SHOW ALL WORKING 1. Consider the hypothesis test given by: H0 : p = 0.5 H1: P < 0.5 a random sample of 625 subjects, the sample proportion is found to bepp 0.55. (a) Determine the test statistic. Show all work; writing the correct test statistic, withoutsupporting work, will receive no credit. (b) Determine the Pvalue for this test. Show all work; writing the correct Pvalue,without supporting work, will receive no credit. (c) Is there sufficient evidence to justify the rejection ofH0at the 0.01level?Explain 2. Consumption of large amounts of alcohol is known to increase reaction time. To investigate the effects of small amounts of alcohol, reaction time was recorded for five individuals before and after the consumption of 2 ounces of alcohol. Do the data below suggest that consumption of 2 ounces of alcohol increases mean reaction time Subject 1 2 3 4 5 Reaction Time (seconds) Before After 6 7 8 8 4 6 7 9 9 8 Assume we want to use a 0.05 significance level to test the claim. (a) Identify the null hypothesis and the alternative hypothesis. (b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. (c) Determine the P-value. Show all work; writing the correct P-value, without supporting work, will receive no credit. (d) Is there sufficient evidence to support the claim that consumption of 2 ounces of alcohol increases mean reaction time? Justify your conclusion 3. A combination lock uses three distinctive numbers between 0 and 39 inclusive. How many different ways can a sequence of three numbers be selected? (Show work) 4.The UMUC Mini Mart sells five different types of coffee mugs. The manager reports that the five types are equally popular. Suppose that a sample of 500 purchases yields observed counts 120, 90, 110, 100, and 80 for types 1, 2, 3, 4, and 5, respectively. Type Number of Mugs 1 120 2 90 3 110 4 100 Assume we want to use a 0.05 significance level to test the claim that the five types are equally popular. a. b. c. d. e. Identify the null hypothesis and the alternative hypothesis. Determine the test statistic. Determine the P-value for the test Is there sufficient evidence to support the manager's claim that the five types are equally popular? 5 80