Question 1

To conduct a test of hypothesis with a small sample, we need to be able to make the following assumption that:

Accepted Answer

A)  a larger computed value of t will be needed to reject the null hypothesis 
B)  the region of acceptance will be wider than for large samples 
C)  the confidence interval will be wider than for large samples 
D)  the population is normally distributed 
E)  None of these statements are true 
A)  a larger computed value of t will be needed to reject the null hypothesis 
B)  the region of acceptance will be wider than for large samples 
C)  the confidence interval will be wider than for large samples 
D)  the population is normally distributed 
E)  None of these statements are true

Question 2

The mean weight of newborn infants at a community hospital is 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. If α = 0.05, what is the critical t value?

Accepted Answer

A)  -2.365 
B)  ±1.96 
C)  ±2.365 
D)  ±2.15 
E)  -2.447 
A)  -2.365 
B)  ±1.96 
C)  ±2.365 
D)  ±2.15 
E)  -2.447

Question 3

A manufacturer claims that less than 1% of all his products do not meet the minimum government standards. A survey of 500 products revealed ten did not meet the standard. If the z-statistic is -1.96 and the level of significance is 0.01, what is your decision?

Accepted Answer

A)  You reject the null hypothesis. 
B)  You have insufficient evidence to reject the null hypothesis. 
C)  You accept the alternate hypothesis and agree that less than 1% meet government standards. 
D)  You should have used the t-test. 
A)  You reject the null hypothesis. 
B)  You have insufficient evidence to reject the null hypothesis. 
C)  You accept the alternate hypothesis and agree that less than 1% meet government standards. 
D)  You should have used the t-test.

Question 4

i. Two types of possible errors always exist when testing hypotheses-a Type I error, in which the null hypothesis is rejected when it should not have been rejected, and a Type II error in which the null hypothesis is not rejected when it should have been rejected.
Ii) A test statistic is a value determined from sample information collected to test the null hypothesis. 
iii. The region or area of rejection defines the location of all those values that are so large or so small that the probability of their occurrence under a true null hypothesis is rather remote.

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)  (i) and, (ii) are correct statements but not (iii). 
E)  All statements are false 
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)  (i) and, (ii) are correct statements but not (iii). 
E)  All statements are false

Question 5

The mean gross annual incomes of certified tack welders are normally distributed with the mean of $50,000 and a standard deviation of $4,000. The ship building association wishes to find out whether their tack welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000.
If the level of significance is 0.10, what is the decision rule?

Accepted Answer

A)  Do not reject the null hypothesis if computed z lies between -1.65 and +1.65; otherwise, reject it 
B)  Do not reject the null hypothesis if computed z is greater than 1.65; otherwise, reject it 
C)  Do not reject the null hypothesis if computed z lies between -1.96 and +1.96; otherwise, reject it 
D)  Reject the null hypothesis if computed z is below -1.96; otherwise, reject it 
E)  None of these statements are true 
A)  Do not reject the null hypothesis if computed z lies between -1.65 and +1.65; otherwise, reject it 
B)  Do not reject the null hypothesis if computed z is greater than 1.65; otherwise, reject it 
C)  Do not reject the null hypothesis if computed z lies between -1.96 and +1.96; otherwise, reject it 
D)  Reject the null hypothesis if computed z is below -1.96; otherwise, reject it 
E)  None of these statements are true

Question 6

One of the major U.S. tire makers wishes to review its warranty for their rainmaker tire. The warranty is for 40,000 miles. The tire company believes that the tire actually lasts more than 40,000 miles. A
Sample 49 tires revealed that the mean number of miles is 45,000 miles with a standard deviation of
15,000 miles. Test the hypothesis with a 0.05 significance level.

Accepted Answer

A) The decision rule is to reject if Z > 1.645. The calculated value of z is +2.33. B) The decision rule is to reject if Z 1.96. The calculated value of z is +2.33. D) The decision rule is to reject if Z < 1.96. The calculated value of z is +2.33. E) None of these statements is correct. A) The decision rule is to reject if Z > 1.645. The calculated value of z is +2.33. B) The decision rule is to reject if Z 1.96. The calculated value of z is +2.33. D) The decision rule is to reject if Z < 1.96. The calculated value of z is +2.33. E) None of these statements is correct.

Question 7

Given: null hypothesis is that the population mean is 16.9 against the alternative hypothesis that the population mean is not equal to 6.9. 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 
E)  None of these statements are true 
A)  t = 2.12 
B)  t = 1.33 
C)  t = 1.753 
D)  t = 0.33 
E)  None of these statements are true

Question 8

What do we call the statement that determines if the null hypothesis is rejected?

Accepted Answer

A)  Decision rule 
B)  Test statistic 
C)  Alternate hypothesis 
D)  Critical value 
E)  None of these statements are true 
A)  Decision rule 
B)  Test statistic 
C)  Alternate hypothesis 
D)  Critical value 
E)  None of these statements are true

Question 9

The dean of a business school claims that the average starting salary of its graduates is more than $50,000. It is known that the population standard deviation is $10,000. Sample data on the starting salaries of 20 randomly selected recent graduates yielded a mean of $55,000. What is the value of the sample test statistic?

Accepted Answer

A)  z = 2.24 
B)  t = 7.2 
C)  t = 5.04 
D)  t = 2.24 
E)  None of these statements are true 
A)  z = 2.24 
B)  t = 7.2 
C)  t = 5.04 
D)  t = 2.24 
E)  None of these statements are true

Question 10

The dean of a business school claims that the average starting salary of its graduates is more than $50,000. It is known that the population standard deviation is $10,000. Sample data on the starting salaries of 25 randomly selected recent graduates yielded a mean of $52,000. What is the value of the sample test statistic?

Accepted Answer

A)  z = 1.0 
B)  t = 7.2 
C)  t = 5.04 
D)  t = 1.22 
E)  None of these statements are true 
A)  z = 1.0 
B)  t = 7.2 
C)  t = 5.04 
D)  t = 1.22 
E)  None of these statements are true

Question 11

What do tests of proportions require of both np and n(1 - p)?

Accepted Answer

A)  Exceed 30 
B)  Exceed 5 
C)  Exceed 100 
D)  Be equal 
E)  None of these statements are true 
A)  Exceed 30 
B)  Exceed 5 
C)  Exceed 100 
D)  Be equal 
E)  None of these statements are true

Question 12

What do we call the statement that determines if the null hypothesis is rejected?

Accepted Answer

A)  Decision rule 
B)  Test statistic 
C)  Alternate hypothesis 
D)  Critical value 
E)  None of these statements are true 
A)  Decision rule 
B)  Test statistic 
C)  Alternate hypothesis 
D)  Critical value 
E)  None of these statements are true

Question 13

For a two-tailed test at the 0.05 significance level, what is the rejection region when n if large?

Accepted Answer

A)  Between ± 1.96 
B)  Between ± 1.65 
C)  Greater than +1.96 and less than -1.96 
D)  Greater than +1.65 and less than -1.65 
E)  None of these statements are true 
A)  Between ± 1.96 
B)  Between ± 1.65 
C)  Greater than +1.96 and less than -1.96 
D)  Greater than +1.65 and less than -1.65 
E)  None of these statements are true

Question 14

i. To prevent bias, the level of significance is selected before setting up the decision rule and sampling the population.
Ii) The fifth and final step in testing a hypothesis is taking a sample and, based on the decision rule, deciding if the null hypothesis should be rejected.
Iii) When the null hypothesis is not rejected, the conclusion is that our sample data does not allow us to reject the null hypothesis.

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)  (i) and, (ii) are correct statements but not (iii). 
E)  All statements are false 
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)  (i) and, (ii) are correct statements but not (iii). 
E)  All statements are false

Question 15

i. To prevent bias, the level of significance is selected before setting up the decision rule and sampling the population.
Ii) The level of significance is the probability that a true hypothesis is rejected.
Iii) If the critical values of the test statistic z are ±1.96, they are the dividing points between the areas of rejection and non-rejection.

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)  (i) and, (ii) are correct statements but not (iii). 
E)  (ii) and (iii) are correct statements but not (i). 
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)  (i) and, (ii) are correct statements but not (iii). 
E)  (ii) and (iii) are correct statements but not (i).

Question 16

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 
E)  None of these statements are true 
A)  0.20 
B)  0.40 
C)  0.50 
D)  0.60 
E)  None of these statements are true

Question 17

If the alternate hypothesis states that μ 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 
E)  None of these statements are true 
A)  Both tails 
B)  Lower or left tail 
C)  Upper or right tail 
D)  Center 
E)  None of these statements are true

Question 18

i. The fifth and final step in testing a hypothesis is taking a sample and, based on the decision rule, deciding if the null hypothesis should be rejected. 
ii. When the null hypothesis is not rejected, the conclusion is that our sample data does not allow us to reject the null hypothesis.
Iii) The level of significance is selected after setting up a decision rule and sampling the population.

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)  (i) and, (ii) are correct statements but not (iii). 
E)  All statements are false 
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)  (i) and, (ii) are correct statements but not (iii). 
E)  All statements are false

Question 19

Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed with a mean of 35,600 kilometres. A manufacturer of spark plugs claims that its plugs have an average life in excess of 35,600 kilometres. The fleet owner purchased 18 sets and found that the sample average life was 37,700 kilometres, the sample standard deviation was 2415 kilometres and the computed t = 3.677.

Accepted Answer

A)  Based on these findings, there is enough evidence to accept the manufacturer's claim at the 0.05 level. 
B)  Based on these findings, there is NOT enough evidence to accept the manufacturer's claim at the
0.05 level. 
C)  Based on these findings, there is enough evidence to accept the manufacturer's claim at the 0.05 level, but NOT at the 0.01 level. 
D)  Based on these findings, there is NOT enough evidence to accept the manufacturer's claim at the
0.01 level. 
E)  Based on these findings, there in NOT enough evidence to accept the manufacturer's claim at either the 0.05 or the 0.01 level. 
A)  Based on these findings, there is enough evidence to accept the manufacturer's claim at the 0.05 level. 
B)  Based on these findings, there is NOT enough evidence to accept the manufacturer's claim at the
0.05 level. 
C)  Based on these findings, there is enough evidence to accept the manufacturer's claim at the 0.05 level, but NOT at the 0.01 level. 
D)  Based on these findings, there is NOT enough evidence to accept the manufacturer's claim at the
0.01 level. 
E)  Based on these findings, there in NOT enough evidence to accept the manufacturer's claim at either the 0.05 or the 0.01 level.

Question 20

The mean gross annual incomes of certified tack welders are normally distributed with the mean of $50,000 and a standard deviation of $4,000. The ship building association wishes to find out whether their tack welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000.
Given the following megastat printout, what conclusions can be made?

Accepted Answer

A)  There is a 1.68% chance of getting these sample results if the annual income is actually $50,000. 
B)  Since the p-value is 7%, we reject the null hypothesis at a 5% level of significance. 
C)  Since the p-value is 9%, we have insufficient evidence to reject the null hypothesis at the 5% level of significance. 
D)  Since the p-value is 9%, we reject the null hypothesis at the 1% level of significance. 
E)  None of these statements are correct. 
A)  There is a 1.68% chance of getting these sample results if the annual income is actually $50,000. 
B)  Since the p-value is 7%, we reject the null hypothesis at a 5% level of significance. 
C)  Since the p-value is 9%, we have insufficient evidence to reject the null hypothesis at the 5% level of significance. 
D)  Since the p-value is 9%, we reject the null hypothesis at the 1% level of significance. 
E)  None of these statements are correct.

To conduct a test of hypothesis with a small sample, we need to be able to make the following assumption that:

The mean weight of newborn infants at a community hospital is 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. If α = 0.05, what is the critical t value?

A manufacturer claims that less than 1% of all his products do not meet the minimum government standards. A survey of 500 products revealed ten did not meet the standard. If the z-statistic is -1.96 and the level of significance is 0.01, what is your decision?

What do we call the statement that determines if the null hypothesis is rejected?

What do tests of proportions require of both np and n(1 - p)?

What do we call the statement that determines if the null hypothesis is rejected?

For a two-tailed test at the 0.05 significance level, what is the rejection region when n if large?

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?

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

What Is Statistics

Describing Data: Frequency Distributions and Graphic Presentation

Describing Data: Numerical Measures

A Survey of Probability Concepts

Discrete Probability Distributions

The Normal Probability Distribution

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 for Nominal Data

Index Numbers

Time Series and Forecasting

An Introduction to Decision Theory

Filters

Exam 9: One-Sample Tests of a Hypothesis

To conduct a test of hypothesis with a small sample, we need to be able to make the following assumption that:

The mean weight of newborn infants at a community hospital is 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. If α = 0.05, what is the critical t value?

A manufacturer claims that less than 1% of all his products do not meet the minimum government standards. A survey of 500 products revealed ten did not meet the standard. If the z-statistic is -1.96 and the level of significance is 0.01, what is your decision?

What do we call the statement that determines if the null hypothesis is rejected?

What do tests of proportions require of both np and n(1 - p)?

What do we call the statement that determines if the null hypothesis is rejected?

For a two-tailed test at the 0.05 significance level, what is the rejection region when n if large?

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?

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

What Is Statistics

Describing Data: Frequency Distributions and Graphic Presentation

Describing Data: Numerical Measures

A Survey of Probability Concepts

Discrete Probability Distributions

The Normal Probability Distribution

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 for Nominal Data

Index Numbers

Time Series and Forecasting

An Introduction to Decision Theory

Filters