Statistics – Hypothesis Test for Proportions

Part 1 (MUST SHOW ALL WORK)

1. An opinion poll asks a random sample of 100 college juniors how they view their job prospects once they graduate. Out of the 100 students 53 said “Excellent.” Find a 95% confidence interval to estimate the proportion of college juniors who think their job prospects are excellent. Assume large samples.
2. In 1999, the Bureau of Justice Statistics³ indicated that 14% of violent crimes are committed by women. Suppose that a random sample of 400 people who committed violent crimes was taken and it was determined that 65 of the 400 were women. Find a large-sample 95% confidence interval based on the sample data. Determine if the 14% is contained in the confidence interval.
3. The IRS is trying to determine which percentage of tax returns claim itemized deductions. A random sample of 2,000 returns was taken and the IRS found that 663 claimed itemized deductions. Find a large-sample 90% confidence interval based on the sample data.
4. What are the conditions that must be checked when performing a test of proportions?

Part 2 (MUST SHOW ALL WORK)

1. Suppose that experts claim that 14% of violent crimes are committed by women. Is there enough evidence to use a benchmark of 0.05 to reject the claim, if in a sample of 400 violent crimes, 65 were committed by women? Use the four-step (state, plan, solve, conclude) process to answer this question.
2. Suppose that California Community Bank is testing the hypothesis that the proportion of deposit slips filled out incorrectly is 2%. A random sample of 1000 customers found that 28 completed the deposit slips incorrectly.
   a) Identify the null and alternate hypotheses.
   b) Determine if strong evidence exists to confirm that 2% of the deposit slips are filled out incorrectly?
   c) If a benchmark of 0.05 was used for the p-value, would the null hypothesis be rejected, or do we fail to reject the null?
3. A member of IRS claims that 30% of tax filers claim itemized deductions. A random sample of 2,000 returns was taken and the IRS found that 663 claimed itemized deductions. Test the claim using the four-step process. Use a significance level of 0.10. Then, compare this problem to Problem 3 of Part 1.