Question

If you were conducting the two-sided hypothesis test,

Ho: μ = 65

Ha: μ ≠ 65

at the 5% significance level, would you reject or fail to reject Ho. I don't want you to conduct a full hypothesis test here. Instead, note that one of the above CIs is equivalent to conducting this test. Tell me which interval and explain why you decided to reject or fail to reject based on this interval.

1. Suppose you are going to construct a 95% CI for the mean height of all the students in this class. Based on our sample of 16 students, we will assume the standard deviation is 2.8. What sample size is needed to get a MOE of 1 inch? Your answer should be a whole number.

2. A poll conducted by NBC took a random sample of 2409 registered voters in Texas. 49% of those surveyed said they planned to vote for Trump. Conduct a 95% confidence interval for the actual proportion of people who will vote for Trump in Texas.

3. Interpret the interval.

4. Based on your interval, is 51% a plausible value for the proportion of people who will vote for Trump in Texas? Explain.

Answer 1

1) At 95% confidence level, the critical value is z_0.025 = 1.96

Margin of error = 1

or, n = (1.96 * 2.8)^2

or, n = 31

2) At 95% confidence level, the critical value is z_0.025 = 1.96

The 95% confidence interval for population proportion is

3) We are 95% confident that the true proportion of people who will vote for Trump in Texas lies in the above confidence interval.

4) Since 0.51 does not lie in the confidence interval, so 51% is not a plausible value for the proportion of people who will vote for Trump in Texas.