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What conditions are necessary for the sampling distribution of the sample proportion to be approximately Normally distributed? (There may be more than one answer. Please check all that apply.)

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?

Which of the following is a property of the t distribution?

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?

The amount of calories in a small serving of French Fries at McDonalds is Normally distributed with a mean of 230 calories and a standard deviation of 15. Suppose that a random sample of 12 small servings was collected. What is the probability that the sample mean is greater than 240 calories?

Your friend decided to survey UF students to find out how many of them have taken a statistics course. She surveyed 200 randomly selected students and asked them if they have taken a statistics course. What would be the parameter that she could estimate with this data?

Suppose that you were interested in conducting a survey of Floridians and asking if they approved of the President. Suppose that you have no idea what this proportion would be, but at the end of the study you want to calculate a 95% confidence interval with a 0.025 margin of error. Find the sample size needed.

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.”  

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?

The average height of men in Cameroon is 1.706 meters with a standard deviation of 0.154 m. Height is approximately normally distributed. Suppose that a sample of 35 men is selected, find the range of the central 99.7% of sample mean heights?