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

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

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.The point estimate for the difference between the means of the two populations is

Exhibit 10-12 The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. -Refer to Exhibit 10-12.The 95% confidence interval for the difference between the two proportions is

A poll was taken this year asking college students if they considered themselves overweight.A similar poll was taken five years ago.Results are summarized below.Has the proportion increased significantly? Let F $\alpha$ = 0.05.

Exhibit 10-11 An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year.The results are shown below. We are interested in determining if the accident proportions differ between the two age groups. -Refer to Exhibit 10-11.The pooled proportion is

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 standard error of Is

A company attempts to evaluate the potential for a new bonus plan by selecting a sample of 4 salespersons to use the bonus plan for a trial period.The weekly sales volume before and after implementing the bonus plan is shown below.(For the following matched samples,let the difference "d" be d = after - before. ) a.State the hypotheses. b.Compute the test statistic. c.Use Alpha = .05 and test to see if the bonus plan will result in an increase in the mean weekly sales.

Exhibit 10-8 In order to determine whether or not there is a significant difference between the hourly wages of two companies,the following data have been accumulated. -Refer to Exhibit 10-8.A point estimate for the difference between the two sample means is

In order to determine whether or not a driver's education course improves the scores on a driving exam,a sample of 6 students were given the exam before and after taking the course.The results are shown below. Let d = Score After - Score Before. a.Compute the test statistic. b.At 95% confidence using the p-value approach,test to see if taking the course actually increased scores on the driving exam.

To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown and it can be assumed the two populations have equal variances,we must use a t distribution with (let n₁ be the size of sample 1 and n₂ the size of sample 2)

Test scores on a standardized test from samples of students from two universities are given below. Provide a 98% confidence interval estimate for the difference between the test scores of the two universities.

Exhibit 10-5 The following information was obtained from matched samples. -Refer to Exhibit 10-5.The null hypothesis tested is H₀: $\mu$ _d = 0.The test statistic for the difference between the two population means is

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. -Refer to Exhibit 10-1.The 95% confidence interval for the difference between the means of the two populations is

A comparative study of organic and conventionally grown produce was checked for the presence of E.coli.Results are summarized below.Is there a significant difference in the proportion of E.Coli in organic vs.conventionally grown produce? Test at $\alpha$ = 0.10.

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.The 95% confidence interval for the difference between the two population means is

Independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known,but are assumed to be equal.The sample sizes are n₁ = 25 and n₂ = 35.The correct distribution to use is the

Exhibit 10-8 In order to determine whether or not there is a significant difference between the hourly wages of two companies,the following data have been accumulated. -Refer to Exhibit 10-8.The p-value is

Consider the following results for two samples randomly taken from two populations. a.Determine the degrees of freedom for the t-distribution. b.Develop a 95% confidence interval for the difference between the two population means.

Of 150 Chattanooga residents surveyed,60 indicated that they participated in a recycling program.In Knoxville,120 residents were surveyed and 36 claimed to recycle. a.Determine a 95% confidence interval estimate for the difference between the proportion of residents recycling in the two cities. b.From your answer in Part a,is there sufficient evidence to conclude that there is a significant difference in the proportion of residents participating in a recycling program?

The following information regarding the number of semester hours taken from random samples of day and evening students is provided. Develop a 95% confidence interval estimate for the difference between the mean semester hours taken by the two groups of students.