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The Lantern wants to conduct an opinion poll to estimate the true population proportion of OSU students who think OSU will win the NCAA tournament this year in basketball.  How many students will the Lantern need to include in their sample to estimate the true population proportion to within 0.05 (i.e., B = 0.05) with probability equal to 0.95?  No prior estimates of p and q are available.

In the 1970’s it was generally assumed that the mean birth weight of Angus beef cattle was 75 lb.  A researcher believes that, due to selection for increased size and growth rate in Angus, the average birth weight is now greater than 75 lb.  He obtains a random sample of n = 144 birth weights of Angus calves and calculates a sample mean of 85 lb and a sample standard deviation of 10 lb. Calculate the test statistic need to test the null hypothesis.  Using the appropriate table and a significance level (α) = 0.05, find the critical value of the test statistic.  Should the researcher reject or not reject the null hypothesis?  Explain.

The Central Limit Theorem guarantees that the population is normally distributed whenever n is sufficiently large (n > 30).

A box of Mr. Phipps Tater Crisps is supposed to contain 156 grams of potato chips.  On the side of the box it says “This package is sold by weight, not by volume.  Packed as full as practicable by modern automatic equipment, it contains full net weight indicated.  If it does not appear full when opened, it is because contents have settled during shipping and handling”.  Periodically, the Nabisco Company receives complaints that their boxes of Tater Crisps are not full (i.e., that they contain less than 156 grams of potato chips).  To test this claim, the Nabisco Company randomly samples 10 boxes and finds the average amount of potato chips held by the 10 boxes is 154 grams and the standard deviation is 30 grams. Using a significance level of α = 0.05, find the rejection region for the test of the null hypothesis.

Assume that the mean length of time required to complete the Columbus Marathon was 4.5 hours.  Further assume that the standard deviation of the times required to complete the race was 0.50 hours.  The winning time was 2.3 hours.  Calculate the z-score for the runner with the winning time of 2.3 hours.  Based on this z-score, is this time of 2.3 hours an outlier?  Why or why not?

For a given sample size, the width of the confidence interval for a parameter increases as the confidence coefficient increases.  In other words, a 95% confidence interval is wider than a 90% confidence interval, and a 99% confidence interval is wider than a 95% confidence interval.

A population of turkeys has a mean weight of 20 lb and a standard deviation of the weights equal to 4 lb.  A turkey breeder selects a large number of samples of 36 turkeys each, calculates the mean weight of the turkeys in each of these samples, and then graphs the sample means. Regardless of the shape of the distribution of the population of turkey weights, would we expect the sample means to be approximately normally distributed?

Find the standard deviation of a binomial probability distribution with a sample size of n = 40 and a probability of success of 0.60.

A random sample of 4,000 U.S. citizens was asked their opinion concerning gun control.  A total of 2,600 of the 4,000 citizens in the sample stated that they are in favor of gun control legislation.  Construct a 98% confidence interval for the true population proportion (p).

Suppose that a random sample of 40 measurements is selected from a population with a mean of 64 and a variance of 64.  What is the mean and standard deviation of the sampling distribution of the sample mean?