Question 1

If the alternate hypothesis states that $\mu$ does not equal 4,000, what is the rejection region for the hypothesis test?

Accepted Answer

A)  Both tails 
B)  Lower or left tail 
C)  Upper or right tail 
D)  Center 
A)  Both tails 
B)  Lower or left tail 
C)  Upper or right tail 
D)  Center A

Question 2

If $\alpha$ = 0.05, what is the probability of making a Type I error?

Accepted Answer

A)  0 
B)  1/20 
C)  19/20 
D)  20/20 
A)  0 
B)  1/20 
C)  19/20 
D)  20/20 B

Question 3

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?

Accepted Answer

A)  0.20 
B)  0.40 
C)  0.50 
D)  0.60 
A)  0.20 
B)  0.40 
C)  0.50 
D)  0.60 B

Question 4

A manufacturer of stereo equipment introduces new models in the fall. Retail dealers are surveyed immediately after the Christmas selling season regarding their stock on hand of each piece of equipment. It has been discovered that unless 40% of the new equipment ordered by the retailers in the fall had been sold by Christmas, immediate production cutbacks are needed. The manufacturer has found that contacting all of the dealers after Christmas by mail is frustrating as many of them never respond. This year 80 dealers were selected at random and telephoned regarding a new receiver. It was discovered that 38% of those receivers had been sold. Since 38% is less than 40%, does this mean that immediate production cutbacks are needed or can this difference of 2 percentage points be attributed to sampling? Test at the 0.05 level. Computed z = -0.37.

Accepted Answer

A)  Cut back production 
B)  Do not cut back production 
C)  Cannot determine based on information given 
A)  Cut back production 
B)  Do not cut back production 
C)  Cannot determine based on information given

Question 5

Given: null hypothesis is that the population mean is 16.9 against the alternative hypothesis that the population mean is not equal to 16.9. A random sample of 16 items results in a sample mean of 17.1 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. Determine the observed "t" value.

Accepted Answer

A)  t = 2.12 
B)  t = 1.33 
C)  t = 1.753 
D)  t = 0.33 
A)  t = 2.12 
B)  t = 1.33 
C)  t = 1.753 
D)  t = 0.33

Question 6

Given: null hypothesis is that the population mean is 16.9 against the alternative hypothesis that the population mean is not equal to 16.9. A random sample of 25 items results in a sample mean of 17.1 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. Determine the observed "t" value.

Accepted Answer

A)  t = 0.83 
B)  t = 1.83 
C)  t = 1.75 
D)  t = 0.42 
A)  t = 0.83 
B)  t = 1.83 
C)  t = 1.75 
D)  t = 0.42

Question 7

Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM 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-statistic?

Accepted Answer

A)  1.02 
B)  1.22 
C)  -1.02 
D)  -1.22 
A)  1.02 
B)  1.22 
C)  -1.02 
D)  -1.22

Question 8

A restaurant that bills its house account monthly is concerned that the average monthly bill exceeds $200 per account. A random sample of twelve accounts is selected, resulting in a sample mean of $220 and a standard deviation of $12. The t-test is to be conducted at the 5% level of significance.

Accepted Answer

A)  The critical value of t is +1.796. The calculated value of t is +5.77. 
B)  The critical value of t is -1.796. The calculated value of t is -5.77. 
C)  The critical value of t is +2.201. The calculated value of t is +5.77. 
D)  The critical value of t is +2.201. The calculated value of t is +1.40. 
E)  The critical value of t is +2.201. The calculated value of t is -5.77. 
A)  The critical value of t is +1.796. The calculated value of t is +5.77. 
B)  The critical value of t is -1.796. The calculated value of t is -5.77. 
C)  The critical value of t is +2.201. The calculated value of t is +5.77. 
D)  The critical value of t is +2.201. The calculated value of t is +1.40. 
E)  The critical value of t is +2.201. The calculated value of t is -5.77.

Question 9

The Jamestown Steel Company manufactures and assembles desks and other office equipment at several plants. The weekly production of the Model A325 desk follows a normal probability distribution, with a mean of 200 and a standard deviation of 16. Recently, due to market expansion, new production methods have been introduced and new employees hired. The vice president of manufacturing would like to investigate whether there has been an increase in the weekly production of the Model A325 desk. The mean number of desks produced last year (50 weeks, because the plant was shut down two weeks for vacation) is 203.5. Is the mean number of desks increased from 200? Test using the.10 significance level.

Accepted Answer

A)  Reject the null hypothesis; there is sufficient evidence to indicate an increase in the weekly production. 
B)  Unable to reject the null hypothesis; there is sufficient evidence to indicate a change in weekly production. 
C)  Unable to reject the null hypothesis; there is insufficient evidence to indicate an increase in weekly production. 
D)  Reject the null hypothesis; there is insufficient evidence to indicate a change in the weekly production. 
A)  Reject the null hypothesis; there is sufficient evidence to indicate an increase in the weekly production. 
B)  Unable to reject the null hypothesis; there is sufficient evidence to indicate a change in weekly production. 
C)  Unable to reject the null hypothesis; there is insufficient evidence to indicate an increase in weekly production. 
D)  Reject the null hypothesis; there is insufficient evidence to indicate a change in the weekly production.

Question 10

It is claimed that in a bushel of peaches less than ten percent are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the sample proportion?

Accepted Answer

A)  0.10 
B)  0.125 
C)  40 
D)  0.40 
A)  0.10 
B)  0.125 
C)  40 
D)  0.40

Question 11

A nationwide survey of college students was conducted and found that students spend two hours per class hour studying. A professor at your school wants to determine whether the time students spend at your school is significantly different from the two hours. A random sample of fifteen statistics students is carried out and the findings indicate an average of 1.75 hours with a standard deviation of 0.24 hours.

Accepted Answer

A)  H0 is $\mu$ $\neq$  2. H1 is $\mu$ = 2. 
B)  H0 is $\mu$ = 2. H1 is  $\mu$ $\neq$ 2. 
C)  H0 is $\mu$ = 2. H1 is $\mu$ > 2. 
D)  H0 is $\mu$ = 2. H1 is $\mu$  2. 
A)  H0 is $\mu$ $\neq$  2. H1 is $\mu$ = 2. 
B)  H0 is $\mu$ = 2. H1 is  $\mu$ $\neq$ 2. 
C)  H0 is $\mu$ = 2. H1 is $\mu$ > 2. 
D)  H0 is $\mu$ = 2. H1 is $\mu$  2.

Question 12

The average cost of tuition, room and board at community colleges is reported to be $11,500 per year, but a financial administrator believes that the average cost is higher. A study conducted using 150 community colleges showed that the average cost per year is $12,000 with a standard deviation of $1,200. Let $\alpha$ = 0.05. What are the null and alternative hypotheses for this study?

Accepted Answer

A) Null: $\mu$ $\le$ $12,000; alternative: $\mu$ > $12,000 B) Null: $\mu$ $\le$ $12,000; alternative: $\mu$ $11,500 D) Null: $\mu$ $\le$ $11,500; alternative: $\mu$ < $11,500 A) Null: $\mu$ $\le$ $12,000; alternative: $\mu$ > $12,000 B) Null: $\mu$ $\le$ $12,000; alternative: $\mu$ $11,500 D) Null: $\mu$ $\le$ $11,500; alternative: $\mu$ < $11,500

Question 13

The mean weight of newborn infants at a community hospital is said to be 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. Does this sample support the original claim? The null hypothesis is:

Accepted Answer

A)  $\mu$ = 6.6 
B)  $\mu$ $\neq$ 6.6 
C)  $\mu$ $\ge$ 6.6 
D)  $\mu$ > 7.6 
E)  $\mu$ $\neq$ 7.6 
A)  $\mu$ = 6.6 
B)  $\mu$ $\neq$ 6.6 
C)  $\mu$ $\ge$ 6.6 
D)  $\mu$ > 7.6 
E)  $\mu$ $\neq$ 7.6

Question 14

The mean length of a small counter balance bar is 43 millimeters. There is concern that the adjustments of the machine producing the bars have changed. Test the claim at the 0.02 level that there has been no change in the mean length. The alternate hypothesis is that there has been a change. Twelve bars (n = 12) were selected at random and their lengths recorded. The lengths are (in millimeters) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43 and 42. The mean of the sample is 41.5 and the standard deviation 1.784. Computed t = -2.913. Has there been a statistically significant change in the mean length of the bars?

Accepted Answer

A)  Yes, because the computed t lies in the area beyond the critical. 
B)  No, because the information given is not complete. 
C)  No, because the computed t lies in the area to the right of -2.718. 
A)  Yes, because the computed t lies in the area beyond the critical. 
B)  No, because the information given is not complete. 
C)  No, because the computed t lies in the area to the right of -2.718.

Question 15

The mean weight of newborn infants at a community hospital is said to be 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What are the degrees of freedom associated with this claim?

Accepted Answer

A)  7 
B)  8 
C)  6 
D)  6.6 
E)  7.6 
A)  7 
B)  8 
C)  6 
D)  6.6 
E)  7.6

Question 16

i. For a one-tailed test using the 0.05 level of significance, the critical value for the z test is 1.645, but for t it is 1.96. ii. For a one-tailed test using the 0.01 level of significance, the critical value for the z-test is 1.645, but for t it is 1.96.
iii. For a two-tailed test using the 0.05 level of significance the critical value for the z-test is 1.96 and it is the same for the t-test.

Accepted Answer

A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) is a correct statement but not (ii) or (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements. 
A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) is a correct statement but not (ii) or (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements.

Question 17

i. If the null hypothesis is $\mu$ $\ge$ 200 and the alternate hypothesis states that $\mu$ is less than 200, then, a two-tail test is being conducted. ii. For a one-tailed test of hypothesis, the area of rejection is only in one tail of the curve.
iii. As the sample size increases, the curve of the t-distribution approaches the standard normal distribution

Accepted Answer

A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) is a correct statement but not (ii) or (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements. 
A)  (i), (ii), and (iii) are all correct statements. 
B)  (i) is a correct statement but not (ii) or (iii). 
C)  (i) and (iii) are correct statements but not (ii). 
D)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements.

Question 18

It is claimed that in a bushel of peaches less than ten percent are defective. A sample of 400 peaches is examined and 50 are found to be defective. If $\alpha$ = 0.025, what will be the decision?

Accepted Answer

A)  Fail to reject the null and conclude the defects are not greater than 10% 
B)  Reject the null and conclude the defects are not greater than 10% 
C)  Reject the null and conclude the defects are greater than 10% 
D)  Fail to reject the null and conclude the defects are not less than 10% 
A)  Fail to reject the null and conclude the defects are not greater than 10% 
B)  Reject the null and conclude the defects are not greater than 10% 
C)  Reject the null and conclude the defects are greater than 10% 
D)  Fail to reject the null and conclude the defects are not less than 10%

Question 19

If the 1% level of significance is used and the computed value of z is +6.00, what is our decision?

Accepted Answer

A)  Do not reject H0 
B)  Reject H0 
C)  Reject H1 
A)  Do not reject H0 
B)  Reject H0 
C)  Reject H1

Question 20

The mean weight of newborn infants at a community hospital is said to be 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. Does this sample support the original claim? What is the decision for a significant increase in the average birthrate at a 5% level of significance?

Accepted Answer

A)  Fail to reject the null hypothesis and conclude the mean is 6.6 lb. 
B)  Reject the null hypothesis and conclude the mean is lower than 6.6 lb. 
C)  Reject the null hypothesis and conclude the mean is greater than 6.6 lb. 
D)  Cannot calculate because population standard deviation is unknown. 
A)  Fail to reject the null hypothesis and conclude the mean is 6.6 lb. 
B)  Reject the null hypothesis and conclude the mean is lower than 6.6 lb. 
C)  Reject the null hypothesis and conclude the mean is greater than 6.6 lb. 
D)  Cannot calculate because population standard deviation is unknown.

If the alternate hypothesis states that $\mu$ does not equal 4,000, what is the rejection region for the hypothesis test?

If $\alpha$ = 0.05, what is the probability of making a Type I error?

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?

Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM 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-statistic?

A restaurant that bills its house account monthly is concerned that the average monthly bill exceeds $200 per account. A random sample of twelve accounts is selected, resulting in a sample mean of $220 and a standard deviation of $12. The t-test is to be conducted at the 5% level of significance.

It is claimed that in a bushel of peaches less than ten percent are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the sample proportion?

The mean weight of newborn infants at a community hospital is said to be 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. Does this sample support the original claim? The null hypothesis is:

The mean weight of newborn infants at a community hospital is said to be 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What are the degrees of freedom associated with this claim?

It is claimed that in a bushel of peaches less than ten percent are defective. A sample of 400 peaches is examined and 50 are found to be defective. If $\alpha$ = 0.025, what will be the decision?

If the 1% level of significance is used and the computed value of z is +6.00, what is our decision?

What Is Statistics

Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation

Describing Data: Numerical Measures

A Survey of Probability Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Methods and the Central Limit Theorem

Estimation and Confidence Intervals

Two-Sample Tests of Hypothesis

Analysis of Variance

Linear Regression and Correlation

Multiple Regression and Correlation Analysis

Chi-Square Applications

Index Numbers

Time Series and Forecasting

An Introduction to Decision Theory

Filters

Exam 9: One-Sample Tests of Hypothesis

If the alternate hypothesis states that μ\muμ does not equal 4,000, what is the rejection region for the hypothesis test?

If α\alphaα = 0.05, what is the probability of making a Type I error?

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?

Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM 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-statistic?

A restaurant that bills its house account monthly is concerned that the average monthly bill exceeds $200 per account. A random sample of twelve accounts is selected, resulting in a sample mean of $220 and a standard deviation of $12. The t-test is to be conducted at the 5% level of significance.

It is claimed that in a bushel of peaches less than ten percent are defective. A sample of 400 peaches is examined and 50 are found to be defective. What is the sample proportion?

The mean weight of newborn infants at a community hospital is said to be 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. Does this sample support the original claim? The null hypothesis is:

The mean weight of newborn infants at a community hospital is said to be 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What are the degrees of freedom associated with this claim?

It is claimed that in a bushel of peaches less than ten percent are defective. A sample of 400 peaches is examined and 50 are found to be defective. If α\alphaα = 0.025, what will be the decision?

If the 1% level of significance is used and the computed value of z is +6.00, what is our decision?

What Is Statistics

Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation

Describing Data: Numerical Measures

A Survey of Probability Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Methods and the Central Limit Theorem

Estimation and Confidence Intervals

Two-Sample Tests of Hypothesis

Analysis of Variance

Linear Regression and Correlation

Multiple Regression and Correlation Analysis

Chi-Square Applications

Index Numbers

Time Series and Forecasting

An Introduction to Decision Theory

Filters

If the alternate hypothesis states that $\mu$ does not equal 4,000, what is the rejection region for the hypothesis test?

If $\alpha$ = 0.05, what is the probability of making a Type I error?

It is claimed that in a bushel of peaches less than ten percent are defective. A sample of 400 peaches is examined and 50 are found to be defective. If $\alpha$ = 0.025, what will be the decision?