Assignment 5

1. From a population of 1,000 individuals incarcerated in a particular jail, the mean number of prior arrests was 5 with a standard deviation of 2. write this statement using statistical notation.

1. What is the shape of a sampling distribution of means where each sample drawn was 50?

1. What are the two situations where the central limit theorem applies?

1. Assume a population of 1,000,000 students in NYC school has a mean eight of 120 lbs with a standard deviation of 20 lbs. For a sample of 100 students, what is the mean and standard deviation of the sampling distribution of mean weights? Show your work.

1. In the example above, assume the average weight for the sample of 100 students was 116 lbs. Calculate the z-statistic for the sample mean. Show your work.

1. Suppose we wanted to know how much time college students spend online. What would be an example of point estimate for the mean number of hours online for this population.

1. What is the corresponding alpha level for a confidence level of 99%.

1. What does a 95% confidence interval for a mean tell us?

1. Assume that from a sample of 100 baseball players the mean weight was 200 lbs with a standard deviation of 10. What is the margin of error for the sample mean with a 95% confidence level? Show your work.

1. With the question above, construct a 95% confidence interval for the mean weight.

1. With question #10 above, now assume the sample size was 500 with the same mean weight and standard deviation. Calculate the margin of error and construct a 95% confidence interval. Did the confidence interval get bigger or smaller?