Exam 10: Statistical Inference About Means and Proportions With Two Populations

Consider the following results for two samples randomly taken from two populations. a.Determine the degrees of freedom for the t distribution. b.At 95% confidence,what is the margin of error? c.Develop a 95% confidence interval for the difference between the two population means.

If two independent large samples are taken from two populations,the sampling distribution of the difference between the two sample means

Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines.We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon)of the two brands of automobiles.A random sample of eight cars from each manufacturer is selected,and eight drivers are selected to drive each automobile for a specified distance.The following data show the results of the test. -Refer to Exhibit 10-9.The test statistic is

The following are the test scores of two samples of students from University A and University B on a national statistics examination.Develop a 95% confidence interval estimate for the difference between the mean scores of the two populations.

The reliability of two types of machines used in the same manufacturing process is to be tested.The first machine failed to operate correctly in 90 out of 300 trials while the second type failed to operate correctly in 50 out of 250 trials. a.Give a point estimate for the difference between the population proportions of these machines. b.Calculate the pooled estimate of the population proportion. c.Carry out a hypothesis test to check whether there is a statistically significant difference in the reliability for the two types of machines using a .10 level of significance.

Exhibit 10-2 The following information was obtained from matched samples. The daily production rates for a sample of workers before and after a training program are shown below. -Refer to Exhibit 10-2.The null hypothesis to be tested is H₀: $\mu$ _d = 0.The test statistic is

Two independent random samples of annual starting salaries for individuals with masters and bachelors degrees in business were taken and the results are shown below a.What are the degrees of freedom for the t distribution? b.Provide a 95% confidence interval estimate for the difference between the salaries of the two groups.

If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2,the

Exhibit 10-10 The results of a recent poll on the preference of shoppers regarding two products are shown below. -Refer to Exhibit 10-10.The point estimate for the difference between the two population proportions in favor of this product is

Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago.A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken.You are given the following information. -Refer to Exhibit 10-3.What is the conclusion that can be reached about the difference in the average final examination scores between the two classes? (Use a .05 level of significance. )

When developing an interval estimate for the difference between two sample means,with sample sizes of n₁ and n₂,

Exhibit 10-5 The following information was obtained from matched samples. -Refer to Exhibit 10-5.If the null hypothesis is tested at the 5% level,the null hypothesis

Consider the following results for two samples randomly taken from two normal populations with equal variances. a.Develop a 95% confidence interval for the difference between the two population means. b.Is there conclusive evidence that one population has a larger mean? Explain.

Of 200 UTC seniors surveyed,60 were planning on attending Graduate School.At UTK,400 seniors were surveyed and 100 indicated that they were planning to attend Graduate School. a.Determine a 95% confidence interval estimate for the difference between the proportion of seniors at the two universities that were planning to attend Graduate School. b.Is there conclusive evidence to prove that the proportion of students from UTC who plan to go to Graduate School is significantly more than those from UTK? Explain.

Among a sample of 50 M.D.'s (medical doctors)in the city of Memphis,Tennessee,10 indicated they make house calls;while among a sample of 100 M.D.'s in Atlanta,Georgia,18 said they make house calls.Determine a 95% interval estimate for the difference between the proportion of doctors who make house calls in the two cities.

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. -Refer to Exhibit 10-1.At 95% confidence,the conclusion is the

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. -Refer to Exhibit 10-4.The point estimate for the difference between the means of the two populations is

In a sample of 40 Democrats,6 opposed the President's foreign policy,while of 50 Republicans,8 were opposed to his policy.Determine a 90% confidence interval estimate for the difference between the proportions of the opinions of the individuals in the two parties.

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. -Refer to Exhibit 10-1.If you are interested in testing whether or not the average salary of males is significantly greater than that of females,the test statistic is

Samples of employees of Companies A and B provided the following information regarding the ages of employees. Develop a 97% confidence interval for the difference between the average ages of the employees of the two companies.