Louis is managing sales agents at a call center. The company expects agents to make 20 cold calls per hour with a standard deviation of 4 calls. He samples 35 of his employees, and finds that they made an average of 23 calls. Louis wants to know if his employees’ calls are significantly different than the company’s expectations at the 2% significance level. What are the null and alternate hypotheses?

Two researchers conducted a study in which two groups of students were asked to answer 42 trivia questions from a board game. The students in group 1 were asked to spend 5 minutes thinking about what it would mean to be a​ professor, while the students in group 2 were asked to think about soccer hooligans. These pretest thoughts are a form of priming. The 200 students in group 1 had a mean score of 23.5 with a standard deviation of 4.3​, while the 200 students in group 2 had a mean score of 17.7 with a standard deviation of 4.1. Complete parts ​(a) and ​(b) below. (a) Determine the 95​% confidence interval for the difference in​ scores, μ1−μ2. Interpret the interval.   The lower bound is __. The upper bound is ___ ​(Round to three decimal places as​ needed.)   B Interpret the interval. Choose the correct answer below.     A. The researchers are 95​% confident that the difference of the means is in the interval.   B. There is a 95​% probability that the difference of the means is…

Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 42 randomly selected people who train in groups and finds that they run a mean of 47.1 miles per week. Assume that the population standard deviation for group runners is known to be 4.4 miles per week. She also interviews a random sample of 47 people who train on their own and finds that they run a mean of 48.5 miles per week. Assume that the population standard deviation for people who run by themselves is 1.8 miles per week. Test the claim at the 0.01 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2.   Step 2 of 3 :   Compute the value of the test statistic. Round your answer to two decimal places.

A publishing company has developed a study guide (reference book) for GRE Math test. They want to test if this reference book does help students perform better on the test. The company recruited a random sample of students who are planning to take this test and let them use the new reference book. Their scores are listed below. Test the null hypothesis that the students' mean score is not different from the national average (at a significance level of .05) by answering the following questions. The national statistics indicates that the average score for the population is 68.5. Scores: 70, 68, 93, 78, 73, 99, 81, 79, 61 (1) Set up hypotheses ( (2) What is the df and the critical value for this test? ( (3) What is the standard error for this test? (4) What is the t_observed for this test? ( (5) Provide the decision and the interpretation