Exam 10: Two-Sample Tests
Exam 1: Introduction145 Questions
Exam 2: Organizing and Visualizing Data210 Questions
Exam 3: Numerical Descriptive Measures153 Questions
Exam 4: Basic Probability171 Questions
Exam 5: Discrete Probability Distributions218 Questions
Exam 6: The Normal Distribution and Other Continuous Distributions191 Questions
Exam 7: Sampling and Sampling Distributions197 Questions
Exam 8: Confidence Interval Estimation196 Questions
Exam 9: Fundamentals of Hypothesis Testing: One-Sample Tests165 Questions
Exam 10: Two-Sample Tests210 Questions
Exam 11: Analysis of Variance213 Questions
Exam 12: Chi-Square Tests and Nonparametric Tests201 Questions
Exam 13: Simple Linear Regression213 Questions
Exam 14: Introduction to Multiple Regression355 Questions
Exam 15: Multiple Regression Model Building96 Questions
Exam 16: Time-Series Forecasting168 Questions
Exam 17: Statistical Applications in Quality Management133 Questions
Exam 18: A Roadmap for Analyzing Data54 Questions
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TABLE 10-10
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let π₁ and π₂ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.
-Referring to Table 10-10, what is the estimated standard error of the difference between the two sample proportions?
(Multiple Choice)
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A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal. For this situation, the professor should use a t test with related samples.
(True/False)
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In testing for differences between the means of two independent populations, the null hypothesis is
(Multiple Choice)
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TABLE 10-10
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let π₁ and π₂ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.
-Referring to Table 10-10, what is/are the critical value(s)when testing whether the current population proportion is higher than before if α = 0.05?
(Multiple Choice)
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The Wall Street Journal recently published an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked of both men and women was: "Do you think sexual harassment is a major problem in the American workplace?" 24% of the men compared to 62% of the women responded "Yes." Assuming W designates women's responses and M designates men's, what hypothesis should The Wall Street Journal test in order to show that its claim is true?
(Multiple Choice)
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TABLE 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: 1 G = 35 months, SG² = 900 Metropolis: M = 50 months, SM² = 1050
-Referring to Table 10-3, suppose α = 0.01. Which of the following represents the correct conclusion?
(Multiple Choice)
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TABLE 10-6
To investigate the efficacy of a diet, a random sample of 16 male patients is selected from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t test for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds.
-Referring to Table 10-6, the computed t statistic is ________.
(Short Answer)
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TABLE 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: 1 G = 35 months, SG² = 900 Metropolis: M = 50 months, SM² = 1050
-Referring to Table 10-3, suppose α = 0.05. Which of the following represents the result of the relevant hypothesis test?
(Multiple Choice)
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TABLE 10-4
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
-Referring to Table 10-4, if you were interested in testing against the one-tail alternative that μ₁ > μ₂ at the α = 0.01 level of significance, the null hypothesis would ________ (be rejected/not be rejected).
(Short Answer)
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A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training. To test whether any improvement occurred, the instructor would use a t-distribution with 10 degrees of freedom.
(True/False)
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TABLE 10-13
The amount of time required to reach a customer service representative has a huge impact on customer satisfaction. Below is the Excel output from a study to see whether there is evidence of a difference in the mean amounts of time required to reach a customer service representative between two hotels. Assume that the population variances in the amount of time for the two hotels are not equal.
t-Test: Two-Sample Assuming Unequal Variances Hotel 1 Hotel 2 Mean 2.214 2.0115 Variance 2.951657 3.57855 Observations 20 20 Hypothesized Mean Difference 0 df 38 t Stat 0.354386 P(T <=t) one-tail 0.362504 t Critical one-tail 1.685953 P(T<=t) two-tail 0.725009 t Critical two-tail 2.024394
-Referring to Table 10-13, what is(are)the critical value(s)of the relevant hypothesis test if the level of significance is 0.10?
(Multiple Choice)
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TABLE 10-10
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let π₁ and π₂ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.
-Referring to Table 10-10, what is/are the critical value(s)when performing a Z test on whether population proportions are different if α = 0.05?
(Multiple Choice)
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TABLE 10-3
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: 1 G = 35 months, SG² = 900 Metropolis: M = 50 months, SM² = 1050
-Referring to Table 10-3, what is(are)the critical value(s)of the relevant hypothesis test if the level of significance is 0.05?
(Multiple Choice)
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TABLE 10-4
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
-Referring to Table 10-4, what is the 95% confidence interval estimate for the difference in the two means?
(Short Answer)
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When testing for the difference between 2 population variances with sample sizes of n₁ = 8 and n₂ = 10, where n₁ has the larger variance, the number of degrees of freedom are
(Multiple Choice)
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The test for the equality of two population variances is based on
(Multiple Choice)
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TABLE 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. The result of the pooled-variance t test of the mean salaries of the females (Population 1) and males (Population 2) in the sample is given below.
Hypothesized Difference 0 Level of Significance 0.05 Population 1 Sample Sample Size 18 Sample Mean 99210 Sample Standard Deviation 13577 Population 2 Sample Sample Size 12 Sample Mean 105820 Sample Standard Deviation 11741 Difference in Sample Means -6610 Test Statistic -1.37631 Lower-Tail Test Lower Critical Value -1.70113 -Value
-Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. The proper conclusion for this test is
(Multiple Choice)
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TABLE 10-4
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
-Referring to Table 10-4, a two-tail test of the null hypothesis of no difference would ________ (be rejected/not be rejected)at the α = 0.05 level of significance.
(Short Answer)
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TABLE 10-10
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let π₁ and π₂ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.
-Referring to Table 10-10, what is/are the critical value(s)when testing whether population proportions are different if α = 0.10?
(Multiple Choice)
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