A goodness of fit test is always conducted as a(n) _____. upper-tail test
A population where each element of the population is assigned to one and only one of several classes or categories is a _____. multinomial population
A random sample of 31 charge sales showed a sample standard deviation of $50. A 90% confidence interval estimate of the population standard deviation is _____. 41.39 to 63.68
A random sample of 31 charge sales showed a sample standard deviation of $50. A 90% confidence interval estimate of the population standard deviation is _____. 41.39 to 63.68
A sample of 20 cans of tomato juice showed a standard deviation of 0.4 ounce. A 95% confidence interval estimate of the variance for the population is _____. .0925 to .3413
A sample of 21 elements is selected to estimate a 90% confidence interval for the variance of the population. The χ2 value(s) to be used for this interval estimation is(are) _____ 12.443 and 28.412
A sample of 28 elements is selected to estimate a 95% confidence interval for the variance of the population. The χ2 values to be used for this interval estimation are _____. 14.573 and 43.195
A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H0: σ2 = 20, the test statistic is _____. 50
A sample of 60 items from population 1 has a sample variance of 8, while a sample of 40 items from population 2 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 __ 1.25
A sample of n observations is taken from a population. When performing statistical inference about a population variance, the appropriate χ2 distribution has n – 1 degrees of freedom
A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a _____ goodness of fit test
An ANOVA procedure is used for data obtained from four populations. Four samples, each comprised of 30 observations, were taken from the four populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are _____. 3 and 116
An important application of the chi-square distribution is _____. testing for goodness of fit OR testing for equality of three or more population proportions OR testing for the independence of two variables
Excel’s ____ function is used to perform a goodness of fit test. CHISQ.DIST.RT
Excel’s CHISQ.DIST function can be used to perform __ a goodness of fit test
Exhibit 11-1
Last year, the standard deviation of the ages of the students at UA was 1.81 years. Recently, a sample of 10 students had a standard deviation of 2.1 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.
Refer to Exhibit 11-1. The test statistic is _____ 12.1
Exhibit 11-10
n = 81 s2 = 625 H0: σ2 = 500
Ha: σ2 ≠ 500
Refer to Exhibit 11-10. The p-value is between _____ .1 and .2
Exhibit 11-10
n = 81 s2 = 625 H0: σ2 = 500
Ha: σ2 ≠ 500
Refer to Exhibit 11-10. At 95% confidence, the null hypothesis _____. should not be rejected
Exhibit 11-10
n = 81 s2 = 625 H0: σ2 = 500
Ha: σ2 ≠ 500
Refer to Exhibit 11-10. At 95% confidence, the null hypothesis ____should not be rejected
Exhibit 11-2
We are interested in determining whether the variances of the sales at two music stores (A and B) are equal. A sample of 25 days of sales at store A has a sample standard deviation of 30, while a sample of 16 days of sales from store B has a sample standard deviation of 20.
Refer to Exhibit 11-2. At 95% confidence, the null hypothesis _____should not be rejected
Exhibit 11-2
We are interested in determining whether the variances of the sales at two music stores (A and B) are equal. A sample of 25 days of sales at store A has a sample standard deviation of 30, while a sample of 16 days of sales from store B has a sample standard deviation of 20.
Refer to Exhibit 11-2. The test statistic is _____. 1.56
Exhibit 11-3

The contents of a sample of 26 cans of apple juice showed a standard deviation of 0.06 ounce. We are interested in testing to determine whether the variance of the population is significantly more than .003.

Refer to Exhibit 11-3. The test statistic is _____. 30
Exhibit 11-3
The contents of a sample of 26 cans of apple juice showed a standard deviation of 0.06 ounce. We are interested in testing to determine whether the variance of the population is significantly more than .003.

Refer to Exhibit 11-3. At 95% confidence, the critical value(s) from the table is(are) _____. 37.6525
Exhibit 11-4
n = 30 H0: σ2 = 500
s2 = 625 Ha: σ2 ≠ 500
Refer to Exhibit 11-4. The null hypothesis _____. should not be rejected
Exhibit 11-4
n = 30 H0: σ2 = 500
s2 = 625 Ha: σ2 ≠ 500
Refer to Exhibit 11-4. The test statistic for this problem equals _____ 36.25
Exhibit 11-5
n = 14 H0: σ2 ≤ 410
s = 20 Ha: σ2 > 410
Refer to Exhibit 11-5. The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the table is(are) _____. 22.3621
Exhibit 11-5
n = 14 H0: σ2 ≤ 410
s = 20 Ha: σ2 > 410
Refer to Exhibit 11-5. The test statistic for this problem equals _____. 12.68
Exhibit 11-5
n = 14 H0: σ2 ≤ 410
s = 20 Ha: σ2 > 410
Refer to Exhibit 11-5. The null hypothesis _ should not be rejected
Exhibit 11-6

Sample A Sample B
s2 32 38
n 24 16
We want to test the hypothesis that the population variances are equal.
Refer to Exhibit 11-6. The test statistic for this problem equals _____ 1.19
Exhibit 11-6
Sample A Sample B
s2 32 38
n 24 16
We want to test the hypothesis that the population variances are equal.
Refer to Exhibit 11-6. The null hypothesis _____. should not be rejected
Exhibit 11-6
Sample A Sample B
s2 32 38
n 24 16
We want to test the hypothesis that the population variances are equal.
Refer to Exhibit 11-6. The null hypothesis is to be tested at the 10% level of significance. The critical value from the table is _____. 2.13
Exhibit 11-7

Sample A Sample B
s2 22 25
n 10 8
We want to test the hypothesis that population B has a smaller variance than population A.
Refer to Exhibit 11-7. The null hypothesis is to be tested at the 5% level of significance. The critical value from the table is _____. 3.29
Exhibit 11-7

Sample A Sample B
s2 22 25
n 10 8
We want to test the hypothesis that population B has a smaller variance than population A.
Refer to Exhibit 11-7. The null hypothesis _____. should not be rejected
Exhibit 11-7
Sample A Sample B
s2 22 25
n 10 8
We want to test the hypothesis that population B has a smaller variance than population A.
Refer to Exhibit 11-7. The test statistic for this problem equals _____. 1.14
Exhibit 11-8
n = 23 H0: σ2 ≥ 66
s2 = 60 Ha: σ2 < 66
Refer to Exhibit 11-8. The test statistic has a value of _____. 20.00
Exhibit 11-8
n = 23 H0: σ2 ≥ 66
s2 = 60 Ha: σ2 < 66
Refer to Exhibit 11-8. The p-value is _____. greater than .10
Exhibit 11-8
n = 23 H0: σ2 ≥ 66
s2 = 60 Ha: σ2 < 66
Refer to Exhibit 11-8. The null hypothesis _____. should not be rejected
Exhibit 11-9
n = 14 s = 20 H0: σ2 ≤ 500
Ha: σ2 ≥ 500
Refer to Exhibit 11-9. The test statistic for this problem equals _____. 12.68
Exhibit 11-9
n = 14 s = 20 H0: σ2 ≤ 500
Ha: σ2 ≥ 500
Refer to Exhibit 11-9. The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the table is(are) _____. 22.362
Exhibit 12-1
Individuals in a random sample of 150 were asked whether they supported capital punishment. The following information was obtained.
Do You Support # of Individuls
Capital Punishment?
Yes 40

No 60
No Opinion 50
We are interested in determining whether the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed.
Refer to Exhibit 12-1. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals _____. 5.99147
Exhibit 12-1
Individuals in a random sample of 150 were asked whether they supported capital punishment. The following information was obtained.

Do You Support # of Individuls
Capital Punishment?
Yes 40
No 60
No Opinion 50
We are interested in determining whether the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed.
Refer to Exhibit 12-1. The calculated value for the test statistic equals ____ 4
Exhibit 12-1
Individuals in a random sample of 150 were asked whether they supported capital punishment. The following information was obtained.
Do You Support # of Individuls
Capital Punishment?
Yes 40
No 60
No Opinion 50
We are interested in determining whether the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed.
Refer to Exhibit 12-1. If the opinions are uniformly distributed, the expected frequency for each group would be _____ 50
Exhibit 12-1
Individuals in a random sample of 150 were asked whether they supported capital punishment. The following information was obtained.
Do You Support # of Individuls
Capital Punishment?
Yes 40
No 60
No Opinion 50
We are interested in determining whether the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed.
Refer to Exhibit 12-1. The number of degrees of freedom associated with this problem is _____ 2
Exhibit 12-2
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A random sample of 300 students taken from this year’s student body showed the following number of students in each class.
Freshmen 83
Sophomores 68
Juniors 85
Seniors 64
We are interested in determining whether there has been a significant change in the distribution of class between the last school year and this school year.
Refer to Exhibit 12-2. The calculated value for the test statistic equals _____ 1.6615
Exhibit 12-2
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A random sample of 300 students taken from this year’s student body showed the following number of students in each class.
Freshmen 83
Sophomores 68
Juniors 85
Seniors 64
We are interested in determining whether there has been a significant change in the distribution of class between the last school year and this school year.
Refer to Exhibit 12-2. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals _ 7.815
Exhibit 12-2
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A random sample of 300 students taken from this year’s student body showed the following number of students in each class.
Freshmen 83
Sophomores 68
Juniors 85
Seniors 64
We are interested in determining whether there has been a significant change in the distribution of class between the last school year and this school year.
Refer to Exhibit 12-2. The null hypothesis _____. should not be rejected
Exhibit 12-2
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A random sample of 300 students taken from this year’s student body showed the following number of students in each class.
Freshmen 83
Sophomores 68
Juniors 85
Seniors 64
We are interested in determining whether there has been a significant change in the distribution of class between the last school year and this school year.
Refer to Exhibit 12-2. If the distribution is the same as the previous year, the expected number of freshmen is _____. 90
Exhibit 12-2
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A random sample of 300 students taken from this year’s student body showed the following number of students in each class.
Freshmen 83
Sophomores 68

Juniors 85
Seniors 64
We are interested in determining whether there has been a significant change in the distribution of class between the last school year and this school year.
Refer to Exhibit 12-2. If the distribution is the same as the previous year, the expected frequency of seniors is ____ 60
Exhibit 12-3
In order to determine whether 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 Patients
Cured Not Cured
Received medication 70 10
Received sugar pills 20 50
We are interested in determining whether the medication was effective in curing the common cold.
Refer to Exhibit 12-3. The number of degrees of freedom associated with this problem is _____.1
Exhibit 12-3
In order to determine whether 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 Patients
Cured Not Cured
Received medication 70 10
Received sugar pills 20 50

We are interested in determining whether the medication was effective in curing the common cold.
Refer to Exhibit 12-3. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals _____ 3.84
Exhibit 12-3
In order to determine whether 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 Patients
Cured Not Cured
Received medication 70 10
Received sugar pills 20 50
We are interested in determining whether the medication was effective in curing the common cold.
Refer to Exhibit 12-3. The test statistic is _____. 54.02
Exhibit 12-4
In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether the proportions have changed, a random sample of 300 students from ABC University was selected. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College.
Refer to Exhibit 12-4. If the proportions are the same as they were in the past, the expected frequency for the Business College is 105
Exhibit 12-4
In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether the proportions have changed, a random sample of 300 students from ABC University was selected. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College.
Refer to Exhibit 12-4. Based upon this test, what can be concluded There is enough evidence to conclude that the proportions have not changed significantly.
Exhibit 12-4
In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether the proportions have changed, a random sample of 300 students from ABC University was selected. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College.
Refer to Exhibit 12-4. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals _____ 5.99
Exhibit 12-5
The table below gives beverage preferences for random samples of teens and adults.
Beverage Teens Adults Total
—————————————————-
Coffee 50 200 250

Tea 100 150 250

Soft drink 200 200 400

Other 50 50 100
————————————–
400 600 1,000
We are asked to test for independence between age (i.e., adult and teen) and drink preferences.
Refer to Exhibit 12-5. The value of the test statistic for this test for independence is_____. 62.5
Exhibit 12-5
The table below gives beverage preferences for random samples of teens and adults.
Beverage Teens Adults Total
—————————————————-
Coffee 50 200 250

Tea 100 150 250
Soft drink 200 200 400
Other 50 50 100
————————————–
400 600 1,000
We are asked to test for independence between age (i.e., adult and teen) and drink preferences.
Refer to Exhibit 12-5. If age and drink preference is independent then the expected number of adults who prefer coffee would be _____. 200
Exhibit 12-5
The table below gives beverage preferences for random samples of teens and adults.

Beverage Teens Adults Total
—————————————————-
Coffee 50 200 250
Tea 100 150 250
Soft drink 200 200 400
Other 50 50 100
————————————–
400 600 1,000
We are asked to test for independence between age (i.e., adult and teen) and drink preferences.
Refer to Exhibit 12-5. With a .05 level of significance, the critical value for the test is _____.7.815
Exhibit 12-5
The table below gives beverage preferences for random samples of teens and adults.
Beverage Teens Adults Total
—————————————————-
Coffee 50 200 250
Tea 100 150 250
Soft drink 200 200 400
Other 50 50 100
————————————–
400 600 1,000
We are asked to test for independence between age (i.e., adult and teen) and drink preferences.
Refer to Exhibit 12-5. What can be concluded from this test? There is enough evidence to conclude that age and drink preference is dependent.
Exhibit 12-6
The following shows the number of individuals in a random sample of 300 adults who indicated they support the new tax proposal.
Political Party Support
Democrats 100
Republicans 120
Independents 80
We are interested in determining whether the opinions of the individuals of the three groups are uniformly distributed.
Refer to Exhibit 12-6. The calculated value for the test statistic equals_____ 8
Exhibit 12-6
The following shows the number of individuals in a random sample of 300 adults who indicated they support the new tax proposal.

Political Party Support
Democrats 100
Republicans 120
Independents 80
We are interested in determining whether the opinions of the individuals of the three groups are uniformly distributed.
The number of categories of outcomes per trial for a multinomial probability distribution is three or more
Exhibit 12-6
The following shows the number of individuals in a random sample of 300 adults who indicated they support the new tax proposal.
Political Party Support
Democrats 100
Republicans 120
Independents 80
We are interested in determining whether the opinions of the individuals of the three groups are uniformly distributed.
The test for goodness of fit, test of independence, and test of multiple proportions are designed for use with _ categorical data
Exhibit 12-6
The following shows the number of individuals in a random sample of 300 adults who indicated they support the new tax proposal.

Political Party Support

Democrats 100

Republicans 120

Independents 80

We are interested in determining whether the opinions of the individuals of the three groups are uniformly distributed.

Refer to Exhibit 12-6. The number of degrees of freedom associated with this problem is _____. 2
Exhibit 12-6
The following shows the number of individuals in a random sample of 300 adults who indicated they support the new tax proposal.
Political Party Support
Democrats 100
Republicans 120
Independents 80
We are interested in determining whether the opinions of the individuals of the three groups are uniformly distributed.
Refer to Exhibit 12-6. This test for goodness of fit _____. is an upper-tail test
Exhibit 12-6
The following shows the number of individuals in a random sample of 300 adults who indicated they support the new tax proposal.
Political Party Support
Democrats 100
Republicans 120

Independents 80
We are interested in determining whether the opinions of the individuals of the three groups are uniformly distributed.
Refer to Exhibit 12-6. The test statistic for goodness of fit has a chi-square distribution with k – 1 degrees of freedom provided that the expected frequencies for all categories are _____. 5 or more
Exhibit 13-2
Source of Variation Sum ofSquares Degrees of Freedom
Mean
Square
F
Between treatments
2,073.6
4
Between blocks
6,000.0
5

1,200
Error
20
288
Total
29
Refer to Exhibit 13-2. The test statistic to test the null hypothesis equals _____. 1.8
For an F distribution, the number of degrees of freedom for the numerator _____. can be larger, smaller, or equal to the number of degrees of freedom for the denominator
In a goodness of fit test, Excel’s CHISQ.DIST.RT function returns a _____. p-value
In Excel, which of the following functions is used to conduct a hypothesis test (using the p-value) for a population variance? CHISQ.DIST
In Excel, which of the following functions is used to construct a confidence interval for a population variance? CHI.INV
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 ____ at least 5
In practice, the most frequently encountered hypothesis test about a population variance is a _____. one-tailed test, with rejection region in upper tail
The 90% confidence interval estimate for a population standard deviation when a sample variance of 50 is obtained from a sample of 15 items is _____. 5.44 to 10.32
The bottler of a certain soft drink claims its equipment to be accurate and that the variance of all filled bottles is .05 or less. The null hypothesis in a test to confirm the claim would be written as ____ H0: σ2 ≤ .05
The degrees of freedom for a contingency table with 10 rows and 11 columns is _____. 90
The degrees of freedom for a contingency table with 12 rows and 12 columns is _____. 121
The degrees of freedom for a contingency table with 6 rows and 3 columns is _____. 10
The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is _____. number of rows minus 1 times number of columns minus 1
The producer of a certain bottling equipment claims that the variance of all its filled bottles is .027 or less. A sample of 30 bottles showed a standard deviation of .2. The p-value for the test is _____. between .025 and .05
The producer of a certain medicine claims that its bottling equipment is very accurate and that the standard deviation of all its filled bottles is 0.1 ounce or less. A sample of 20 bottles showed a standard deviation of .11. The test statistic to test the claim is ____ 22.99
The sampling distribution for a goodness of fit test is the _____. chi-square distribution
The sampling distribution of the ratio of independent sample variances extracted from two normal populations with equal variances is the _____. Z distribution
The sampling distribution of the ratio of two independent sample variances taken from normal populations with equal variances is a(n) _____ distribution. F
The symbol used for the variance of the sample is s2
The value of F.05 with 8 numerator and 19 denominator degrees of freedom is _____. 2.48
The χ2 value for a one-tailed (upper tail) hypothesis test at 95% confidence and a sample size of 25 is _____. 36.4151
The χ2 value for a one-tailed test (lower tail) when the level of significance is .1 and the sample size is 15 is _____. 7.78453
The χ2 values (for interval estimation) for a sample size of 10 at 95% confidence are _____. 2.70039 and 19.0228
To avoid the problem of having access to tables of the F distribution with values for the lower tail when a one-tailed test is required, let the _____ variance be the numerator of the test statistic. sample variance from the population with the smaller hypothesized
To avoid the problem of not having access to tables of F distribution with values given for the lower tail, the numerator of the test statistic should be the one with the larger sample variance
To avoid the problem of not having access to tables of the F distribution with values given for the lower tail when a two-tailed test is required, let the smaller sample variance be _____. the denominator of the test statistic
at least 1
We are interested in testing whether the variance of a population is significantly less than 1.44. The null hypothesis for this test is _____ H0: σ2 ≥ 1.44
Which of the following has a χ2 distribution? (n – 1)σ2/s2
Which of the following rejection rules is proper? Reject H0 if p-value < a
x^2 .975= 8.9066 indicates that ____ 97.5% of the chi-square values are greater than 8.9066

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BA6933 FINAL EXAM (11,12,13)

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