There are two problems from the WeBWorK Hypothesis Test for a ProportionProblem Setfor which you will write out the full hypothesis test as instructed below(examples in the Class Notes and other resources) and submit your work.

Problems 1 and 2:Conduct a hypothesis test to determine if the data given provide strong evidence supporting the statement below.

Statement

• Problem 1More than halfof registered voters in the state would vote for the Republican candidate.
• Problem 245 percent of Harvard students have brown eyes.

Step 1: Identify the parameter of interest (in words in the context of the problem) for this problem.

Step 2:Write out the null and alternative hypotheses in both words(in the context of the problem) and mathematical symbols (already given on WW).

Step 3:Identifyp^ (p hat, sample proportion), p0 (null value), n (sample size) and assume a value for alpha (significance level).

Step 4:Verify the conditions for applying the CLT (Central Limit Theorem): independence and success-failure (using the null value).

Step 5:Calculate the SE (standard error - using the null value) and the test statistic (z-score). Show all formulas and calculations.

Step 6:Find the p-value using the normal distributionappand submit a screen shot of your work http://onlinestatbook.com/2/calculatorsormal_dist.html

Step 7: Evaluate the hypothesis by comparing the p-value to the alpha value (either reject orfail to reject the null hypothesis) and give your reasoning.

Step 8:Provide a conclusion in the context of the problem. More help with this:

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Hypothesis Test for a Proportion: Problem 1 Previous Problem Problem List Next Problem (1 point) A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a SRS of n = 1300 registered voters and found that 670 would vote for the Republican candidate. Let p represent the proportion of registered voters in the state who would vote for the Republican candidate. We test Ho : p = .50 Ha : p > .50 (@) What is the z-statistic for this test? 1.1094 (b) What is the P-value of the test? 0.13363Hypothesis Test for a Proportion: Problem 2 Previous Problem Problem List Next Problem (1 point) An article in the Washington Post on March 16, 1993 stated that nearly 45 percent of all Americans have brown eyes. A random sample of n = 82 Harvard University students found 30 with brown eyes. We test Ho : p = .45 Ha : p #.45 (a) What is the z-statistic for this test? -1.528 (b) What is the P-value of the test? 0.128