Exam 10: Two-Sample Tests
Exam 1: Defining and Collecting Data205 Questions
Exam 2: Organizing and Visualizing Variables212 Questions
Exam 3: Numerical Descriptive Measures163 Questions
Exam 4: Basic Probability171 Questions
Exam 5: Discrete Probability Distributions117 Questions
Exam 6: The Normal Distribution144 Questions
Exam 7: Sampling Distributions127 Questions
Exam 8: Confidence Interval Estimation187 Questions
Exam 9: Fundamentals of Hypothesis Testing: One-Sample Tests177 Questions
Exam 10: Two-Sample Tests300 Questions
Exam 11: Chi-Square Tests128 Questions
Exam 12: Simple Linear Regression204 Questions
Exam 13: Multiple Regression307 Questions
Exam 14: Business Analytics254 Questions
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When testing , the observed value of the Z test statistic was found to be - 2.13.The p-value for this test is
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In testing for differences between the means of two related populations, the null hypothesis is a) .
b) .
c) .
d) .
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SCENARIO 10-9
The following EXCEL output contains the results of a test to determine whether the proportions of satisfied customers at two resorts are the same or different. Hypothesized Difference 0 Level of Significance 0.05 Group 1 Number of Items of Interest 160 Sample Size Group 2 Number of Items of Interest 172 Sample Size Intermediate Calculations Group 1 Proportion 0.8 Group 2 Proportion 0.688 Difference in Two Proportions 0.112 Average Proportion 0.737777778 Z Test Statistic 2.684103363 Two-Tail Test Lower Critical Value -1.959963985 Upper Critical Value 1.959963985 2-tailed p-Value 0.007272462
-Referring to Scenario 10-9, allowing for 1% probability of committing a Type I error, what are the decision and conclusion on testing whether there is any difference in the proportions of satisfied customers in the two resorts?
(Multiple Choice)
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SCENARIO 10-5
A hotel chain has identically small sized resorts in 5 locations in different small islands.The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the 5 locations. ROW Location A Location B Location C Location D Location E 1 28 40 21 37 22 2 33 35 21 47 19 3 41 33 27 45 25 Analysis of Variance Source df SS MS F p Location 4 963.6 11.47 0.001 Error 10 210.0 Total
-Referring to SCENARIO 10-5, what are the numerator and denominator degrees of freedom forLevene's test for homogeneity of variances respectively?
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SCENARIO 10-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles.She took 3 of each brand and determined their maximum downhill speeds.The results are presented in miles per hour in the table below. Trial Barth Tornado Reiser Shaw 1 43 37 41 43 2 46 38 45 45 3 43 39 42 46
-Referring to SCENARIO 10-3, the null hypothesis for Levene's test for homogeneity of variances is a)
b)
c)
d)
(Short Answer)
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SCENARIO 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 Scenario 10-6, the p-value for a two-tail is .
(Essay)
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SCENARIO 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:
-Referring to Scenario 10-3, what is the 99% confidence interval estimate for the difference in the two means?


(Essay)
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SCENARIO 10-15
The table below presents the summary statistics for the starting annual salaries (in thousands of dollars) for individuals entering the public accounting and financial planning professions.
Sample I (public accounting):
Sample II (financial planning): Test whether the mean starting annual salaries for individuals entering the public accounting professions is higher than that of financial planning assuming that the two population variances are the same.
-Referring to Scenario 10-15, suppose = 0.01.Which of the following represents the correct conclusion?
(Multiple Choice)
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SCENARIO 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 Scenario 10-4, what is the 90% confidence interval estimate for the difference in the two means?
(Essay)
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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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SCENARIO 10-5
A hotel chain has identically small sized resorts in 5 locations in different small islands.The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the 5 locations. ROW Location A Location B Location C Location D Location E 1 28 40 21 37 22 2 33 35 21 47 19 3 41 33 27 45 25 Analysis of Variance Source df SS MS F p Location 4 963.6 11.47 0.001 Error 10 210.0 Total
-Referring to SCENARIO 10-5, what should be the conclusion for the Levene's test for homogeneity of variances at a 5% level of significance?
(Multiple Choice)
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SCENARIO 10-1
An airline wants to select a computer software package for its reservation system.Four software packages (1, 2, 3, and 4) are commercially available.The airline will choose the package that bumps as few passengers as possible during a month.An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks.(A total of 20 weeks was included in the experiment.) The number of passengers bumped each week is obtained, which gives rise to the following Excel output: ANOVA Source of Variation SS df MS F P-value F crit Between Groups 212.4 3 8.304985 0.001474 3.238867 Within Groups 136.4 8.525 Total 348.8
-Referring to SCENARIO 10-1, the total degrees of freedom is
(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? a) versus
b) versus
c) versus
d) versus
(Short Answer)
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SCENARIO 10-5
A hotel chain has identically small sized resorts in 5 locations in different small islands.The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the 5 locations. ROW Location A Location B Location C Location D Location E 1 28 40 21 37 22 2 33 35 21 47 19 3 41 33 27 45 25 Analysis of Variance Source df SS MS F p Location 4 963.6 11.47 0.001 Error 10 210.0 Total
-Referring to SCENARIO 10-5, the within-group variation or SSW is .
(Essay)
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SCENARIO 10-7
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging.In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on various identical materials.He wants to compare these prices with those of his primary supplier.The data collected is presented in the table below, with some summary statistics presented (all of
these might not be necessary to answer the questions which follow).The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01. Material Primary Supplier Secondary Supplier Difference 1 \ 55 \ 45 \ 10 2 \ 48 \ 47 \ 1 3 \ 31 \ 32 -\ 1 4 \ 83 \ 77 \ 6 5 \ 37 \ 37 \ 0 6 \ 55 \ 54 \ 1 Sum: \ 309 \ 292 \ 17 Sum of Squares: \ 17,573 \ 15,472 \ 139
-Referring to Scenario 10-7, what is the 99% confidence interval estimate for the mean difference in prices?
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SCENARIO 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 Scenario 10-13, suppose = 0.10.Which of the following represents the correct conclusion?
(Multiple Choice)
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The F test in a completely randomized model is just an expansion of the t test for independent samples.
(True/False)
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If we are testing for the difference between the means of 2 independent populations presuming equal variances with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to
(Multiple Choice)
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SCENARIO 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 Scenario 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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SCENARIO 10-5
To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course.The results are given below. Student Exam Score BeforeCourse(1) Exam Score AfterCourse(2) 1 530 670 2 690 770 3 910 1,000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610
-Referring to Scenario 10-5, the number of degrees of freedom is
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