Suppose that, for two populations, the distributions of the variable under consideration have the same shape. Further suppose that you want to perform a hypothesis test based on independent random samples to compare the two population means. If the distributions of the variable are normal, would you use the pooled t-test or the Mann–Whitney test? Explain your answer.

Question

Suppose that, for two populations, the distributions of the variable under consideration have the same shape. Further suppose that you want to perform a hypothesis test based on independent random samples to compare the two population means. If the distributions of the variable are normal, would you use the pooled t-test or the Mann–Whitney test? Explain your answer.

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Statistics

Related Statistics Q&A

Find answers to questions asked by students like you.

Q: Tornadoes During a recent 64-year period, New Mexico had a total of 153 tornadoes that measured 1 or...

A: Mean of Poisson distribution:The mean (m) of the Poisson distribution is defined as the mean number ...

Q: A bus comes by every 14 minutes. The times from when a person arives at the busstop until the bus ar...

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case yo...

Q: Interpreting Displays. In Exercises 5 and 6, use the results from the given displays. Treating Carpa...

A: State the test hypotheses.Let first population denote the surgery and second population denote the s...

Q: Curving Test Scores A professor gives a test and the scores are normally distributed with a mean of ...

A: Note:Hey there! Thank you for posting the question. However, since your question has more than 3 sub...

Q: Technology. In Exercises 9–12, test the given claim by using the display provided from technology. U...

A: The claim is to test that the mean of tornado length is greater than 2.5 miles at 5% level of signif...

Q: Electricity Costs. The monthly service charge for electricity for a residential customer who is usin...

A: Solution:Solution: It is given that:The monthly service charge for electricity for a residential cus...

Q: Confidence Interval for Lightning Deaths Use the sample values given in Cumulative Review Exercise 1...

A: In this case, Cumulative review Exercise 1 is considered as follows:

Q: Problems pertain to the critical-value approach to hypothesis testing. Determine the critical value(...

A: Click to see the answer

Q: Detecting Fraud The Brooklyn District Attorney’s office analyzed the leading (leftmost) digits of ch...

A: (a)Define the random variable x as the number of checks with the leading digit as 1. Here, the numbe...

Q: Births In a recent year, NYU-Langone Medical Center had 4221 births. Find the mean number of births ...

A: Mean of Poisson distribution:The formula is given by,

Q: In Exercises, hypothesis tests are proposed. For each hypothesis test, a.determine the null hypothes...

A: a).Let µ be the mean annual salary of classroom teachers.The null hypothesis for the test is given b...

Q: Body Temperatures Based on the sample results in Data Set 3 “Body Temperatures” in Appendix B, assum...

A: a.The random variable x represents the body temperature.The formula to convert the x value into z sc...

Q: Explain the difference between a point estimate of a parameter and a confidence-interval estimate of...

A: A point estimate gives us a particular value as an estimate of the population parameter.

Q: Exercises pertain to critical values for a Wilcoxon signed-rank test. Use Table V in Appendix A to d...

A: a)For 1% level of significance,

Q: Technology. In Exercises 9–12, test the given claim by using the display provided from technology. U...

A: In an Airport Data Speeds, the population mean is 4, the sample mean is 3.71, the test statistic is ...

Q: State whether each of the following is true or false and explain your answer. a. The estimate of the...

A: (a)Justification:

Q: What is the difference between a STATISTIC and PARAMETER

A: Solution:We have to determine the difference between a STATISTIC and PARAMETER.

Q: In each of Exercises, we have provided a sample mean, sample standard deviation, and sample size. In...

A: The null and alternative hypotheses are stated below:

Q: Uncertainty True or false: If correct methods of hypothesis testing are used with a large simple ran...

A: Click to see the answer

Q: The symbolФ(z) is often used to denote the area under the standard normal curve that lies to the lef...

A: In a one mean z test z0 is the observed value of the test statistic z. F(z) is used to denote the ar...

Q: In Exercises, we have given the value obtained for the test statistic, z, in a one-mean z-test. We h...

A: Click to see the answer

Q: Understanding the Concepts and SkillsExplain the meaning ofa. qualitative variable.b. discrete, quan...

A: From the given question,The variables can be defined into broad category which as follows:Qualitativ...

Q: Problems pertain to the critical-value approach to hypothesis testing. Explain the meaning of each t...

A: a.Rejection region:The range of set of values by which it can be concluded whether the null hypothes...

Q: Wildfires. Wildfires are uncontrolled fires that usually spread quickly and are common in wilderness...

A: The Boxplot and Histogram for the given data can be obtained as follows:Step-by-step procedure to ob...

Q: Testing Hypotheses. In Exercises 13–24, assume that a simple random sample has been selected and tes...

A: The data shows that the heights of supermodels. Also, the level of significance is 0.01.The claim is...

Q: Given are the data for two variables x and y. xi  6 11 15 18 20 yi  6  8  12  20  30 D. Compute the ...

A: Step-by-step procedure to obtain the standard residuals using Excel.In Excel sheet, enter X in one c...

Q: Lightning Deaths Refer to the sample data in Cumulative Review Exercise 1. a. What is the level of m...

A: In this case, Cumulative review Exercise 1 is considered as follows:

Q: What is the difference between class boundaries and class limits

A: Class limit: The smallest and the largest value for a class are called as class limits. The smallest...

Q: Finding P-values. In Exercises 5–8, either use technology to find the P-value or use Table A-3 to fi...

A: Given info: The claim is that for Version data speeds at airports with the mean 14 mbps, the sample ...

Q: Suppose x1 and x2 are predictor variables for a response variable y. a. The distribution of all poss...

A: a. Yes, the distribution of the response or dependent variable is the distribution of all the possib...

Q: Testing Hypotheses. In Exercises 13–24, assume that a simple random sample has been selected and tes...

A: The data shows that the measurements of National Highway Traffic Safety Administration, a car crash ...

Q: Problems pertain to the P-value approach to hypothesis testing. State the decision criterion for a h...

A: In this case, we need to find the decision criterion for a hypothesis test using the P-value approac...

Q: Number 14 parts d and e.

A: From the given Histogram, let us consider the following frequency table,

Q: Lightning Deaths The graph in Cumulative Review Exercise 5 was created by using data consisting of 2...

A: Click to see the answer

Q: Explain the meaning of the term hypothesis as used in inferential statistics.

A: Hypothesis testing:         Hypothesis testing was introduced by R.A.Fisher (Ronald Fisher).It is a ...

Q: Unbiased Estimators Data Set 4 “Births” in Appendix B includes birth weights of 400 babies. If we co...

A: The data represents the birth weights of 400 babies.The statistics sample mean, sample variance and ...

Q: In the section we introduced a descriptive measure of the utility of the multiple linear regression ...

A: a.Coefficient of multiple determination:

Q: In each of Exercises, use the technology of your choice to decide whether applying the t-test to per...

A: Step by step procedure to draw the normal probability plot, using MINITAB software.Choose Graph >...