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In order to compare the means of two populations, independent random samples are selected from each population, with the following results:                                             Sample 1     Sample 2 Sample size                            500                400 Sample mean                       5,280             5,240 Sample standard deviation     150                200 Construct a 95% confidence interval for the difference in the two population means.

A swine producer reads a report stating that the average litter size in the US is 7.8 pigs per litter.  However, he feels that the average litter size on his farm is not 7.8 pigs/litter (he wants to detect departure in either direction from the hypothesized mean of 7.8 pigs/litter).  To test his hypothesis, he reviews his records for the past year and randomly selects 16 litters, which averaged 8.0 pigs/litter.  The standard deviation is 1 pig/litter. State the null and alternative hypothesis.

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 is a member of the American League, what is the probability that the winning team plays in the Eastern Division?

The American Journal of Public Health published a study of the relationship between passive smoking and nasal allergies in Japanese female students.  The study revealed that 80% (i.e., p = 0.80) of the students from heavy-smoking families showed signs of nasal allergies on physical examinations.  Consider a sample of 10 Japanese female students exposed daily to heavy smoking in their families.  What is the probability that exactly 8 of the 10 students will have nasal allergies?

The person in charge of genetic evaluation of beef cattle wants to know if birth weights of calves are influenced by breed and if they are influenced by the region of the U.S. (i.e., Northern U.S. vs Southern U.S.) in which the calf is born.  She has heard that calves born in the South are usually lighter at birth than are calves born in the North.  In order to answer these questions, she sets up a 2 x 3 factorial experiment with 3 replications and obtains the birth weights (in pounds) shown in the following table:                   Angus       Charolais       Simmental North             85                93                 91                       85                92                 92                       83                94                 92 South            85                84                  82                      76                85                   83                      74                83                   83     The partially completed ANOVA table is as follows: Source               df             SS            MS          F       Total                                 548.00 Location Breed                               174.33       87.165     13.643 Location x breed                  9.00         4.500 Error                                                                                       State the null and alternative hypothesis for location.

Frame score in beef cattle is based on height at the hips and is used as a measure of skeletal size.  Frame scores range from 1 to 10 with a higher number indicating a taller animal.  Independent random samples of frame scores were selected from the Angus and Simmental breeds of beef cattle with the following results: Angus Simmental 5 7 6 7 7 8 5 6 7 7 6   Calculate the Correction Factor (Correction for the 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 (B)

Assume X is a binomial random variable.  If n = 15 and p = 0.60, find P (r ≤ 5 successes).

The probability of a male offspring is 1/2 and the probability of a female offspring is 1/2.  What is the probability that a mare will give birth to a female offspring in four consecutive years, assuming that the sexes of the offspring in different years are independent events?

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?