MTH Pre-Qualifying Exam 2023.

MTH Pre-Qualifying Exam 2023. The shift supervisor of a pizza parlor claimed that the population mean total time to deliver a pizza is exactly 45 minutes. Paige, the owner, would like to find evidence that the population mean total time to deliver a pizza is less than 45 minutes so she records the total delivery time of 71 randomly selected deliveries and she finds that the sample mean is 44.06 minutes with a sample standard deviation of 3.46 minutes. The test statistic t for a hypothesis test of H0:μ=45 versus Ha:μ45 is t≈−2.29. If 0.01p-value0.025 and the level of significance is α=0.05, which of the following statements are accurate for this hypothesis test to evaluate the claim that the true population mean total time to deliver a pizza is less than 45 minutes? - ANSWER Reject the null hypothesis that the true population mean total time to deliver a pizza is equal to 45 minutes. There is enough evidence at the α=0.05 level of significance to support the claim that the true population mean total time to deliver a pizza is less than 45 minutes. Compare the p-value to α=0.05. Since the p-value is less than α, reject the null hypothesis H0. Therefore, there is enough evidence at the α=0.05 level of significance to support the claim that the true population mean total time to deliver a pizza is less than 45 minutes. A college professor claims the proportion of students that complete a homework assignment is 70%. To test this claim, a random sample of students are monitored and checked if they completed the home the algebra class. Assume that the test statistic for this hypothesis test is −1.73. Since this is a two tailed hypothesis test, assume that the critical values for this hypothesis test are −1.96 and 1.96. Come to a decision for the hypothesis test and interpret your results with respect to the original claim. - ANSWER Fail to reject the null hypothesis.There is not enough evidence to reject the claim that the proportion of students that complete a homework assignment is 70%.In this example this hypothesis test is a two tailed test and thus the rejection region is both on the left and right side. Any values of the test statistic that are less than 1.96will fall in the rejection region, and also any values of the test statistic that are more than 1.96will fall in the rejection region According to a survey, the average American person watches TV for 3 hours per week. To test if the amount of TV in New York City is less than the national average, a researcher decides to do a hypothesis test, at a 1% significance level. She surveys 19 New Yorkers randomly and asks them about their amount of TV each week, on average. From the data, the sample mean time is 2.5 hours per week, and the sample standard deviation (s) is 0.9 hours. H0: μ≥3; Ha: μ3. α=0.01 (significance level) What is the test statistic (t-value) of this one-mean hypothesis test (with σ unknown)? Round your final answer to two decimal places. - ANSWER -2.42