A university president believes that, over the past few years, the average ageof students attending his university has changed. To test this hypothesis, an experimentis conducted in which the age of 20 students, who have been randomly sampled from thestudent body, is measured. The mean age of these 20 students is 25 years. A completecensus taken at the university a few years before the experiment showed a mean age of23 years, with a standard deviation of 7. Assume that the population standard deviationis 7 and the population data are normally distributed.(a) State the suitable null and alternative hypotheses that address the research question.(b) Compute the z-statistic for our sample data. Show work.(c) Based on the z-statistic, compute the p-value. Show work and attach R code.(d) Suppose a = 0.05. Based on the p-value, decide whether you can reject the null.(e) Using the same a level, compute the upper critical value for the z-test. Show workand attach R. code.(f) Compare the upper z-critical with the z-statistic and decided whether you can rejectthe null. Did you reach the same conclusion as part (d)?(g) Compute the 95% confidence intervals for the mean.Suppose we have the same scenario as the above question except the samplesize n changes.(a) Suppose the sample size changes from n = 20 to n = 100. What are the new z-statistic and p-value? Are we more likely or less likely to reject the null hypothesis?(b) Based on your answer in the previous part, complete the following sentence."As the sample size increases, the z-statistic becomesHo becomes-, the p-value becomesto be rejected, and the power of the test33

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A college student is interested in investigating the claim that students who graduate with a master’s degree earn higher salaries, on average, than those who finish with a bachelor’s degree. She surveys, at random, 49 recent graduates who completed their master’s degrees, and finds that their mean salary is $⁢37,400 per year. The standard deviation of annual salaries for the population of recent graduates who have master’s degrees is known to be $⁢2400. She also surveys, at random, 37 recent graduates who completed their bachelor’s degrees, and finds that their mean salary is $⁢36,700 per year. The standard deviation of annual salaries for the population of recent graduates with only bachelor’s degrees is known to be $⁢1900. Test the claim at the 0.05 level of significance. Let recent graduates with a master's degree be Population 1 and let recent graduates with a bachelor's degree be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to…
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