Suppose that a random sample of 100 measurements is selected from a population with a mean = 200 lb and a variance = 1,600 lb2.  What is the mean of the sampling distribution of the sample mean?

An animal scientist is interested in determining the proportion of ewes (i.e., female sheep) that give birth to twins.  Rather than examine the records for all ewes in the United States, the animal scientist randomly selects 500 ewes and finds that 220 of them gave birth to twins. Construct a 99% confidence interval to estimate the true population proportion of ewes, p, who give birth to twins.

A study was conducted to determine whether a student’s final grade in a high school math class is linearly related to his or her performance on the math ability test administered before college entrance.  The math test scores and final grades for a random sample of 10 students are shown below. Final Grade in Math Class (X)          Math Ability Test Score (Y) 65                                                             39 78                                                             43 52                                                             21 82                                                             64 92                                                             57 89                                                             47 73                                                             28 98                                                             75 56                                                             34 75                                                             52 Given that the variance of the final grades in the math class (i.e., variable X) is 228.4444 and the variance of the math ability test scores (i.e, variable Y) is 274.8889, calculate the correlation coefficent for the correlation between variables X and Y.

Assume that P(A) = 0.6, P(B) = 0.3, and P(A|B) = 0.6, where A and B are two different events.  Which one of the following statements is correct?

Consider the following sample of data points for variable X and variable Y.    X          Y      3          4    5          3    6          2    4          1    3          2    7          3    6          3    5          5    4          4    7          3 Find the covariance between variable X and variable Y.

For normal distributions, __________ % of the observations are expected to lie within plus or minus two standard deviations of the mean.

In an Analysis of Variance the plan for collecting the sample is called the ____________.

Assume that, when we plot the data points for variables X and Y, all of the points lie on a straight line with a positive slope.  This indicates that the correlation between these two variables is equal to __________.

Health care issues are receiving a great deal of attention in both the academic and political arenas.  A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid, but who have no private health insurance.  The mean age of the 50 uninsured senior citizens in the survey was 74.04 years and the standard deviation of their ages was 9.75 years.  If we assume that the distribution of ages is symmetric and mound-shaped, what percentage of the respondents in the survey would be expected to be between 64.29 and 83.79 years old?

It seems reasonable to assume that ovulation rate and litter size in pigs would be positively correlated.  In other words, if a sow releases more eggs (i.e., ova) in a given estrus period, she will probably end up producing more pigs in her litter.  Number of eggs ovulated and litter size for a random sample of 6 sows are as follows: Number of Eggs, X       Number of Pigs Born, Y                14                                  7                15                                  7                16                                  9                17                                 10                17                                 10                17                                  11 We want to test our assumption of a positive correlation between number of eggs ovulated and number of pigs in the litter.  State the appropriate null and alternative hypotheses.