Business Statistics Test 4
What are the degrees of freedom for a contingency table analysis?
(Rows - 1) � (Columns - 1)
Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the critical value if the level of significance is 0.10?
+/-1.645
Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the critical value if ? equal 0.01?
+/-2.576
Product FIFO LIFO 1 ; 225 ; 221 2 ; 119 ; 100 3 ; 100 ; 113 4 ; 212 ; 200 5 ; 248 ; 245 Accounting procedures allow a business to evaluate its inventory costs based on two methods: LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000s) for five products with the LIFO and FIFO methods. To analyze the difference, they computed (FIFO - LIFO) for each product. Based on the following results, and testing if the LIFO method result in a lower cost of inventory than the FIFO method. What is the value of calculated t?
+0.933
Accounting procedures allow a business to evaluate their inventory costs based on two methods: LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000s) for five products with the LIFO and FIFO methods. To analyze the difference, they computed (FIFO - LIFO) for each product. Based on the following results, and testing if the LIFO method result in a lower cost of inventory than the FIFO method. If you use the 5% level of significance, what is the critical t value?
+2.132
Which value of the correlation coefficient indicates a stronger correlation than 0.40?
-0.8
What is the range of values for a coefficient of correlation?
-1.0 to +1.0 inclusive
Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the z test statistic?
-1.02
It is claimed that in a bushel of peaches, less than 10% are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the critical value for ? equal 0.025?
-1.96
A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results: What is the Y-intercept of the linear equation?
-12.201
A frequency distribution has a mean of 100 and a standard deviation of 20. The class limits for one class are 50 up to 60. What are the standard normal z-statistics for the class limits?
-2.5 and -2.0
A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are shown on the table. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. What is the computed value of t?
-3.299
If all the plots on a scatter diagram lie on a straight line, what is the standard error of estimate?
0
The results of a mathematics placement exam at two different campuses of Mercy College follow: Given that the two population standard deviations are known, what is the p-value?
0
What is the range of values for the coefficient of determination?
0% to 100% inclusive
A recent study focused on the number of times men and women send a Twitter message in a day. The sample information is summarized below. We want to know if, at the .01 significance level, is there a difference in the mean number of times men and women send a Twitter message in a day. What is the p-value for this hypothesis test?
0.0164
A frequency distribution has a mean of 100 and a standard deviation of 20. The class limits for one class are 50 up to 60. Based on the normal distribution, what is the probability that an observation would be in this class?
0.0166
Consider a regression analysis, where the correlation coefficient is 0.18. Then, the coefficient of determination is _______.
0.0324
Manufacturer 1 n1 = 81 x1 = $15.80 o1 = $3.00 Manufacturer 2 n1 = 64 x1 = $15.00 o1 = $2.25 Use the following table to determine whether or not there is a significant difference between the average hourly wages at two manufacturing companies. The p-value is ______.
0.0336
It is claimed that in a bushel of peaches, less than 10% are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the sample proportion?
0.125
A frequency distribution has a mean of 200 and a standard deviation of 20. The class limits for one class are 220 up to 240. Based on the normal distribution, what is the probability that an observation would be in this class?
0.1359
A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results: What is the standard error of the slope?
0.176
Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the sample proportion?
0.36
If 20 out of 50 students sampled live in a college dormitory, what is the estimated proportion of students at the University living in a dormitory?
0.4
If the correlation coefficient (r) = 0.65, what does the coefficient of determination equal?
0.4225
A sample of 250 adults tried the new multigrain cereal Wow! A total of 187 rated it as excellent. In a sample of 100 children, 66 rated it as excellent. Using the 0.1 significance level, the researcher wishes to show that adults like the cereal better than children. What is the pooled proportion?
0.723
What does the coefficient of determination equal if the correlation coefficient (r) = 0.89?
0.7921
Use the following table to determine whether or not there is a significant difference between the average hourly wages at two manufacturing companies. What is the point estimate of the difference between the means?
0.8
Using the following information: What is the correlation coefficient?
0.9583
A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression ANOVA shows the following results: What is the value of the coefficient of correlation?
0.9754
Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested in finding out if exceeding the speed limit was related to social activity. They collected the following responses from 100 randomly selected students. The degrees of freedom for the analysis are ________.
1
A frequency distribution has a mean of 200 and a standard deviation of 20. The class limits for one class are 220 up to 240. What are the standard normal z-statistics for the class limits?
1.0 and 2.0
A recent study focused on the amount of money single men and women save monthly. The information is summarized next. Assume that the population standard deviations are equal. The researcher want to know if, at the .01 significance level, do women save more money than men. What is the value of the test statistic for this hypothesis test?
1.318
It is claimed that in a bushel of peaches, less than 10% are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the z-test statistic?
1.667
For a hypothesis comparing two population means, H0: μ1 ≤ μ2, what is the critical value for a one-tailed hypothesis test, using a 5% significance level, with both sample sizes equal to 13? Assume the population standard deviations are equal.
1.711
The net weights (in grams) of a sample of bottles filled by a machine manufactured by Edne, and the net weights of a sample filled by a similar machine manufactured by Orno, Inc., are shown on the table: Testing the claim at the 0.05 level that the mean weight of the bottles filled by the Orno machine is greater than the mean weight of the bottles filled by the Edne machine, what is the critical value? Assume equal standard deviations for both samples.
1.782
An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and post-training customer survey. To compare the differences, they computed (post-training survey score - pre-training survey score). Seven customers were randomly selected and completed both surveys. The results follow. For a 0.05 significance level, what is the critical value?
1.943
A personnel manager is concerned about absenteeism. She decides to sample employee records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are shown. What is the expected frequency?
10
A survey of property owners opinions about a street-widening project was taken to determine if owners opinions were related to the distance between their home and the street. A randomly selected sample of 100 property owners was contacted and the results are shown. What is the expected frequency for people who are in favor of the project and have less than 45 feet of property foot-frontage?
10
The degrees of freedom for a contingency table with 6 rows and 3 columns is ______.
10
A personnel manager is concerned about absenteeism. She decides to sample employee records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are shown. What is the critical value of chi-square with ? equal 0.05?
11.07
What is the critical value at the 0.05 level of significance for a goodness-of-fit test if there are six categories?
11.07
For people released from prison, the following table shows their adjustment to civilian life and place of residence. What is the critical value for this contingency table at the 0.01 level of significance?
11.345
Using the following information: What is the standard error of the estimate?
11.6985
A distributor of personal computers has five locations in a city. In the years first quarter, the sales in units are shown: For a goodness-of-fit test that sales were the same for all locations, what is the critical value at the 0.01 level of risk?
13.277
Students were sampled in order to determine their support for the legalization of gambling in their community. A sample of 150 students were asked whether or not they supported legalization of gambling, and the following results were obtained. The number of degrees of freedom associated with this scenario is _____.
150
A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results: What is the slope of the linear equation?
2.195
A company is researching the effectiveness of a new website design to decrease the time to access a website. Five website users were randomly selected, and their times (in seconds) to access the website with the old and new designs were recorded. To compare the times, they computed (new website design time - old website design time). The results follow. What is the value of the test statistic?
2.256
Men: Sample Size: 25 Sample Mean: 23 Population St. Dev: 5 Women Sample Size: 30 Sample Mean: 28 Population St. Dev: 10 A recent study focused on the amount of money single men and women save monthly. The information is summarized next. Assume that the population standard deviations are equal. The question is, at the .01 significance level, do women save more money than men? What is the critical value for this hypothesis test?
2.369
A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized next. At the .01 significance level, testing if there a difference in the mean number of times men and women send a Twitter message in a day. What is the value of the test statistic for this hypothesis test?
2.4
An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and post-training customer survey. To compare the differences they computed (post-training survey score - pre-training survey score). Seven customers were randomly selected and completed both surveys. The results follow. What is the value of the test statistic?
2.542
The contingency table for a sample of corporate executives classified by educational level and the social activity follows. What does the expected frequency for the above average social activity and high school education equal?
22.5
A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are shown on the table. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. What are the degrees of freedom?
24
Two samples, one of size 14 and the second of size 13, are selected to test the difference between two population means. How many degrees of freedom are used to find the critical value? Assume the population standard deviations are equal.
25
We test for a hypothesized difference between two population means: H0: ?1 = ?2. The population standard deviations are unknown but assumed equal. The number of observations in the first sample is 15, and 12 in the second sample. How many degrees of freedom are associated with the critical value?
25
A sample of 100 production workers is obtained. The workers are classified by gender (male, female) and by age (under 20, 20-29, 30-39, and 40 or over). How many degrees of freedom are there?
3
The results of a mathematics placement exam at two different campuses of Mercy College follow: What is the computed value of the test statistic?
3.37
User Old Website Design New Website Design A ; 30 ; 25 B ; 45 ; 30 C ; 25 ; 20 D ; 32 ; 30 E ; 28 ; 27 A company is researching the effectiveness of a new website design to decrease the time to access a website. Five website users were randomly selected, and their times (in seconds) to access the website with the old and new designs were recorded. To compare the times, they computed (new website design time - old website design time). The results follow. For a 0.01 significance level, what is the critical value?
3.747
Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested in finding out if exceeding the speed limit was related to social activity. They collected the following responses from 100 randomly selected students: Using 0.05 as the significance level, what is the critical value for the test statistic?
3.841
A survey of property owners opinions about a street-widening project was taken to determine if owners opinions were related to the distance between their home and the street. A randomly selected sample of 100 property owners was contacted and the results are shown next. What is the expected frequency for people against the project and who have over 120 feet of property foot-frontage?
3.9
A question has these possible responses: excellent, very good, good, fair, and unsatisfactory. What are the degrees of freedom for a goodness-of-fit test to test the hypothesis that responses are uniformly distributed?
4
A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. The degrees of freedom for the analysis are __________.
4
A survey of property owners opinions about a street-widening project was taken to determine if owners opinions were related to the distance between their home and the street. A randomly selected sample of 100 property owners was contacted and the results are shown. How many degrees of freedom are there?
4
Accounting procedures allow a business to evaluate their inventory costs based on two methods: LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000s) for five products with the LIFO and FIFO methods. To analyze the difference, they computed (FIFO - LIFO) for each product. Based on the following results, and testing if the LIFO method result in a lower cost of inventory than the FIFO method. What are the degrees of freedom?
4
Students were sampled in order to determine their support for the legalization of gambling in their community. A sample of 150 students were asked whether or not they supported legalization of gambling, and the following results were obtained. The value of the chi-square test statistic equals _____.
4
Given the least squares regression equation, Ŷ = 1,202 + 1,133X, when X = 3, what does Ŷ equal?
4,601
A personnel manager is concerned about absenteeism. She decides to sample employee records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis is: Absenteeism is distributed evenly throughout the week. Use the 0.01 level of significance. The sample results are shown. How many degrees of freedom are there?
5
A survey of property owners opinions about a street-widening project was taken to determine if owners opinions were related to the distance between their home and the street. A randomly selected sample of 100 property owners was contacted and the results are shown. What is the expected frequency for people who are undecided about the project and have property front-footage between 45 and 120 feet?
7.7
A survey of property owners opinions about a street-widening project was taken to determine if owners opinions were related to the distance between their home and the street. A randomly selected sample of 100 property owners was contacted and the results are shown. What is the critical value at the 10% level of significance?
7.779
A personnel manager is concerned about absenteeism. She decides to sample employee records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are shown. What is the calculated value of chi-square?
8
A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. What is the value of the chi-square test statistic?
83.67
Sample Size (n): 81 (Bachelor's) 49 (Associates) Sample Mean Salary (in $1,000): 60 (Bachelors) 51 (Associates) Population Variance: 175 (Bachelors) 90 (Associates) The following table shows sample salary information for employees with bachelor's and associate degrees for a large company in the Southeast United States. The point estimate of the difference between the means of the two populations is ______.
9
A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. Using 0.05 as the significance level, what is the critical value for the test statistic?
9.488
A survey of property owners opinions about a street-widening project was taken to determine if owners opinions were related to the distance between their home and the street. A randomly selected sample of 100 property owners was contacted and the results are shown. What is the critical value at the 5% level of significance?
9.488
Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested in finding out if exceeding the speed limit was related to social activity. They collected the following responses from 100 randomly selected students: What is the value of the test statistic?
9.89
Using the following information: What is the coefficient of determination? Round the percentage to one decimal point.
91.80%
If the coefficient of determination is 0.94, what can we say about the relationship between two variables?
94% of the total variation of the dependent variable is explained by the independent variable.
A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. The appropriate test to analyze the relationship between social activity and education is __________.
A contingency table analysis
Which of the following can be used to test the hypothesis that two nominal variables are related?
A contingency table analysis
An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and post-training customer survey. To compare the differences, they computed (post-training survey score - pre-training survey score). Seven customers were randomly selected and completed both surveys. The results follow. This analysis is an example of _____________.
A paired t-test
Twenty randomly selected statistics students were given 15 multiple-choice questions and 15 open-ended questions, all on the same material. The professor was interested in determining if students scored higher on the multiple-choice questions. This experiment is an example of ________________.
A paired t-test
Accounting procedures allow a business to evaluate its inventory costs based on two methods: LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000s) for five products with the LIFO and FIFO methods. To analyze the difference, they computed (FIFO - LIFO) for each product. Based on the following results, and testing if he LIFO method result in a lower cost of inventory than the FIFO method. This example is what type of test?
A paired t-test.
What is the chart called when the paired data (the dependent and independent variables) are plotted?
A scatter diagram
Using the following information: The regression analysis can be summarized as follows:
A significant positive relationship exists between the variables.
A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are shown on the table The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. This example is what type of test?
A two-sample test of means
The chi-square statistic has __________.
A uniform distribution
A sample of 250 adults tried the new multigrain cereal Wow! A total of 187 rated it as excellent. In a sample of 100 children, 66 rated it as excellent. Using the 0.1 significance level, the researcher wishes to show that adults like the cereal better than children. What test statistic should we use to compare the ratings of adults and children?
A z-statistic
Which of the following are true assumptions underlying linear regression? (1) For each value of X, there is a group of Y values that is normally distributed. (2) The means of these normal distributions of Y values all lie on the regression line. (3) The standard deviations of these normal distributions are equal.
All of them
A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. What is the dependent variable?
Amount of sales dollars
A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. The appropriate test statistic for the analysis is a(n) __________.
Chi-square statistic
The following table classifies 100 individuals using two variables, gender and college attended. What is this two-way classification called?
Contingency table
To test if an observed frequency distribution with five classes is normally distributed, we need to ___________.
Convert the class limits to standard normal z-statistics
The chi-square distribution becomes more symmetrical as the ____________.
Degrees of freedom increase
In a goodness-of-fit test, the null hypothesis (no difference between sets of observed and expected frequencies) is rejected when the ________________.
Difference between the observed and expected frequencies is significantly large
To test the hypothesis that 55% of those families who plan to purchase a vacation residence in Florida want a condominium, the null hypothesis is the population proportion equal 0.55 and the alternate is the population proportion not equal .55. A random sample of 400 families who planned to buy a vacation residence revealed that 228 families want a condominium. What decision should be made regarding the null hypothesis using the 0.01 level of significance?
Do not reject it.
The claim that 40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job was available is to be investigated at the 0.02 significance level. If 74 out of the 200 workers sampled said they would return to work, what is our decision?
Do not reject the null hypothesis because -0.879 lies in the region between +2.326 and -2.326.
Suppose we test H0: the population proportion1 equal the population proportion2 at the 0.05 level of significance. If the z-test statistic is -1.07, what is our decision?
Do not reject the null hypothesis.
What is our decision for a goodness-of-fit test with a computed chi-square value of 1.273 and a critical value of 13.388?
Do not reject the null hypothesis.
Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested in finding out if exceeding the speed limit was related to social activity. They collected the following responses from 100 randomly selected students; Based on the analysis, what can be concluded?
Driving behavior and gender are related.
Accounting procedures allow a business to evaluate its inventory costs based on two methods: LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000s) for five products with the LIFO and FIFO methods. To analyze the difference, they computed (FIFO - LIFO) for each product. Based on the following results, and testing if the LIFO method result in a lower cost of inventory than the FIFO method. What is the decision at the 5% level of significance?
Fail to reject null hypothesis
Men: Sample Size: 25 Sample Mean: 23 Population St. Dev: 5 Women Sample Size: 30 Sample Mean: 28 Population St. Dev: 10 A recent study focused on the amount of money single men and women save monthly. The information is summarized next. Assume that the population standard deviations are equal. At the .01 significance level, what is the conclusion about the way women and men save?
Fail to reject the null hypothesis
A company is researching the effectiveness of a new website design to decrease the time to access a website. Five website users were randomly selected, and their times (in seconds) to access the website with the old and new designs were recorded. To compare the times, they computed (new website design time - old website design time). The results follow. For a 0.01 significance level, what is the decision regarding the hypothesis that the training was effective in improving customer relationships?
Fail to reject the null hypothesis.
A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized next. At the .01 significance level, and testing if there a difference in the mean number of times men and women send a Twitter message in a day. Based on the p-value, what is your conclusion?
Fail to reject the null hypothesis.
Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is your decision if ? equal 0.01?
Fail to reject the null hypothesis.
What is the decision regarding the differences between the observed and expected frequencies if the critical value of chi-square is 9.488 and the computed chi-square value is 6.079?
Fail to reject the null hypothesis; the difference is probably due to sampling error.
It is claimed that in a bushel of peaches, less than 10% are defective. A sample of 400 peaches is examined and 50 are found to be defective. If ? equal 0.025, what will be the decision?
Fail to reject the null.
A t-statistic is useful for computing an expected normal distribution.
False
For a contingency table, the expected frequency for a cell is found by dividing the row total by the grand total.
False
If we are testing the difference between two population proportions, it is assumed that the two populations are approximately normal and have equal variances.
False
In regression analysis, error is defined as the difference between the measured value, Y, and the predicted Y value,
False
One assumption underlying linear regression is that the X values are normally distributed.
False
Some important uses of the chi-square include testing for the association of two categorical variables.
False
The claim that male and female students at Coastal Carolina University prefer different parking lots on campus is an example of a chi-square null hypothesis.
False
The coefficient of determination is the square root of the coefficient of correlation.
False
The hypothesis to test the slope of a regression equation is H0: ? = 0.
False
The pooled estimate of the proportion is found by dividing the total number of samples by the total number of successes.
False
The shape of the chi-square distribution depends on the size of the sample.
False
The strength of the correlation between two variables depends on the sign of the coefficient of correlation.
False
The use of the chi-square statistic would be permissible in the following goodness-of-fit test.
False
The variance of the chi-square distribution is equal to one.
False
In the past five years, 45% of the tourists who visited Orlando, Florida, went to see local attractions. The city council recently spent a significant amount of money on advertising and promoting visits to area attractions. They are interested in knowing whether the advertising campaign was effective�whether it increased the proportion of tourists visiting local attractions. The proper set of hypotheses is ________________.
H0: p > 0.45 H1: p is less than or equal to 0.45
Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the null hypothesis?
H0: the population proportion equal 0.41
It is claimed that in a bushel of peaches, less than 10% are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the null hypothesis?
H0: the population proportion greater than or equal to 0.10
In a market test of a new chocolate raspberry coffee, a poll of 400 people from Dobbs Ferry showed 250 preferred the new coffee. In Irvington, 170 out of 350 people preferred the new coffee. To test the hypothesis that there is no difference in preferences between the two villages, what is the null hypothesis?
H0: the population proportion1 equal the population proportion2
When testing the hypothesized equality of two population means, the implied null hypothesis is ____________.
H0: µ1 - µ2 = 0
Campus Sample Size Mean Pop. St. Dev 1 ; 330 ; 33 ; 8 2 ; 310 ; 31 ; 7 The results of a mathematics placement exam at two different campuses of Mercy College follow: What is the *null hypothesis* if we want to test the hypothesis that the mean score on Campus 1 is higher than on Campus 2?
H0: µ1 ≤ µ2
A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are presented on the table shown. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. What is the null hypothesis?
H0: µA = µB
Accounting procedures allow a business to evaluate their inventory costs based on two methods: LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000s) for five products with the LIFO and FIFO methods. To analyze the difference, they computed (FIFO - LIFO) for each product. Based on the following results, testing if the LIFO method result in a lower cost of inventory than the FIFO method. What is the null hypothesis?
H0: µd ≤ 0
A company is researching the effectiveness of a new website design to decrease the time to access a website. Five website users were randomly selected, and their times (in seconds) to access the website with the old and new designs were recorded. To compare the times, they computed (new website design time - old website design time). The results follow. What is the null hypothesis?
H0: µd ≥ 0
Accounting procedures allow a business to evaluate their inventory costs based on two methods: LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000s) for five products with the LIFO and FIFO methods. To analyze the difference, they computed (FIFO - LIFO) for each product. Based on the following results, the question if the LIFO method results in a lower cost of inventory than the FIFO method. What is the alternate hypothesis?
H0: µd ≥ 0
What is the null hypothesis to test the significance of the slope in a regression equation?
H0: β = 0
It is claimed that in a bushel of peaches, less than 10% are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the alternate hypothesis for a one-sided test?
H1: the population proportion < 0.10
Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the alternate hypothesis?
H1: the population proportion not equal 0.41
In a market test of a new chocolate raspberry coffee, a poll of 400 people (sample 1) from Dobbs Ferry showed 250 preferred the new coffee. In Irvington, 170 out of 350 people (sample 2) preferred the new coffee. To test the hypothesis that a higher proportion of people in Dobbs Ferry prefer the new coffee, what is the alternate hypothesis?
H1: the population proportion1 > the population proportion2
If the decision is to reject the null hypothesis of no difference between two population proportions at the 5% level of significance, what are the alternative hypothesis and rejection region?
H1: the population proportion1 not equal the population proportion2; z > +1.960 and z < -1.960
A sample of 250 adults tried the new multigrain cereal Wow! A total of 187 rated it as excellent. In a sample of 100 children, 66 rated it as excellent. Using the 0.1 significance level, the researcher wishes to show that adults like the cereal better than children. Which of the following is the alternate hypothesis?
H1: the population prportion A > the population proportion C
Campus Sample Size Mean Pop. St. Dev 1 ; 330 ; 33 ; 8 2 ; 310 ; 31 ; 7 The results of a mathematics placement exam at two different campuses of Mercy College follow: What is the *alternative hypothesis* if we want to test the hypothesis that the mean score on Campus 1 is higher than on Campus 2?
H1: µ1 > µ2
A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are shown on the table. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but assumed equal. What is the alternate hypothesis?
H1: µA ≠ µB
User Old Website Design New Website Design A ; 30 ; 25 B ; 45 ; 30 C ; 25 ; 20 D ; 32 ; 30 E ; 28 ; 27 A company is researching the effectiveness of a new website design to decrease the time to access a website. Five website users were randomly selected, and their times (in seconds) to access the website with the old and new designs were recorded. To compare the times, they computed (new website design time - old website design time). The results follow. What is the alternative hypothesis?
H1: µd < 0
What is the alternate hypothesis to test the significance of the slope in a regression equation?
H1: β ≠ 0
In regression analysis, what is the predictor variable called?
Independent variable
What is the variable used to predict another variable called?
Independent variable
The chi-square statistic _______________.
Is greater than or equal to zero
Which of the following statements regarding the coefficient of correlation is true?
It describes the relationship between two variables.
Which of the following is true about the standard error of estimate?
It is a measure of the accuracy of the prediction.
If we reject the null hypothesis, what can we conclude about the population correlation coefficient?
It is not zero.
In the equation, Ŷ = a + bX, what is Ŷ?
It is the predicted value of Y, given a specific X value.
A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. What is the independent variable?
Number of contacts
A personnel manager is concerned about absenteeism. She decides to sample employee records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are:
Observed frequencies
The chi-square distribution is _____________.
Positively skewed
Based on the regression equation, we can _______________.
Predict the value of the dependent variable given a value of the independent variable
An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and post-training customer survey. To compare the differences they computed (post-training survey score - pre-training survey score). Seven customers were randomly selected and completed both surveys. The results follow. For a 0.05 significance level, what is the decision regarding the hypothesis that the training was effective in improving customer relationships?
Reject the null hypothesis and conclude that the training was effective.
A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are shown on the table. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. If we test the null hypothesis at the 1% level of significance, what is the decision?
Reject the null hypothesis and conclude the means are different.
For a chi-square test involving a contingency table, suppose the null hypothesis is rejected. We conclude that the two variables are __________.
Related
A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. Based on the analysis, what can be concluded?
Social activity and education are related.
The computed chi-square value is positive because the difference between the observed and expected frequencies is _____________.
Squared
When testing the difference between two dependent population means, the test statistic is based on a ______________.
Standard deviation of the differences
To test if an observed frequency distribution with five classes is normally distributed, we compute probabilities for each class based on a(n) _________________.
Standard normal distribution
If the correlation between two variables is close to one, the association between the variables is ___________.
Strong
In the least squares equation, Ŷ = 10 + 20X, the value of 20 indicates ____________.
That Y increases by 20 units for each unit increase in X
Three new colors have been proposed for the Jeep Grand Cherokee vehicle. They are silvered-blue, almond, and willow green. The null hypothesis for a goodness-of-fit test would be _______________.
That there is no preference between the colors
In the regression equation, what does the letter "a" represent?
The Y-intercept
What does a coefficient of correlation of 0.70 infer?
The coefficient of determination is 0.49.
When comparing the 95% confidence and prediction intervals for a given regression analysis ______________.
The confidence interval is narrower than a prediction interval
Which of the following assumptions is necessary to apply a goodness-of-fit test?
The data are measured with a nominal or ordinal scale.
In the regression equation, what does the letter "Y" represent?
The dependent variable
Which chi-square distribution would be closest to a normal distribution?
The distribution with 15 degrees of freedom.
To test if an observed frequency distribution with five classes is normally distributed, we need to find ___________________.
The expected, normally distributed class frequencies
In the regression equation, what does the letter "X" represent?
The independent variable
When testing the difference between two population means, the sample variances are pooled to estimate the population variance when ________________.
The population variances are assumed equal but unknown
Which of the following statements is correct regarding the chi-square distribution?
The shape of the distribution is based on the degrees of freedom.
In the regression equation, what does the letter "b" represent?
The slope of the line
Assuming the population variances are known, the population variance of the difference between two means is _____________.
The sum of two population variances
Which condition must be met to conduct a test for the difference in two sample means using a z-statistic?
The two population standard deviations must be known.
If the correlation coefficient between two variables, X and Y, equals zero, what can be said of the variables X and Y?
The variables are not related.
Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested in finding out if exceeding the speed limit was related to gender. They collected the following responses from 100 randomly selected students. The null hypothesis for the analysis is ____________.
There is no relationship between gender and speeding
A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. The null hypothesis for the analysis is __________________________.
There is no relationship between social activity and education
Which of the following are the same between a confidence interval and a prediction interval?
They both use the standard error of estimate.
A confidence interval can be determined for the mean value of Y for a given value of X.
True
A scatter diagram is a graph that portrays the correlation between a dependent variable and an independent variable.
True
An economist is interested in predicting the unemployment rate based on gross domestic product. Since the economist is interested in predicting unemployment, the independent variable is gross domestic product.
True
Because the coefficient of determination is expressed as a percent, its value is between 0% and 100%.
True
Correlation analysis is a statistical technique used to measure the strength of the relationship between two variables.
True
For a goodness-of-fit test, the following are possible null and alternate hypotheses: H0: Sales are uniformly distributed among the five locations. H1: Sales are not uniformly distributed among the five locations.
True
In testing the difference between two population proportions, we pool the two sample proportions to estimate the population proportion.
True
In the goodness-of-fit test, the chi-square distribution is used to determine how well an observed distribution of observations fits an expected distribution of observations.
True
Nonparametric tests require no assumptions about the shape of the population distribution.
True
The chi-square distribution is positively skewed.
True
The chi-square test statistic used in a goodness-of-fit test has k - 1 degrees of freedom..
True
The coefficient of determination is the proportion of total variation in Y that is explained by X.
True
The least squares technique minimizes the sum of the squares of the vertical distances between the actual Y values and the predicted values of Y.
True
The regression equation is used to estimate a value of the dependent variable Y based on a selected value of the independent variable X.
True
The shape of the chi-square distribution depends on the number of degrees of freedom.
True
The standard error of estimate measures the accuracy of a prediction.
True
The values of a and b in the regression equation are called the regression coefficients.
True
There is not one, but a family of chi-square distributions. There is a chi-square distribution for 1 degree of freedom, another for 2 degrees of freedom, another for 3 degrees of freedom, and so on.
True
To test the null hypothesis that a set of sample data is normally distributed, we compare an expected normal distribution of the data to an observed distribution of the data.
True
Which of the following statements is correct regarding the goodness-of-fit test?
Variables are based on the nominal measurement scale.
An electronics retailer believes that, at most, 40% of their cell phone inventory was sold during November. The retailer surveyed 80 dealers and found that 38% of the inventory was sold. Since 38% is less than 40%, is this difference of 2 percentage points sampling error or a significant difference? Test at the 0.05 level. The computed z equal -0.37.
We cannot determine if the 2% is a significant difference.
Assume the least squares equation is Y = 10 + 20X. What does the value of 10 in the equation indicate?
When X = 0, Y = 10.
When is it appropriate to use the paired difference t-test?
When two dependent samples are compared
What is the general form of the regression equation?
Y = a + (bX)
The Pearson product-moment correlation coefficient, r, requires that variables be measured with _____________.
an interval or ratio scale
The value of the correlation coefficient (r):
can be equal to the value of the coefficient of determination (r2).
An example of a way to rescale a variable to create a linear relationship is:
computing the log of all values of the dependent and independent variable.
For any chi-square goodness-of-fit test, the number of degrees of freedom is found by ______.
k - 1
If the correlation coefficient has a negative value, then the coefficient of determination:
must be positive.
What are the degrees of freedom used to test the significance of the slope in a simple linear regression equation?
n - 2
The number of trials and the population proportion are respectively represented by what symbols?
n and the population proportion
For a hypothesis test comparing two population means, the combined degrees of freedom are 24. Which of the following statements about the two sample sizes is NOT true? Assume the population standard deviations are equal.
n1 = 11; n2 = 13
How is a pooled estimate of the population proportion represented?
pc
In regression, if the relationship between the dependent and independent variables is non-linear, a linear relationship between the variables can be achieved by:
rescaling the variables.
Consider independent simple random samples that are taken to test the difference between the means of two populations. The variances of the populations are unknown, but are assumed to be equal. The sample sizes of each population are n1 = 37 and n2 = 45. The appropriate distribution to use is the:
t distribution with df = 80.
What is the test statistic to test the significance of the slope in a regression equation?
t-statistic
When determining how well an observed set of frequencies fit an expected set of frequencies, what is the test statistic?
t-statistic.
Some important uses of the chi-square distribution include:
testing for goodness-of-fit.
In regression, the difference between the confidence interval and prediction interval formulas is ________________.
the addition of "1" to the quantity under the radical sign
The sample proportion is defined as _________.
x/n
Men: Sample Size: 25 Sample Mean: 23 Population St. Dev: 5 Women Sample Size: 30 Sample Mean: 28 Population St. Dev: 10 A recent study focused on the amount of money single men and women save monthly. The information is summarized next. Assume that the population standard deviations are equal. The question is, at the .01 significance level, do women save more money than men. What is the test statistic for this hypothesis?
z-statistic
If the null hypothesis that two means are equal is true, where will 97% of the computed z values lie between?
±2.17
A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is measured in millimeters. The results are shown on the table. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but assumed equal. What is the critical t value at the 1% level of significance?
±2.797
