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.

Measures of variation include

The mean grade on an Organic Chemistry exam is a 50 and the standard deviation of the grades is 10.  The highest grade in the class was a 95.  Calculate the z-score for the student with the highest score of 95.  Based in the z-score, is this grade of 95 an outlier?  Why or why not?

Suppose that 80% of the Holstein cows in the U.S. give birth to their calves with no calving difficulty.  We randomly select 7 Holstein cows from the population consisting of all Holstein cows in the U.S.  What is the probability that at least 5 of the 7 (i.e., 5 or more) cows in this sample will give birth to their calves with no calving difficulty?  To find the answer to this question, you can use the equation for the binomial distribution or a binomial probability table.

A litter of 5 pigs is produced.  What is the probability that exactly 3 of the 5 pigs will be females, assuming that the probability of a male pig is 1/2 and the probability of a female pig is 1/2?

The Environmental Science & Technology journal reported on a study of contaminated soil in The Netherlands.  A total of 81 soil specimens were sampled, dried, and analyzed for the contaminant cyanide.  The cyanide concentation (in milligrams per kilogram, mg/kg, of soil) of each soil specimen was determined using an infrared microscopic method.  The samples had a mean cyanide level of 95 mg/kg and a standard deviation of 50 mg/kg.  The authors of the journal article tested the hyothesis that the true mean cyanide level in the soil in The Netherlands was less than 100 mg/kg using a significance level of α = 0.10. Should the authors of the journal article reject the null hypothesis?  Explain.