In seeking a free agent NFL running back, a general manager is looking for a player with a high mean for yards gained per carry and a small standard deviation.  Suppose the GM wishes to compare the mean yards gained per carry for two free agents based on independent random samples of their yards gained per carry.  Data from last year’s pro football season indicate that σ1 and σ2 are both equal to approximately 5 yards.  If the GM wants to estimate the difference in means for yards gained per carry by the two running backs correct to within 1 yard with a confidence level of 0.90, how many carries would have to be observed for each of the two players?  Assume equal sample sizes.

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                                                                                   The results of the Analysis of Variance for this experiment are as follows: Source           df       SS            MS          F     Total                       222.21     Supermarket              2.64       1.32       39.23 Item                        215.59       3.65     108.54 Error                           3.97      0.0337                                                                                Using a significance level of α = 0.05 from Table IX in the back of our textbook, the critical value of F is approximately 3.07.  What is the proper conclusion from this experiment?

An experiment results in four possible outcomes with the following probabilities:  P(A) = 0.10, P(B) = 0.15, P(C) = 0.20, and P(D) = 0.55.  Assume that these four events are mutually exclusive.  What is the probability that event B, C, or D occurs?

If we roll a single die, the sample points are 1, 2, 3, 4, 5, or 6.  Consider the following two events:      Event A:  toss an even number on the die      Event B:  toss a number less than or equal to 3 on the die List the sample points that would be included in the intersection of events A and B (i.e., A ∩ B).

Suppose that a random sample of 625 measurements is selected from a population with a mean µ = 500 lb and a variance σ2 = 100 lb2.  What is the mean and standard deviation of the sampling distribution of the sample mean?

Two fair coins are tossed and the events A and B are defined as follows: A: {At least one head appears} B: {Exactly one head appears} Find P (A)

Breeders of the Longhorn breed of cattle select to increase the length of the horns (i.e., the distance from the tip of one horn to the tip of the other horn).  A Longhorn breeder would like to know the average length of horns found on Longhorn cattle in Texas.  A random sample of 144 Longhorn cattle yields a mean horn length of 70 inches and a standard deviation of 10 inches. Estimate the population mean for length of horns of Longhorn cattle in Texas using a 90% confidence interval.

The table shown below summarizes the 10 winners of the World Series from 1990 to 2000 by division and league.  There was no World Series in 1994 due to a strike by the players.  One of these 10 World Series winners is to be chosen at random.                                                     League                                                   National        American                        Eastern          2                     6 Division           Central          1                     1                         Western        0                     0 Given that the winning team plays in the Central Division, what is the probability that the winning team is a member of the National League?

Find the proportion of the population expected to lie within one standard deviation of the mean of a binomial probability distribution with a sample size of n = 20 and a probability of success of 0.60.

A speed training program was effective in improving the 40-yard sprint times of high school athletes.  A study of 500 high school athletes was conducted to estimate p, the true proportion of all high school athletes who attained improved sprint times after participating in the speed training program.  The study showed that 425 of the 500 athletes had improved sprint times. Perform the calculations needed to determine if the sample size of n = 500 is large enough for large-sample confidence interval procedures to be valid.  Is the sample size large enough?