In 2012, the General Social Survey asked its respondents if they had volunteered in the past month. The 95% confidence interval for this result was (0.313, 0.378). Is the following a correct or incorrect interpretation statement? “The probability that the sample proportion is between 0.313 and .378 is 0.95.”

Suppose the sampling distribution for average height for NFL players is normally distributed with a mean of 74 and a standard error of 2 inches.  Find the range of central 99.7% of sample means.

Suppose that you had the following hypothesis Ho: p = 0.5 versus Ha: p > 0.5. If you had the test statistic equal to 1.34, what would be the p-value?

A survey of 20 randomly selected people from Gainesville were asked if they planned on purchasing a new house in the next year. Out of 20 people, 5 said yes. Can you make a 95% confidence interval for the population proportion?

Suppose that you were going to take a sample of Florida students. You were interested in estimating the proportion who had ever called/emailed/spoken with their congressmen. You believe that the proportion is close to 0.08; however, you wanted to be 95% confident with a margin of error equal to 0.028. What sample size do you need?

A researcher was interested in testing the hypothesis to see if there was majority support for a new bill. She found a p-value equal to 0.002. What would be her conclusion?

Suppose that you took a sample of 20 students at UF and asked them how many minutes they exercised yesterday. Suppose that you wanted to make a 90% confidence interval for the population mean. What value would you use for t?

Suppose the sampling distribution for average height for soccer players is normally distributed with a mean of 71.5 and a standard error of 2 inches.  Find the range of central 95% of sample means.

A sample of 2,419 US residents were asked if they considered their home “very clean” right now. The 95% confidence interval was (0.0146. 0.0259). Is the following interpretation of the confidence interval correct? “We are 95% confident that the sample proportion of Americans that consider their home very clean is between 0.0146 and 0.0259.”  

For a confidence interval for the population mean, if you increase the confidence level, what happens to the width of the interval (everything else remains the same)?