CH 11-13 TestBank

Which of the following has a chi-square distribution? a. (n - 1) σ/S2 b. (n - 2) σ/S2 c. (n - 1)S/ σ d. (n - 1)S2/ σ

(n - 1)S^2/ σ Chi Square Test statistic for Hypothesis tests about a population variance.

A sample of 20 cans of tomato juice showed a standard deviation of 0.4 ounces. A 95% confidence interval estimate of the population variance is a. 0.2313 to 0.8533 b. 0.2224 to 0.7924 c. 0.0889 to 0.3169 d. 0.0925 to 0.3413

0.0925 to 0.3413

Exhibit 11-2 The variance in a production process is an important measure of the quality; large variance indicates an opportunity for improvement. Management believes that in order to reduce the variance of the bag weights, the current filling machine should be replaced by a new machine. Excel was used on a sample data, and the following printout was obtained at a 1% significance level. The sample standard deviation of the bag weights filled by the current machine is approximately a. 0.049 b. 0.221 c. 8.284 d. 2.801

0.221

In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. Patients Cured Patients Not Cured Received medication 70 10 Received sugar pills 20 50 We are interested in determining whether or not the medication was effective in curing the common cold. The number of degrees of freedom associated with this test is a. 4 b. 149 c. 1 d. 3

1

A sample of 60 items from a population has a sample variance of 8 while a sample of 40 items from another population has a sample variance of 10. If we test whether the variances of the two populations are equal, the test statistic will have a value of a. 0.8 b. 1.56 c. 1.5 d. 1.25

1.25 Larger variance in numerator 10/8=

In the past, 35% of the students at ABC University were in Business College, 35% of the students were in Liberal Arts College, and 30% of the students were in Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in Business College, 120 are in Liberal Arts College, and 90 are in Education College. The expected frequency for Business College is a. 0.3 b. 0.35 c. 90 d. 105

105

In the past, 35% of the students at ABC University were in Business College, 35% of the students were in Liberal Arts College, and 30% of the students were in Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in Business College, 120 are in Liberal Arts College, and 90 are in Education College. The calculated value of the test statistic equals a. 0.01 b. 0.75 c. 4.29 d. 4.38

4.29

The manager of the service department of a local car dealership has noted that the service times of a sample of 30 new automobiles has a variance of 36 (minute)2. A 95% confidence interval estimate for the standard deviation of the service times for all their new automobiles is a. 16.047 to 45.722 b. 4.778 to 8.066 c. 2.93 to 6.31 d. 22.833 to 65.059

4.778 to 8.066

Exhibit 11-2 The variance in a production process is an important measure of the quality; large variance indicates an opportunity for improvement. Management believes that in order to reduce the variance of the bag weights, the current filling machine should be replaced by a new machine. Excel was used on a sample data, and the following printout was obtained at a 1% significance level. The alternative hypothesis is: a. Ha : σ2 1 > σ2 2 b. Ha : σ2 1 < σ2 2 c. Ha : σ2 1 ≠ σ2 2 d. Ha : σ2 1 ≥ σ2 2

Ha : σ2 1 > σ2 2

We are interested in testing whether the variance of a population is significantly more than 625. The null hypothesis for this test is a. Ho: σ > 625 b. Ho: σ < 625 c. Ho: σ >= 625 d. Ho: σ <= 625

Ho: σ <= 625 Test is to prove significantly more than therefore null wants to disprove less than or equal to 625.

Which of the following is not a characteristic of the completely randomized design? a. All recorded numerical values can be regarded as independent b. The random variables under study are approximately normally distributed with equal variances c. Anova test for the completely randomized design can be conducted by Anova: Single Factor of Data Analysis in Excel d. Populations have equal means

Populations have equal means

Which of the following is not a characteristic of the randomized block design? a. The major purpose of blocking is to reduce the error variation b. Blocking uses the same experimental units for all treatments c. The random variables under study are approximately normally distributed with equal variances d. Anova test for the randomized block design can be conducted by Anova: Two-Factor Without Replications of Data Analysis in Excel e. Populations have equal means

Populations have equal means

Which of the following is not a characteristic of Anova? a. The random variables under study are approximately normally distributed b. The random variables under study have equal variances c. At least two populations are of interest d. Populations have equal means.

Populations have equal means.

Which of the following statistics has an F distribution? a. (n - 1)S/ σ b. S1/S2 c. (n - 1)S1/S2 d. S 2/1 / S 2/2

S 2/1 / S 2/2

In Anova, treatments refer to a. experimental units b. different levels of a factor c. the dependent variable d. applying an antibiotic to a wound

different levels of a factor

A population where each element of the population is assigned to one and only one of several classes or categories is a a. multinomial population b. Poisson population c. normal population d. None of these alternatives is correct.

multinomial population

Exhibit 11-1 Last year, the standard deviation of the ages of the students at UA was 1.8 years. We are interested in testing to see if there has been a significant change in the standard deviation of the ages of the students at UA. A sample of 61 students showed a standard deviation of 2.1 years. The p-value for this test is a. 0.05 b. between 0.025 and .05 c. between .05 and .1 d. 1.96

between .05 and .1

The sampling distribution for a goodness of fit test is the a. Poisson distribution b. t distribution c. normal distribution d. chi-square distribution

chi-square distribution

Exhibit 11-2 The variance in a production process is an important measure of the quality; large variance indicates an opportunity for improvement. Management believes that in order to reduce the variance of the bag weights, the current filling machine should be replaced by a new machine. Excel was used on a sample data, and the following printout was obtained at a 1% significance level. The p-value of the test is a. about 3.611 b. about 2.801 c. about 8.284 d. close to 0

close to 0

The independent variable of interest in ANOVA is called a. a partition b. a treatment c. either a partition or a treatment d. a factor

a factor

In the past, 35% of the students at ABC University were in Business College, 35% of the students were in Liberal Arts College, and 30% of the students were in Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in Business College, 120 are in Liberal Arts College, and 90 are in Education College. The p-value of the test is a. greater than 0.10 b. between 0.05 and 0.10 c. between 0.025 and 0.05 d. between 0.01 and .025

greater than 0.10

Exhibit 11-2 The variance in a production process is an important measure of the quality; large variance indicates an opportunity for improvement. Management believes that in order to reduce the variance of the bag weights, the current filling machine should be replaced by a new machine. Excel was used on a sample data, and the following printout was obtained at a 1% significance level. At a 1% significance level, the null hypothesis is rejected if the value of the test statistic is a. greater than or equal to the p-value b. greater than or equal to 8.284 c. greater than or equal to 2.801 d. less than or equal to 2.801

greater than or equal to 2.801

The contents of a sample of 26 cans of apple juice showed a standard deviation of 0.06 ounces. We are interested in testing to determine whether the population variance is significantly more than 0.003. a. Provide the null hypothesis to be tested. b. Compute the value of the test statistic. c. Determine the p-value of the test. d. With a 90% confidence, state your conclusion based on the p-value approach.

a. σ 2<= 0.003 b. The value of the test statistic is 30 c The p-value for this test is greater than 0.10 d.With 90% confidence, the null hypothesis should not be rejected.

An important application of the chi-square distribution is a. making inferences about a single population variance b. testing for goodness of fit c. testing for the independence of two qualitative variables d. testing the equality of three or more population proportions e. all these alternatives are correct

all these alternatives are correct

A random variable having the chi-square distribution (or the F distribution) may assume a. any value between -1 to 1 b. any value between - infinity to +infinity c. any negative value d. any non-negative value

any non-negative value

In order not to violate the requirements necessary to use the chi-square distribution, each expected frequency in a goodness of fit test must be a. at least 5 b. at least 10 c. no more than 5 d. less than 2

at least 5

Exhibit 11-2 The variance in a production process is an important measure of the quality; large variance indicates an opportunity for improvement. Management believes that in order to reduce the variance of the bag weights, the current filling machine should be replaced by a new machine. Excel was used on a sample data, and the following printout was obtained at a 1% significance level. The value of the test statistic is approximately a. 24 b. 8.284 c. 2.801 d. 3.611

b. 8.284

In the past, 35% of the students at ABC University were in Business College, 35% of the students were in Liberal Arts College, and 30% of the students were in Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in Business College, 120 are in Liberal Arts College, and 90 are in Education College. The alternative hypothesis is: a. pBC = 0.35, pLAC = 0.35, pEC = 0.30 b. pBC 0.35, and pLAC 0.35, and pEC 0.30 c. pBC 0.35, or pLAC 0.35, or pEC 0.30 d. The population means are equal

pBC /= 0.35, or pLAC /= 0.35, or pEC /= 0.30

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support capital punishment? Number of individuals Yes 40 No 60 No Opinion 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. Let p1 = the proportion of all individuals who support capital punishment, p2 = the proportion of all individuals who are against capital punishment, and p3 = the proportion of all individuals who have no opinion.The null hypothesis is a. p_1=p_2=p_3=1/3 b. p_1≠1/3 or p_2≠1/3 or p_3≠1/3 c. p_1=1/3,p_2+p_3=2/3 d. p_1=p_2=p_3=1

p_1=p_2=p_3=1/3

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support capital punishment? Number of individuals Yes 40 No 60 No Opinion 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. Let p1 = the proportion of all individuals who support capital punishment, p2 = the proportion of all individuals who are against capital punishment, and p3 = the proportion of all individuals who have no opinion. The p-value of the test is a. larger than 0.10 b. between 0.05 and 0.10 c. between 0.01 and 0.05 d. less than 0.01

larger than 0.10

In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. Patients Cured Patients Not Cured Received medication 70 10 Received sugar pills 20 50 We are interested in determining whether or not the medication was effective in curing the common cold. The p-value of the test is a. less than 0.005 b. between 0.005 and 0.01 c. between 0.01 and 0.025 d. between 0.025 and 0.05

less than 0.005

In the past, 35% of the students at ABC University were in Business College, 35% of the students were in Liberal Arts College, and 30% of the students were in Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in Business College, 120 are in Liberal Arts College, and 90 are in Education College. At a 10% significance level, the conclusion of the test is that the a. proportions have changed significantly b. proportions have not changed significantly c. test is inconclusive d. None of these alternatives is correct.

proportions have not changed significantly

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support capital punishment? Number of individuals Yes 40 No 60 No Opinion 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. Let p1 = the proportion of all individuals who support capital punishment, p2 = the proportion of all individuals who are against capital punishment, and p3 = the proportion of all individuals who have no opinion. The conclusion of the test (at 95% confidence) is that a. the population proportions might be equal b. the population proportions are not all the same c. the test is inconclusive d. none of these alternatives is correct.

the population proportions might be equal

A goodness of fit test is always conducted as a a. lower-tail test b. upper-tail test c. middle test d. None of these alternatives is correct.

upper-tail test

To avoid the problem of not having access to the F distribution table with values given for the lower tail, the numerator of the test statistic F=S 2/1 / S 2/2 should be the one with a. the larger sample size b. the smaller sample size c. the larger sample variance d. the smaller sample variance

the larger sample variance

ANOVA is a statistical method for determining whether or not a. the means of two samples are equal b. the means of two or more samples are equal c. the means of more than two samples are equal d. the means of two or more populations are equal

the means of two or more populations are equal

Exhibit 11-2 The variance in a production process is an important measure of the quality; large variance indicates an opportunity for improvement. Management believes that in order to reduce the variance of the bag weights, the current filling machine should be replaced by a new machine. Excel was used on a sample data, and the following printout was obtained at a 1% significance level At a 1% significance level, your conclusion is a. the new machine is better than the current one b. the new machine is surprisingly worse than the current one c. the new machine is not significantly better than the current one d. the sample were too small to make a conclusion

the new machine is better than the current one

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support capital punishment? Number of individuals Yes 40 No 60 No Opinion 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. Let p1 = the proportion of all individuals who support capital punishment, p2 = the proportion of all individuals who are against capital punishment, and p3 = the proportion of all individuals who have no opinion. The number of degrees of freedom associated with this test is a. 150 b. 149 c. 2 d. 3

2

The critical F value at 95% confidence when there is a sample size of 21 for the sample with the smaller variance, and there is a sample size of 9 for the sample with the larger sample variance is a. 2.45 b. 2.94 c. 2.37 d. 2.10

2.45 f table df; n1 -1 (9-1=8) n2-1 (21-1=20) 1-.95 = .05 Look up table for 8/20 at .05

In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. Patients Cured Patients Not Cured Received medication 70 10 Received sugar pills 20 50 We are interested in determining whether or not the medication was effective in curing the common cold. The hypothesis is to be tested at the 5% level of significance. The corresponding critical value from the chi-squared table equals a. 3.841 b. 7.815 c. 5.024 d. 9.340

3.841

The critical chi-square value for an upper (right) tail test at 95% confidence and a sample size of 25 is a. 33.196 b. 36.415 c. 39.364 d. 37.652

36.415

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support capital punishment? Number of individuals Yes 40 No 60 No Opinion 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. Let p1 = the proportion of all individuals who support capital punishment, p2 = the proportion of all individuals who are against capital punishment, and p3 = the proportion of all individuals who have no opinion. The value for the test statistic equals a. 2 b. -2 c. 20 d. 4

4

A sample of 61 observations yielded a sample standard deviation of 6. If we want to test Ho: σ = 40, the test statistic is

54 (n-1)s^2/ σ (61-1)*6^2/40

In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. Patients Cured Patients Not Cured Received medication 70 10 Received sugar pills 20 50 We are interested in determining whether or not the medication was effective in curing the common cold. The value of the test statistic is a. 10.08 b. 54.02 c. 1.96 d. 1.645

54.02

The critical chi-square value for a lower (left) tail test, when the level of significance is 0.10 and the sample size is 15 is a. 21.064 b. 23.685 c. 7.790 d. 6.571

7.790

A random sample of 25 employees of a local utility firm showed that their monthly incomes had a sample standard deviation of $112. Provide a 90% confidence interval estimate for the variance of the incomes for all the firm's employees.

8,268 to 21,736 (rounded)

Exhibit 11-1 Last year, the standard deviation of the ages of the students at UA was 1.8 years. We are interested in testing to see if there has been a significant change in the standard deviation of the ages of the students at UA. A sample of 61 students showed a standard deviation of 2.1 years. The value of the test statistic is a. 44.08 b. 79.08 c. 81.67 d. 3.24

81.67

In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. Patients Cured Patients Not Cured Received medication 70 10 Received sugar pills 20 50 We are interested in determining whether or not the medication was effective in curing the common cold. The expected frequency of those who received medication and were cured is a. 70 b. 150 c. 28 d. 48

48

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support capital punishment? Number of individuals Yes 40 No 60 No Opinion 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. Let p1 = the proportion of all individuals who support capital punishment, p2 = the proportion of all individuals who are against capital punishment, and p3 = the proportion of all individuals who have no opinion. The expected frequency for each group is a. 0.333 b. 0.50 c. 1/3 d. 50

50

Exhibit 11-1 Last year, the standard deviation of the ages of the students at UA was 1.8 years. We are interested in testing to see if there has been a significant change in the standard deviation of the ages of the students at UA. A sample of 61 students showed a standard deviation of 2.1 years. At 5% significance level the null hypothesis a. should be rejected b. should not be rejected c. should be revised d. None of these alternatives is correct.

should not be rejected

Exhibit 11-1 Last year, the standard deviation of the ages of the students at UA was 1.8 years. We are interested in testing to see if there has been a significant change in the standard deviation of the ages of the students at UA. A sample of 61 students showed a standard deviation of 2.1 years. The alternative hypothesis is: a. σ^2≠1.80 b. σ^2≠3.24 c. σ^2≠2.10 d. σ^2≠4.41

σ^2≠3.24

Exhibit 11-1 Last year, the standard deviation of the ages of the students at UA was 1.8 years. We are interested in testing to see if there has been a significant change in the standard deviation of the ages of the students at UA. A sample of 61 students showed a standard deviation of 2.1 years. At 5% significance level the null hypothesis is rejected if a. χ2 ≥ 79.082 b. χ2 ≥ 83.298 c. χ2 ≤ 40.482 or χ2 ≥ 83.298 d. χ2 ≤ 43.188 or χ2 ≥ 79.082

χ2 ≤ 40.482 or χ2 ≥ 83.298