Question 1

In hypothesis testing, if the null hypothesis has been rejected when the alternative hypothesis has been true,

Accepted Answer

A)  a Type I error has been committed. 
B)  a Type II error has been committed. 
C)  either a Type I or a Type II error has been committed. 
D)  the correct decision has been made. 
A)  a Type I error has been committed. 
B)  a Type II error has been committed. 
C)  either a Type I or a Type II error has been committed. 
D)  the correct decision has been made. D

Question 2

A juice drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of drink on an average.A random sample of 49 bottles is selected, and the contents are measured.The sample yielded a mean content of 11.88 ounces with a standard deviation of .35 ounces.
a.
Formulate the hypotheses for a test to determine if the machine is in perfect adjustment.
b.
Compute the value of the test statistic.
c.
Compute the p-value and give your conclusion regarding the adjustment of the machine.Let α = .05.

Accepted Answer

a. H₀: μ = 12 ounces H_a: μ ≠ 12 ounces b. t = -2.4 c. p-value is between .02 and .05; therefore, reject H₀; the machine needs to be adjusted.

Question 3

A school's newspaper reported that the proportion of students majoring in business is at least 30%.You plan on taking a sample to test the newspaper's claim.The correct set of hypotheses is

Accepted Answer

A)  H0: p a: p   .30. 
B)  H0: p   .30 Ha: p > .30. 
C)  H0: p   .30 Ha: p 0: p > .30 Ha: p   .30. 
A)  H0: p a: p   .30. 
B)  H0: p   .30 Ha: p > .30. 
C)  H0: p   .30 Ha: p 0: p > .30 Ha: p   .30. C

Question 4

In a two-tailed hypothesis test, the area in each tail corresponding to the critical values is equal to

Accepted Answer

A)  ​α. 
B)  ​α/2. 
C)  ​2α. 
D)  ​1 - α/2. 
A)  ​α. 
B)  ​α/2. 
C)  ​2α. 
D)  ​1 - α/2.

Question 5

The level of significance, in hypothesis testing, is the probability of _____ null hypothesis.

Accepted Answer

A)  accepting a true 
B)  accepting a false 
C)  rejecting a true 
D)  rejecting a false 
A)  accepting a true 
B)  accepting a false 
C)  rejecting a true 
D)  rejecting a false

Question 6

As a general guideline, the research hypothesis should be stated as the​

Accepted Answer

A)  ​null hypothesis. 
B)  ​alternative hypothesis. 
C)  ​tentative hypothesis. 
D)  ​hypothesis the researcher wants to disprove. 
A)  ​null hypothesis. 
B)  ​alternative hypothesis. 
C)  ​tentative hypothesis. 
D)  ​hypothesis the researcher wants to disprove.

Question 7

When the area corresponding to the critical value is in the lower tail of the sampling distribution, the p-value is the area under the curve​

Accepted Answer

A)  ​less than or equal to the critical value. 
B)  ​less than or equal to the test statistic. 
C)  ​greater than or equal to the critical value. 
D)  ​greater than or equal to the test statistic. 
A)  ​less than or equal to the critical value. 
B)  ​less than or equal to the test statistic. 
C)  ​greater than or equal to the critical value. 
D)  ​greater than or equal to the test statistic.

Question 8

Last year, a soft drink manufacturer had 21% of the market.In order to increase their portion of the market, the manufacturer has introduced a new flavor in their soft drinks.A sample of 400 individuals participated in the taste test and 100 indicated that they like the taste.We are interested in determining if more than 21% of the population will like the new soft drink.
a.
Set up the null and the alternative hypotheses.
b.
Determine the test statistic.
c.
Determine the p-value.
d.
Using α = .05, test to determine if more than 21% of the population will like the new soft drink.

Accepted Answer

a. H₀: p @#IMG-DLM& .21 H_a: p > .21 b. T

Question 9

You are given the following information obtained from a random sample of 4 observations.   ​
You want to determine whether or not the mean of the population from which this sample was taken is significantly different from 48.(Assume the population is normally distributed.) 
a.
State the null and the alternative hypotheses.
b.
Determine the test statistic.
c.
Determine the p-value; and at the 5% level of significance, test to determine whether or not the mean of the population is significantly different from 48.

Accepted Answer

a. H₀: μ = 48 H_a: μ ≠ 48 b. t

Question 10

The critical value of t for a two-tailed test with 10 degrees of freedom using α = .05 is

Accepted Answer

A)  1.833. 
B)  1.812. 
C)  2.262. 
D)  2.228. 
A)  1.833. 
B)  1.812. 
C)  2.262. 
D)  2.228.

Question 11

If the null hypothesis is rejected at the .05 level of significance, it will _____ be rejected at the .10 level of significance.

Accepted Answer

A)  always not 
B)  always 
C)  sometimes 
D)  sometimes not 
A)  always not 
B)  always 
C)  sometimes 
D)  sometimes not

Question 12

For a one-tailed (upper tail) hypothesis test with a sample size of 26 and a .01 level of significance, the critical value of the test statistic t is

Accepted Answer

A)  2.797. 
B)  2.787. 
C)  2.485. 
D)  2.479. 
A)  2.797. 
B)  2.787. 
C)  2.485. 
D)  2.479.

Question 13

Ahmadi, Inc., has been manufacturing small automobiles that have averaged 50 miles per gallon of gasoline in highway driving.The company has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 50 miles per gallon in highway driving.An independent testing service road-tested 64 of the automobiles.The sample showed an average of 51.5 miles per gallon with a standard deviation of 4 miles per gallon.
a.
Formulate the hypotheses to determine whether or not the manufacturer's advertising campaign is legitimate.
b.
Compute the test statistic.
c.
What is the p-value associated with the sample results and what is your conclusion? Let α = .05.

Accepted Answer

a. H₀: μ @#IMG-DLM& 50 miles per gallo

Question 14

The p-value is a probability that measures the support (or lack of support) for

Accepted Answer

A)  the null hypothesis. 
B)  the alternative hypothesis. 
C)  either the null or the alternative hypothesis. 
D)  neither the null nor the alternative hypothesis. 
A)  the null hypothesis. 
B)  the alternative hypothesis. 
C)  either the null or the alternative hypothesis. 
D)  neither the null nor the alternative hypothesis.

Question 15

Read the t statistic from the t distribution table and circle the correct answer.For a one-tailed test (lower tail) with 22 degrees of freedom at α = .05, the value of t =

Accepted Answer

A)  1.717. 
B)  1.721. 
C)  -1.717. 
D)  -1.721. 
A)  1.717. 
B)  1.721. 
C)  -1.717. 
D)  -1.721.

Question 16

An official of a large national union claims that the fraction of women in the union is not significantly different from one-half.Using the critical value approach and the sample information reported below, carry out a test of this statement.Let α = .05.

Accepted Answer

H₀: p = .5 H_a: p ≠ .5

Question 17

An automobile manufacturer stated that it will be willing to mass produce electric-powered cars if more than 30% of potential buyers indicate they will purchase the newly designed electric cars.In a sample of 500 potential buyers, 160 indicated that they would buy such a product.
a.
State the hypotheses for this problem.
b.
Compute the standard error of   . 
c.
Compute the test statistic.
d.
At the 5% level of significance, what is your conclusion? Should the manufacturer produce the new electric-powered car?

Accepted Answer

a. H₀: p @#IMG-DLM& .3 H_a: p > .3 b. .02

Question 18

A lathe is set to cut bars of steel into lengths of 6 centimeters.The lathe is considered to be in perfect adjustment if the average length of the bars it cuts is 6 centimeters.A sample of 121 bars is selected randomly and measured.It is determined that the average length of the bars in the sample is 6.08 centimeters with a standard deviation of .44 centimeters.
a.
Formulate the hypotheses to determine whether or not the lathe is in perfect adjustment.
b.
Compute the test statistic.
c.
Using the p-value approach, what is your conclusion? Let α = .05.

Accepted Answer

a. H₀: μ = 6 centimeters H_a: μ

Question 19

A sample of 1400 items had 280 defective items.For the following hypothesis test, ​
H0: p ≤ .20
Ha: p > .20
​
The test statistic is

Accepted Answer

A)  .28. 
B)  .14. 
C)  .20. 
D)  zero. 
A)  .28. 
B)  .14. 
C)  .20. 
D)  zero.

Question 20

Consider the following hypothesis test:
H0: p   .8
Ha: p > .8
A sample of 400 provided a sample proportion of .853. 
a.
Determine the standard error of the proportion.
b.
Compute the value of the test statistic.
c.
Determine the p-value; and at a 5% level, test the above hypotheses.

Accepted Answer

​
a.
.02
b

In hypothesis testing, if the null hypothesis has been rejected when the alternative hypothesis has been true,

A school's newspaper reported that the proportion of students majoring in business is at least 30%.You plan on taking a sample to test the newspaper's claim.The correct set of hypotheses is

In a two-tailed hypothesis test, the area in each tail corresponding to the critical values is equal to

The level of significance, in hypothesis testing, is the probability of _____ null hypothesis.

As a general guideline, the research hypothesis should be stated as the

When the area corresponding to the critical value is in the lower tail of the sampling distribution, the p-value is the area under the curve

The critical value of t for a two-tailed test with 10 degrees of freedom using α = .05 is

If the null hypothesis is rejected at the .05 level of significance, it will _____ be rejected at the .10 level of significance.

For a one-tailed (upper tail) hypothesis test with a sample size of 26 and a .01 level of significance, the critical value of the test statistic t is

The p-value is a probability that measures the support (or lack of support) for

Read the t statistic from the t distribution table and circle the correct answer.For a one-tailed test (lower tail) with 22 degrees of freedom at α = .05, the value of t =

A sample of 1400 items had 280 defective items.For the following hypothesis test, H₀: p ≤ .20 H_a: p > .20 The test statistic is

Consider the following hypothesis test: H₀: p .8 H_a: p > .8 A sample of 400 provided a sample proportion of .853. a. Determine the standard error of the proportion. b. Compute the value of the test statistic. c. Determine the p-value; and at a 5% level, test the above hypotheses.

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Inference About Means and Proportions With Two Populations

Inferences About Population Variances

Comparing Multiple Proportions, Tests of Independence and Goodness of Fit

Experimental Design and Analysis of Variance

Simple Linear Regression

Multiple Regression

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Exam 9: Hypothesis Tests

In hypothesis testing, if the null hypothesis has been rejected when the alternative hypothesis has been true,

A school's newspaper reported that the proportion of students majoring in business is at least 30%.You plan on taking a sample to test the newspaper's claim.The correct set of hypotheses is

In a two-tailed hypothesis test, the area in each tail corresponding to the critical values is equal to

The level of significance, in hypothesis testing, is the probability of _____ null hypothesis.

As a general guideline, the research hypothesis should be stated as the​

When the area corresponding to the critical value is in the lower tail of the sampling distribution, the p-value is the area under the curve​

The critical value of t for a two-tailed test with 10 degrees of freedom using α = .05 is

If the null hypothesis is rejected at the .05 level of significance, it will _____ be rejected at the .10 level of significance.

For a one-tailed (upper tail) hypothesis test with a sample size of 26 and a .01 level of significance, the critical value of the test statistic t is

The p-value is a probability that measures the support (or lack of support) for

Read the t statistic from the t distribution table and circle the correct answer.For a one-tailed test (lower tail) with 22 degrees of freedom at α = .05, the value of t =

An official of a large national union claims that the fraction of women in the union is not significantly different from one-half.Using the critical value approach and the sample information reported below, carry out a test of this statement.Let α = .05.

A sample of 1400 items had 280 defective items.For the following hypothesis test, ​ H0: p ≤ .20 Ha: p > .20 ​ The test statistic is

Consider the following hypothesis test: H0: p .8 Ha: p > .8 A sample of 400 provided a sample proportion of .853. a. Determine the standard error of the proportion. b. Compute the value of the test statistic. c. Determine the p-value; and at a 5% level, test the above hypotheses.

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Inference About Means and Proportions With Two Populations

Inferences About Population Variances

Comparing Multiple Proportions, Tests of Independence and Goodness of Fit

Experimental Design and Analysis of Variance

Simple Linear Regression

Multiple Regression

Filters

As a general guideline, the research hypothesis should be stated as the

When the area corresponding to the critical value is in the lower tail of the sampling distribution, the p-value is the area under the curve

A sample of 1400 items had 280 defective items.For the following hypothesis test, H₀: p ≤ .20 H_a: p > .20 The test statistic is

Consider the following hypothesis test: H₀: p .8 H_a: p > .8 A sample of 400 provided a sample proportion of .853. a. Determine the standard error of the proportion. b. Compute the value of the test statistic. c. Determine the p-value; and at a 5% level, test the above hypotheses.