Blog

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?

It seems reasonable to assume that the number of times a team punts the ball in a football game would be negatively correlated with the number of points that the team scores (i.e., if a team is forced to punt frequently they are probably not moving the ball very well and probably are not scoring many points).  Number of punts (variable X) and number of points scored (variable Y) for a particular team in a random sample of five games are as follows: Number of Punts, X          Number of Points, Y              2                                         35              5                                         14              3                                         21              2                                         21              2                                         28   We want to test our assumption of a negative correlation between number of punts and number of points scored in a football game.  State the appropriate null and alternative hypothesis.  Using a significance level of 0.05, do you reject or not reject the null hypothesis?  Why?

An experiment is conducted to compare the starting salaries of male and female college graduates who find jobs.  Pairs are formed by choosing a male and a female with the same major and similar grade point averages.  Suppose a random sample of 10 pairs is formed in this manner and the starting annual salary of each person is recorded.  The differences within the pairs are obtained by subtracting the female salary from the male salary. The following results are obtained:      Mean difference in starting salaries = $400      Standard deviation of the difference in starting salaries = $435 Construct a 95% confidence interval for the true mean difference in starting salaries of the male and female graduates.

The general rule of thumb is that we need a sample size of n >  _________ to use large-sample confidence interval procedures to estimate the population mean.

Assuming equal numbers of observations in each of the two samples, find the sample sizes needed to estimate the difference in population means correct to within 2.5 with probability 0.90.  From prior experience, we know that the standard deviation of population 1 is 18 and the standard deviation of population 2 is 16.

The average height of a certain ornamental plant is 14 inches and the standard deviation of the heights is 2 inches.  Find the probability that a randomly selected plant will have a height of more than 17.5 inches.

Null and alternative hypotheses must be stated in terms of population parameters, and not in terms of sample statistics.

Assume that a 90% confidence interval for the mean weight of the population consisting of male students attending OSU is (150 lb,  200 lb).  What is the meaning of this 90% confidence interval?

The mean length of time required to complete the Columbus Marathon was 4.5 hours and the standard deviation of the times was 0.50 hours.  Assume that the racing times were approximately normally distributed.  Only 10% of the runners would be expected to complete the race in less than x hours.  Find the value of x.

Which one of the following statements about the sampling distribution of the sample mean is incorrect?