Test for the best ~ A major financial services company uses a set of pre-employment tests to evaluate potential employees before they are hired. All applicants sign a confidentiality agreement not to divulge any content from the tests, which has allowed the company to use the same tests over many years. The test scores are known to be normally distributed with a mean of 76.7.In an effort to hire more talented employees, the company recently hired a recruiting firm to find better qualified applicants. A random sample of 21 applicants provided by the recruiting firm had a mean test score of 81.02 and a standard deviation of 7.5.The company wants to determine if the mean test score for all applicants supplied by the recruiting firm is higher than the historical mean of 76.7.Round all calculated values to 4 decimal places as appropriate.1. Which inference procedure should the company use?A. t test for a population mean B. Randomization test for the difference of two population proportions C. Z confidence interval for a population proportion D. Z test for one population proportion E. 22 test of independence

2. Which set of hypotheses should the company use to answer the research question?A. H0:=76.7H0:=76.7 vs. Ha:>76.7Ha:>76.7 B. H0:=76.7H0:=76.7 vs. Ha:76.7Ha:76.7 C. H0:=76.7H0:=76.7 vs. Ha:<76.7Ha:<76.7 D. H0:x=81.02H0:x=81.02 vs. Ha:x>81.02Ha:x>81.02

3. Recall that the company knows from many years of testing that the test scores are normally distributed. What additional condition or conditions must be met for the hypothesis test to be valid? Select all that apply: A. The sample test scores must be normally distributed. B. The sample size must be at least 3 times the standard deviation. C. There must be an expected variation in the test scores of at least 5 points. D. The sample observations must be independent.

4. What is the test statistic? ? z t X^2 =

5. The company calculates a p-value of 0.0079. Which of the following are correct interpretations of the p-value? Select all that apply: A. A p-value of 0.0079 means we have very strong evidence against the null hypothesis. B. A p-value of 0.0079 means we have very strong evidence that the null hypothesis is true. C. Under the null model, we would expect a sample mean of 81.02 or more approximately 0.79% of the time in repeated sampling. D. A p-value of 0.0079 means that there is a 0.79% chance that the null model is a good fit for the observed data.

6. Calculate the effect size for the company's hypothesis test.d^=d^=

Romain is the marketing manager for the recruiting firm. He wonders if this financial company's hypothesis test and effect size can be replicated with other, similar companies that use the same pre-employment test. Romain obtains the historical mean for another company and conducts two hypothesis tests using sample data from new applicants found by the recruiting firm.For the first test, Romain uses a sample size of 27 test results, and finds a p-value of 0.09 and an effect size of 0.35.For the second test, Romain uses a sample size of 62 test results, and finds a p-value of 0.033 and an effect size of 0.37.

7. The results from the second test ? confirm conflict with the results from the first test because the ? p-values effect sizes sample sizes are ? similar dissimilar .