A university president believes that, over the past few years, the average age of students attending his university has changed. To test this hypothesis, an experiment is conducted in which the age of 20 students, who have been randomly sampled from the student body, is measured. The mean age of these 20 students is 25 years. A complete census taken at the university a few years before the experiment showed a mean age of 23 years, with a standard deviation of 7. Assume that the population standard deviation is 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.

According to the College Board, scores on the math section of the SAT Reasoning college entrance test for the class of 2010 had a mean of 516 and a standard deviation of 116. Assume that they are roughly normal.One of the quartiles of the scores from the math section of the SAT Reasoning test is 438. The other quartile is _______.

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…

A pizza delivery chain advertises that it will deliver your pizza in 35 minutes from when the order is placed. Being a skeptic, you decide to test and see if the mean delivery time is actually more than 35 minutes. For the simple random sample of 14 customers who record the amount of time it takes for each of their pizzas to be delivered, the mean is 37.0 minutes with a standard deviation of 9.9 minutes. Assume that the population distribution is approximately normal. Perform a hypothesis test using a 0.05 level of significance. Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places.