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Suppose we want to estimate the average height of all young growing maple trees found on a certain nursery.  We select a random sample of 25 trees and measure their heights.  The sample mean is 70 inches and the sample standard deviation is 10 inches.  Construct a 90% confidence interval for the population mean (μ).  Assume that any necessary assumptions have been met.

Assuming that n1 = n2, find the sample sizes needed to estimate (μ1 – μ2) correct to within 2.5 with probability 0.90.  From prior experience we know that σ1 = 18 and σ2 = 16.

The average weight of a kennel of dogs is 40 lb and the standard deviation of the weights is 5 lb.  Find the probability that a randomly selected dog will weigh between 44 and 48 lb.

Health care issues are receiving a greal deal of attention in both the academic and political arenas.  A sociologist recently conducted a survey of senior citizens whose net worth is too high to quality for Medicaid, but who have no private health insurance.  The ages (in years) of 9 uninsured senior citizens were as follows: Senior Citizen Age 1 65 2 70 3 64 4 84 5 74 6 72 7 87 8 79 9 80 Find the range for the ages of these 9 senior citizens.

A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets – Kroger, Giant Eagle, and Meier.  Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets.  In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket. Item                          Kroger    Giant Eagle    Meier     1) Big Thirst Towel      $1.21       $1.49          $1.59 2) Post Golden Crisp    2.78         2.99            3.35 3) Tylenol Tablets         5.98         5.29            5.98           .                              .              .                   .           .                              .              .                   . 59) Colgate Shave       0.94         1.10            1.19 60) Kidney Beans        0.45          0.56            0.38                                                                                   Identify the dependent (response) variable for this experiment.

Health care issues are receiving a greal deal of attention in both the academic and political arenas.  A sociologist recently conducted a survey of senior citizens whose net worth is too high to quality for Medicaid, but who have no private health insurance.  The ages (in years) of 9 uninsured senior citizens were as follows: Senior Citizen Age 1 65 2 70 3 64 4 84 5 74 6 72 7 87 8 79 9 80 Find the median age of these 9 senior citizens.

You are interested in purchasing a really good bull to breed your cows.  You look up the sale prices of a sample of 16 bulls that were sold in last year’s National Western Stock Show sale in Denver.  The average sale price was $10,000 with a standard deviation of $1,000.  Estimate the population mean for the sale prices of the bulls using a 95% confidence interval.

The mean height of a herd of cows is 55 inches.  The standard deviation of the heights is 10 inches.  Assume that the heights are approximately normally distributed. What proportion of the cows would be expected to be between 50 and 62 inches tall?

Suppose that an 85% confidence interval for μ turns out to be (100 lb, 500 lb).  To make more useful inferences from the data, it is desired to reduce the width of the confidence interval.  What action should we take to reduce the width of the confidence interval?

Assume X is a binomial random variable.  If n = 10 and p = 0.40, find P (r = 2 successes).