Assume X is a binomial random variable.  If n = 15 and p = 0.90, find P (r ≥ 10 successes).

We want to test the hypothesis that the mean number of credit hours taken per semester by OSU undergraduates is less than 16 hours.  Therefore, we obtain a random sample of credit hours for 49 students. The sample mean is 15 hours and the sample standard deviation is 4 hours.  We want to test:    Ho:  μ = 16 hours    Ha:  μ < 16 hours using a significance level (α) = 0.01. Should we reject or not reject the null hypothesis?  Why?

A 2 x 4 factorial experiment is conducted to compare yields of 4 varieties of soybeans that are planted in rows either 15 inches or 30 inches apart.  Two plots of ground are randomly assigned to each combination of soybean variety and row spacing.  The yields of soybeans (in bushels per acre) are as follows:           Rows 1 2 3 4 15″ 45 46 47 46   46 46 48 43 30″ 35 41 42 39   32 39 38 41 The partially completed ANOVA table is as follows: Source df SS MS F Total   319.75     Variety   41.25 13.75 5.0 Row spacing   225 225 81.8 Variety x row spacing   31.5     Error   22 2.75   Calculate the mean squares and then the F value for the variety x row spacing interaction.

Toyota would like to know how many miles per gallon the average person gets when driving the hybrid Toyota Prius.  A random sample of 225 drivers yields a mean of 50 mpg and a standard deviation of 7.5 mpg.  The point estimate of the population mean for the miles per gallon of the Toyota Prius would be:

The average height of a certain ornamental plant is 15 inches and the standard deviation of the heights is 3 inches.  Only 20% of the plants are expected to be more than X inches tall.  Find the value of X.

Assume that we want to test the null hypothesis that the correlation between two variables is 0 vs. the alternative hypothesis that the correlation between these two variables is positive.  Based on a random sample of n = 20 observations, we calculate the sample correlation coefficient of r = 0.50.  Using a significance level of 0.05, which one of the following statements represents the correct conclusion?

The manager of a swine operation wants to compare the litter sizes of three pigs of pigs – Duroc, Yorkshire, and Large White.  The manager obtains a random sample of litter sizes of sows of the three breeds as shown in the table below.  Use Analysis of Variance to test at the 0.05 significance level if there is a difference in the average litter sizes of the three breeds of pigs. Litter size Large White Duroc Yorkshire 10 6 11 6 7 8 8 9 13 12 4 10 6 6 10 10 12 5 6 8 6 Total 42 67 64 Average 8.4 6.7 10.7 What are the mean squares (MS) for breed and error in the Analysis of Variance table given that the sums of squares are 131.81, 59.18, and 72.63 for total, breed, and error, respectively.

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 cost of grocery items purchased at 3 different supermarkets:  Kroger, Giant Eagle, and Sam’s Club.  Prices (in dollars) were recorded for a sample of 10 randomly selected grocery items at each of the 3 supermarkets (i.e., a total of 10 x 3 = 30 prices were recorded).  We will consider this to be a one-way analysis of variance (i.e., a completely randomized design).  The partially completed Analysis of Variance table is shown below: Source               df          SS          MS          F        Total                               120 Supermarkets                  20 Error                               100                                          State the null and alternative hypothesis being tested by the consumer reporter.  Using a significance level of α = 0.05, should the consumer reporter reject the null hypothesis?  Explain.

The Empirical Rule can be applied to any set of data regardless of the shape of the distribution.