Question 1

Provide an appropriate response.
-The mean utility bill in one city during the summer was less than $93. Write the null and alternative hypotheses.

Accepted Answer

The answer of Provide an appropriate response.
-The mean utility bill...

Question 2

Test Hypotheses about a Population Mean with Unknown
-A local hardware store claims that the mean waiting time in line is less than $3.5$ minutes. A random sample of 20 customers has a mean of $3.7$ minutes with a standard deviation of $0.8$ minute. If $\alpha = 0.05$, test the store's claim using P-values.

Accepted Answer

Standardized test statistic @#LAT-DLM&; Therefore,

Question 3

Test Hypotheses about a Population Proportion
-A Type II error is an error that

Accepted Answer

A)  fails to reject $\mathrm { H } _ { 0 }$, given that $\mathrm { H } _ { 1 }$ is true. 
B)  rejects $\mathrm { H } _ { 0 }$, given that $\mathrm { H } _ { 1 }$ is false. 
C)  fails to reject $\mathrm { H } _ { 0 }$, given that $\mathrm { H } _ { 1 }$ is false. 
D)  rejects $\mathrm { H } _ { 0 }$, given that $\mathrm { H } _ { 1 }$ is true. 
A)  fails to reject $\mathrm { H } _ { 0 }$, given that $\mathrm { H } _ { 1 }$ is true. 
B)  rejects $\mathrm { H } _ { 0 }$, given that $\mathrm { H } _ { 1 }$ is false. 
C)  fails to reject $\mathrm { H } _ { 0 }$, given that $\mathrm { H } _ { 1 }$ is false. 
D)  rejects $\mathrm { H } _ { 0 }$, given that $\mathrm { H } _ { 1 }$ is true.

Question 4

Test Hypotheses about a Population Proportion
-The commute times (in minutes) of 20 randomly selected adult males are listed below. Test the claim that the variance is less than $6.25$. Use $\alpha = 0.05$. Assume the population is normally distributed.
$\begin{array} { l l l l l l l l l l } 70 & 72 & 71 & 70 & 69 & 73 & 69 & 68 & 70 & 71 \end{array}$
$\begin{array} { l l l l l l l l l l } 67 & 71 & 70 & 74 & 69 & 68 & 71 & 71 & 71 & 72 \end{array}$

Accepted Answer

critical value @#LAT-DLM&; standardized

Question 5

Test Hypotheses about a Population Proportion
-A new gun-like apparatus has been devised to replace the needle in administering vaccines. The apparatus, which is connected to a large supply of vaccine, can be set to inject different amounts of the serum, but the variance in the amount of serum injected to a given person must not be greater than $0.07$ to ensure proper inoculation. A random sample of 36 injections was measured. Suppose the $\mathrm { P }$-value for the test is $\mathrm { p } = 0.0024$. State the proper conclusion using $\alpha = 0.01$.

Accepted Answer

Since @#LAT-DLM& can be rejected. There

Question 6

Test Hypotheses about a Population Proportion
-$$\text { Test the claim that } \sigma ^ { 2 } \neq 54.4 \text { if } \mathrm { n } = 10 , \mathrm {~s} ^ { 2 } = 60 \text {, and } \alpha = 0.01 \text {. Assume that the population is normally distributed. }$$

Accepted Answer

critical values @#LAT-DLM& and @#LAT-DLM&; standar

Question 7

State Conclusions to Hypothesis Tests
-The mean monthly gasoline bill for one household is greater than $\$ 130$. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

Accepted Answer

A)  There is not sufficient evidence to support the claim $\mu > \$ 130$. 
B)  There is sufficient evidence to reject the claim $\mu > \$ 130$. 
C)  There is not sufficient evidence to reject the claim $\mu > \$ 130$. 
D)  There is sufficient evidence to support the claim $\mu > \$ 130$. 
A)  There is not sufficient evidence to support the claim $\mu > \$ 130$. 
B)  There is sufficient evidence to reject the claim $\mu > \$ 130$. 
C)  There is not sufficient evidence to reject the claim $\mu > \$ 130$. 
D)  There is sufficient evidence to support the claim $\mu > \$ 130$.

Question 8

Test Hypotheses about a Population Proportion
-Test the claim that $\sigma ^ { 2 } > 7.6$ if $\mathrm { n } = 18 , \mathrm {~s} ^ { 2 } = 10.8$, and $\alpha = 0.01$. Assume that the population is normally distributed.

Accepted Answer

critical value @#LAT-DLM&; standardized

Question 9

Test Hypotheses about a Population Proportion
-The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion exceeds $25 \%$, then the lab will scale back a proposed enlargement of its facilities. Suppose 300 business students were randomly sampled and 75 have PC's at home. What assumptions are necessary for this test to be satisfied?

Accepted Answer

A)  No assumptions are necessary. 
B)  The sample variance equals the population variance. 
C)  The population has approximately normal distribution. 
D)  The sample mean equals the population mean. 
A)  No assumptions are necessary. 
B)  The sample variance equals the population variance. 
C)  The population has approximately normal distribution. 
D)  The sample mean equals the population mean.

Question 10

Test Hypotheses about a Population Mean with Known Using Confidence Intervals
-A group of 40 homeowners showed that their average monthly gasoline bill was $\$ 192$ with a standard deviation of $\$ 8$. According to a national consumer group, their mean bill should be $\mu = \$ 188$. Test this hypothesis by constructing a $95 \%$ confidence interval for the population mean.

Accepted Answer

The answer of Test Hypotheses about a Population Mean with...

Question 11

Provide an appropriate response.
-The _____hypothesis contains the " $=$ " sign.

Accepted Answer

A)  null 
B)  alternative 
C)  explanatory 
D)  conditional 
A)  null 
B)  alternative 
C)  explanatory 
D)  conditional

Question 12

Explain Type I and Type II Errors
-What is the probability associated with not making a Type II error?

Accepted Answer

A)  $( 1 - \beta )$ 
B)  $\alpha$ 
C)  $\beta$ 
D)  $( 1 - \alpha )$ 
A)  $( 1 - \beta )$ 
B)  $\alpha$ 
C)  $\beta$ 
D)  $( 1 - \alpha )$

Question 13

Test Hypotheses about a Population Proportion
-It is desired to test $\mathrm { H } _ { 0 } : \mu = 8$ against $\mathrm { H } _ { 1 } : \mu \neq 8$ using $\alpha = 0.05$. The population in question is uniformly distributed with a standard deviation of 1.0. A random sample of 100 will be drawn from this population. If $\mu$ is really equal to $7.9$, what is the value of $\beta$ associated with this test?

Accepted Answer

A)  $0.1700$ 
B)  $0.8300$ 
C)  $0.3300$ 
D)  $0.0850$ 
A)  $0.1700$ 
B)  $0.8300$ 
C)  $0.3300$ 
D)  $0.0850$

Question 14

State Conclusions to Hypothesis Tests
-The mean age of professors at a university is greater than $53.7$ years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

Accepted Answer

A)  There is sufficient evidence to support the claim $\mu > 53.7$. 
B)  There is sufficient evidence to reject the claim $\mu > 53.7$. 
C)  There is not sufficient evidence to reject the claim $\mu > 53.7$. 
D)  There is not sufficient evidence to support the claim $\mu > 53.7$. 
A)  There is sufficient evidence to support the claim $\mu > 53.7$. 
B)  There is sufficient evidence to reject the claim $\mu > 53.7$. 
C)  There is not sufficient evidence to reject the claim $\mu > 53.7$. 
D)  There is not sufficient evidence to support the claim $\mu > 53.7$.

Question 15

Test Hypotheses about a Population Proportion
-A survey claims that 9 out of 10 doctors (i.e., $90 \%$ ) recommend brand $Z$ for their patients who have children. To test this claim against the alternative that the actual proportion of doctors who recommend brand $Z$ is less than $90 \%$, a random sample of 100 doctors results in 85 who indicate that they recommend brand $Z$. The test statistic in this problem is approximately:

Accepted Answer

A)  $- 1.67$ 
B)  $1.67$ 
C)  $- 1.17$ 
D)  $- 1.33$ 
A)  $- 1.67$ 
B)  $1.67$ 
C)  $- 1.17$ 
D)  $- 1.33$

Question 16

Test Hypotheses about a Population Proportion
-Increasing numbers of businesses are offering child-care benefits for their workers. However, one union claims that more than $85 \%$ of firms in the manufacturing sector still do not offer any child-care benefits to their workers. A random sample of 460 manufacturing firms is selected and asked if they offer child-care benefits. Suppose the $\mathrm { P }$-value for this test was reported to be $\mathrm { p } = 0.1070$. State the conclusion of interest to the union. Use $\alpha = 0.10$.

Accepted Answer

At @#LAT-DLM&-value @#LAT-DLM&, so @#LAT-DLM& cannot be reje

Question 17

Test Hypotheses about a Population Mean with Known Using the Classical Approach
-$$\text { Test the claim that } \mu < 29 \text {, given that } \alpha = 0.01 \text { and the sample statistics are } n = 40 , \bar { x } = 30.8 \text {, and } \sigma = 4.3 \text {. }$$

Accepted Answer

The answer of Test Hypotheses about a Population Mean with...

Question 18

Distinguish between Statistical Significance and Practical Significance
-True or False: Results that are statistically significant are always practically significant.

Accepted Answer

A)  False 
B)  True 
A)  False 
B)  True

Question 19

Test Hypotheses about a Population Mean with Known Using P-values
-A bank claims that the mean waiting time in line is less than $3.9$ minutes. A random sample of 60 customers has a mean of $3.8$ minutes with a standard deviation of $0.6$ minute. If $\alpha = 0.05$, test the bank's claim using $\mathrm { P }$-values.

Accepted Answer

@#LAT-DLM&-value @#LAT-DLM&, fail to reject @#LAT-DLM&; Ther

Question 20

Test Hypotheses about a Population Proportion
-Compute the standardized test statistic, $\chi ^ { 2 }$, to test the claim $\sigma ^ { 2 } < 16.8$ if $n = 28$, $s ^ { 2 } = 10.5$, and $\alpha = 0.10$.

Accepted Answer

A)  $16.875$ 
B)  $14.324$ 
C)  $18.132$ 
D)  $21.478$ 
A)  $16.875$ 
B)  $14.324$ 
C)  $18.132$ 
D)  $21.478$

Provide an appropriate response. -The mean utility bill in one city during the summer was less than $93. Write the null and alternative hypotheses.

Test Hypotheses about a Population Proportion -A Type II error is an error that

Test Hypotheses about a Population Proportion - $\text { Test the claim that } \sigma ^ { 2 } \neq 54.4 \text { if } \mathrm { n } = 10 , \mathrm {~s} ^ { 2 } = 60 \text {, and } \alpha = 0.01 \text {. Assume that the population is normally distributed. }$

State Conclusions to Hypothesis Tests -The mean monthly gasoline bill for one household is greater than $\$ 130$ . If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

Test Hypotheses about a Population Proportion -Test the claim that $\sigma ^ { 2 } > 7.6$ if $\mathrm { n } = 18 , \mathrm {~s} ^ { 2 } = 10.8$ , and $\alpha = 0.01$ . Assume that the population is normally distributed.

Provide an appropriate response. -The _____hypothesis contains the " $=$ " sign.

Explain Type I and Type II Errors -What is the probability associated with not making a Type II error?

State Conclusions to Hypothesis Tests -The mean age of professors at a university is greater than $53.7$ years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

Test Hypotheses about a Population Mean with Known Using the Classical Approach - $\text { Test the claim that } \mu < 29 \text {, given that } \alpha = 0.01 \text { and the sample statistics are } n = 40 , \bar { x } = 30.8 \text {, and } \sigma = 4.3 \text {. }$

Distinguish between Statistical Significance and Practical Significance -True or False: Results that are statistically significant are always practically significant.

Test Hypotheses about a Population Proportion -Compute the standardized test statistic, $\chi ^ { 2 }$ , to test the claim $\sigma ^ { 2 } < 16.8$ if $n = 28$ , $s ^ { 2 } = 10.5$ , and $\alpha = 0.10$ .

Data Collection

Creating Tables and Drawing Pictures of Data

Numerically Summarizing Data

Describing the Relation Between Two Variables

Probability

Discrete Probability Distributions

The Normal Probability Distribution

Sampling Distributions

Estimating the Value of a Parameter Using Confidence Intervals

Inference on Two Samples

Inference on Categorical Data

Comparing Three or More Means

Inference of the Least-Squares Regression Model and Multiple Regression

Nonparametric Statistics

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Exam 10: Hypothesis Tests Regarding a Parameter