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A college professor wants to estimate the difference in mean test scores of students who have taken his statistics and genetics classes in the past 10 years.  He selects a random sample of 20 student records from the statistics course and a random sample of 22 student records from the genetics course.  These two samples were independent random samples.  The study provided the results shown in the table below.  Construct a 95% confidence interval for the true difference in population means of these two populations of students.   Statistics Genetics Sample size 20 22 Sample mean 78 75 Sample standard dev. 10 12

Scientists are interested in determining if the mean alkalinity level of water specimens from the Han River in Seoul, Korea is greater than 50 milligrams per liter (mpl).  They select a random sample of 100 water specimens from the river and find a sample mean of 70 mpl and a sample standard deviation of 15 mpl.  They decide to test the hypothesis that the population mean for alkalinity level of water in the Han River exceeds 50 mpl using a significance level of 0.01.  Should the scientists reject or not reject the null hypothesis?  Explain.

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..

In the 1970’s it was generally assumed that the mean birth weight of Angus beef cattle was 75 lb.  A researcher believes that, due to selection for increased size and growth rate in Angus, the average birth weight is now greater than 75 lb.  He obtains a random sample of n = 144 birth weights of Angus calves and calculates a sample mean of 85 lb and a sample standard deviation of 10 lb. Calculate the test statistic needed to test the null hypothesis.

The College of Food, Agricultural, and Environmental Sciences wants to estimate the proportion of students that are female.  In a small pilot study, they obtain a sample estimate of 0.60 for the proportion of students in the college that are female.  What sample size would be needed if the college administration wanted to estimate the proportion of students that are female correct to within 0.03 with a probability of 0.98?

Assuming that n1 = n2, find the sample sizes needed to estimate (p1 – p2) correct to within 0.07 with probability 0.90.  Assume that there is no prior information available to obtain sample estimates of p1 and p2.

The probability of making a Type I error in hypothesis testing is called the __________________ for a hypothesis test.

If we conduct a matched pairs experiment using small samples, what assumptions are needed for the small-sample confidence interval for the mean difference to be valid?

You are interested in purchasing a new car.  One of the many points you wish to consider is the resale value of the car after 5 years of ownership.  Since you are particulary interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 90% confidence interval.  You manage to obtain data on 16 recently resold 5-year-old foreign sedans of that model.  These 16 cars were resold at an average price of $10,000 with a standard deviation of $1,500. You estimate the true population mean for the resale value of this model of foreign car using a 90% confidence interval.  What assumption must be met in order for the confidence interval that you constructed to be valid?

A Gallop poll is conducted to estimate the proportion of voters who plan to vote in favor of a certain issue on the ballet.  A random sample of 500 people of voting age is selected.  Results of the poll show that 300 of the 500 people polled plan to vote in favor of the issue.  Construct a 99% confidence interval for the true population proportion of people who plan to vote in favor of the issue.