sigma or 68- -99.7 rule, is a sta s cal rule which states 95that for normally distributed data, almost all observed data will fall within three standard devia ons (denoted by t he Greek letter sigma, or σ) of the mean or average (represented by the Greek le er mu, or µ) of the data.

In par cular, the empirical rule predicts that in normal distribu ons, 68% of observa ons fall within the rst standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ) of the mean.

<b>2.3. Sampling Distribu on </b>

Central Limit Theorem:

The probability density func on of the sampling distribu on of means is normally distributed regardless of the underlying distribu on of the popula on observa ons and the standard devia on of the sampling distribu on decreases as the size of the samples that were used to calculate the means for the sampling distribu on increases.

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Central Limit Theorem for xˉ

Let denote the sample mean computed from a random n measurements from a popula on having a mean, xˉ ofμ and finite standard devia on σ. Let xμ ˉ and σ ˉ denote the mean and standard devia on x of the sampling distribu on of xˉ, respec vely. Based on repeated random samples size n from the popula on, of we can conclude the following:

1.μ xˉ = μ 2. σ xˉ = /√𝑛 σ

3. when n is large, the sampling distribu on xˉ will of be approximately normal (with the approxima on becoming more precise n increases) as

4. When the popula on distribu on is normal, the sampling distribu on of xˉis exactly normal for any sample size n

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For example:

Foot Locker Store Produc vity. Foot Locker uses sales per square foot as a measure of store produc vity. Sales are currently running at an annual rate of $406 per square foot. You have been asked by management to conduct a study of a sample of 16 Foot Locker stores. Assume the standard devia on in annual sales per square foot for the popula on of all 3400 Foot Locker stores is $80.

Show the sampling distribu on of x, the sample means annual sales per square foot for a sample of 64 Foot Locker stores.

Sampling Distribu on of xˉ:

The sampling distribu on of the sample mean ( ) is approximately normal if the sample size is large enough due xˉto the Central Limit Theorem. The mean of the sampling distribu on (μxˉ) is equal to the popula on mean ( ), μand the standard devia on of the sampling distribu on (σxˉ) is calculated using the formula:

So, the standard devia on of the sampling distribu on (σxˉ) is 20$

<b>2.4.Inferen al Sta s cs </b>

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<b>2.4 1.. Principles </b>

Sampling is the methodical process of selec ng a subset, or sample, from a larger popula on to collect data that can be used to answer a research ques on about the en re popula on. The sample is chosen because it is o en imprac cal or impossible to collect data from the en re popula on. The results obtained from the sample are considered es mates, or approxima ons, of the actual values of popula on characteris cs. Proper sampling methods are crucial in obtaining reliable es mates, ensuring that the sample is representa ve and can provide accurate insights into the broader popula on.

The sample data helps us to make an estimate of a popula on parameter. There are 2 types of es ma on for popula on parameters:

Point Es mate: we use the data from the sample to compute a value of a sample sta s c that serves as an es mate of a popula on parameter.

Interval Es mate: is a range of values.

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𝑛 𝑎 𝑛 𝑎 𝑎 𝑛 𝑎

<b>2.4.2.Point Es mate </b>

Point es ma on is a sta s cal inference technique where data from a sample is u lized to calculate a speci c value for a sample sta s c. This calculated value then serves as an es mate or approxima on of a corresponding popula on parameter. The objec ve of point es ma on is to provide a single, best guess for the true value of the parameter based on the informa on obtained from the sample. It is a fundamental aspect of sta s cal analysis that enables researchers and analysts to make predic ons and draw conclusions about a popula on using informa on gathered from a representa ve subset.

We refer to xˉ as the point es mator the popula on mean. ofS is the point es mator the popula on standard devia on of

is the point es mator the popula on propor on p ofCalcula on formula:

x = , s = √<small> </small> , p =

Example Point Es mate of Propor on:

A survey was conducted using a sample of 300 teacher trainees in a training school to determine what propor on of them view the services provided to them favorably. Out of 150 trainees, 103 of them responded that they viewed the services provided to them by the school as favorable. Find the point es ma on for this data.

<b>Solu on: </b>

The point es ma on here will be of the popula on propor on. The characteris c of interest is the teacher trainees having a favorable view about the services provided to them. So, all trainees with a favorable view are

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successful, x=103. n =150. that means. p = ₌<small> </small> = 0.686

The researchers of this survey can establish the point es mate, which is the sample proportion to be 0.686 or 68.7%

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score for the standard normal distribu on to calculate the margin of error.

<b>Interval Estimate of a Population Mean: σ Known: </b>

Zα/2* ^𝝈<small>√ </small>Where:

<b> : the sample mean </b>

1 – : the con dence coef cient

<small> 𝟐</small><b>: the z-value providing an area of in the upper tail of the standard normal distribu on. </b> 𝝈: the popula on standard devia on

: the sample size.

For example:

Discount Sounds has 260 retail outlets throughout the United States. The rm is evalua ng a poten al loca on for a new outlet, based in part on the mean annual income of the individuals in the marke ng area of the new loca on.

A sample of size = 36 was taken; the sample mean income is $41,100. The popula on is not believed to be nhighly skewed. The popula on standard devia on is es mated to be $4,500, and the con dence coe cient to be used in the interval es mate is 0.95.

Ques on: es mate the popula on mean. n =36

𝑥 = 41100 σ = 4500

 <b> = </b> Zα/2* ^𝝈<b> =41110 1.959*</b><small> </small> = ($39,630& $42,570)

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<b>2.4.4.Hypothesis tes ng </b>

Hypothesis tes ng in sta s cs is a way for you to test the results of a survey or experiment to see if you have meaningful results. You’re basically testing whether your results are valid by figuring out the odds that your results have happened by chance. If your results may have happened by chance, the e periment won’t be repeatable and so has li le use.

The alternate hypothesis, denoted by Ha, is the opposite of what is stated in the null hypothesis; the null hypothesis, donated by Ho, is a tenta ve assump on about a popula on parameter.

Hypothesis tes ng can be used to determine whether a statement about the value of a popula on parameter should or should not be rejected.

The null hypothesis, denoted by Ho, is a tenta ve assump on about a popula on parameter. The alterna ve hypothesis, denoted by Ha, is the opposite of what is stated in the null hypothesis. The hypothesis tes ng

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procedure uses data from a sample to test the two competing statements indicated by Ho and Ha. P – value ≤ 0: Reject Ho, accept Ha.

P - value > 0: Accept Ho, reject Ha Steps of hypothesis tes ng:

Step 1: Develop the null and alterna ve hypotheses. Step 2: Specify the level of significance α

Step 3: collect the sample data and compute the value of the test sta s c P- value approach

Step 4: Use the value of the test sta s c to compute the p-value Step 5: Reject Ho if p-value ≤ α

For example: Hypothesis tes ng σ Known

A major west coast city provides one of the most comprehensive emergency medical services in the world. Opera ng in a mul ple hospital system with approximately 20 mobile medical units, the service goal is to respond to medical emergencies with a mean me of 12 minutes or less.

The response mes for a random sample of 40 medical emergencies were tabulated. The sample mean is 13.25 minutes. The popula on standard devia on is believed to be 3.2 minutes.

The EMS director wants to perform a hypothesis test, with a .05 level of signi cance, to determine whether the service goal of 12 minutes or less is being achieved.

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