Assume that the mean length of time required to complete the Columbus Marathon was 4.5 hours and that the standard deviation of the times was 0.70 hours.  Assume that the racing times were approximately normally distributed.  What proportion of the runners would be expected to require more than 5.9 hours to complete the race?

Suppose that a scientist has 60 mice that she could  use in an experiment involving a new drug to treat a disease.  The scientist decides to use 6 of the 60 available mice for a small preliminary experiment before conducting a larger study.  The scientist arbitrarily begins at row 15 column 1 of the random number table and goes from left to right across the row.  Which one of the following is the correct random sample of 6 mice? For your convenience, here are rows 15 and 16 of the random number table:       Column       Row 1 2 3 4 5 6 15 07119 97336 71048 08178 77233 13916 16 51085 12765 51821 51259 77452 16308

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?

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

The FDA wants to compare the mean caffeine contents of two brands of cola, Brand A and Brand B.  In a preliminary study, a small number of independent random samples of cans of each brand were selected and the caffeine content of each can was determined.  The results were as follows:   Brand A Brand B Sample size 15 10 Mean (ounces) 18 20 Variance 1.2 1.5 How many cans of each brand of cola would need to be sampled in order to estimate the difference in poppulation mean caffeine contents to within 0.5 ounces with probability 0.95?

A sales representative for a seedcorn company tells his boss that within the past year he has contacted 80% of the farmers in his sales district.  However, his boss makes random phone calls to 36 farmers in the sales district and finds that the sales rep only contacted 24 of them in the past year. Based on the hypothesis test, what should the boss conclude?  Explain.

USA Today reported the results of a study that suggests frequently heading the ball in soccer lowers players’ IQs.  A psychologist tested 60 male soccer players ages 14 to 29 who played soccer up to five times per week.  Players who averaged 10 or more headers per game had an average IQ of 103, whereas players who headed the ball one or fewer times per game had an average IQ of 112.  The experimental units in this study are:

The types of trees (maple, oak, elm, etc.) in a nursery are an example of a ____________ variable.

We randomly select 100,000 samples of size n from a population.  We calculate the sample mean (X-bar) for each of the 100,000 random samples and graph the relative frequency distribution for these 100,000 values of X-bar.  This relative frequency distribution is called the ____________________ of X-bar.

An Animal Scientist wants to estimate the average weaning weight of the Angus breed of beef cattle.  Therefore, he selects a random sample of 100 Angus calves and weighs them on the day they are weaned from their mothers.  The sample mean for these 100 calves is 500 lb and the sample standard deviation is 40 lb.  What is the point estimate of the mean of the entire population of all Angus calves?