Question 1

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol  (μ,p,σ) ( \mu , p , \sigma ) (μ,p,σ)   for the indicated parameter. An entomologist writes an article in a scienti journal which claims that fewer than 16 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter  p\mathrm { p }p , the true proportion of fireflies unable produce light.

Accepted Answer

A) H0:p=0.0016H _ { 0 } : p = 0.0016H0:p=0.0016 H1:p<0.0016H _ { 1 } : p < 0.0016H1:p<0.0016 B) H0:p<0.0016H _ { 0 } : p < 0.0016H0:p<0.0016 H1:p≥0.0016H _ { 1 } : p \geq 0.0016H1:p≥0.0016 C) H0:p=0.0016H _ { 0 } : p = 0.0016H0:p=0.0016 0.0016">H1:p>0.0016H _ { 1 } : p > 0.0016H1:p>0.0016 D) 0.0016">H0:p>0.0016H _ { 0 } : p > 0.0016H0:p>0.0016 H1:p≤0.0016H _ { 1 } : p \leq 0.0016H1:p≤0.0016E) C) and D) F) None of the above

Question 2

Solve the problem. For large numbers of degrees of freedom, the critical  χ2\chi ^ { 2 }χ2  values can be approximated as follows:  χ2=12(z+2k−1) 2\chi ^ { 2 } = \frac { 1 } { 2 } ( z + \sqrt { 2 k - 1 } )  ^ { 2 }χ2=21​(z+2k−1​) 2 , where  k\mathrm { k }k  is the number of degrees of freedom and  zzz  is the critical value. To find the lower critical value, the negative  zzz -value is used, to find the upper critical value, the positive  zzz -value is used. Use this approximation to estimate the critical value of  χ2\chi ^ { 2 }χ2  in a two-tailed hypothesis test with  n=104n = 104n=104  and  α=0.10\alpha = 0.10α=0.10 .

Accepted Answer

A)    χ2≈84.992\chi ^ { 2 } \approx 84.992χ2≈84.992  and  χ2≈121.646\chi ^ { 2 } \approx 121.646χ2≈121.646 
B)    χ2≈81.186\chi ^ { 2 } \approx 81.186χ2≈81.186  and  χ2≈128.520\chi ^ { 2 } \approx 128.520χ2≈128.520 
C)    χ2≈80.300\chi ^ { 2 } \approx 80.300χ2≈80.300  and  χ2≈127.406\chi ^ { 2 } \approx 127.406χ2≈127.406 
D)    χ2≈85.903\chi ^ { 2 } \approx 85.903χ2≈85.903  and  χ2≈122.735\chi ^ { 2 } \approx 122.735χ2≈122.735E) None of the above
F) A) and B)

Question 3

Find the value of the test statistic  zzz  using  z=p^−ppqnz = \frac { \hat { p } - p } { \sqrt { \frac { p q } { n } } }z=npq​​p^​−p​ .
A claim is made that the proportion of children who play sports is less than  0.50.50.5 , and the sample statistics include  n=1320n = 1320n=1320  subjects with  30%30 \%30%  saying that they play a sport.

Accepted Answer

A)    14.5314.5314.53 
B)    29.6629.6629.66 
C)    −29.66- 29.66−29.66 
D)    −14.53- 14.53−14.53E) A) and D)
F) B) and C)

Question 4

Express the original claim in symbolic form.
Claim: 20% of adults smoke

Accepted Answer

A)    p≠0.2p 
eq 0.2p=0.2 
B)    p=0.2p = 0.2p=0.2 
C)    μ≠0.2\mu 
eq 0.2μ=0.2 
D)    μ=0.2\mu = 0.2μ=0.2E) B) and C)
F) A) and D)

Question 5

Find the value of the test statistic  zzz  using  z=p^−ppqnz = \frac { \hat { p } - p } { \sqrt { \frac { p q } { n } } }z=npq​​p^​−p​ . The claim is that the proportion of
drowning deaths of children attributable to beaches is more than  0.250.250.25 , and the sample statistics include  n=696\mathrm { n } = 696n=696  drowning deaths of children with  30%30 \%30%  of them attributable to beaches.

Accepted Answer

A)    2.882.882.88 
B)    3.053.053.05 
C)    −3.05- 3.05−3.05 
D)    −2.88- 2.88−2.88  . E) B) and C)
F) A) and B)

Question 6

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol  (μ,p,σ) ( \mu , p , \sigma ) (μ,p,σ)   for the indicated parameter. A psychologist claims that more than  5.85.85.8  percen of the population suffers from professional problems due to extreme shyness. Use  ppp , the true percentage of the population that suffers from extreme shyness.

Accepted Answer

A) H0:p=5.8%H _ { 0 } : p = 5.8 \%H0:p=5.8% H1:p<5.8%H _ { 1 } : p < 5.8 \%H1:p<5.8% B) H0:p=5.8%H _ { 0 } : p = 5.8 \%H0:p=5.8% H1:p≤5.8%H _ { 1 } : p \leq 5.8 \%H1:p≤5.8% C) H0:p=5.8%H _ { 0 } : p = 5.8 \%H0:p=5.8% 5.8 \%">H1:p>5.8%H _ { 1 } : p > 5.8 \%H1:p>5.8% D) H0:p<5.8%H _ { 0 } : p < 5.8 \%H0:p<5.8% H1:p≥5.8%H _ { 1 } : p \geq 5.8 \%H1:p≥5.8%E) A) and C) F) B) and C)

Question 7

A hypothesis test is performed to test the claim that a population proportion is greater than 0.7. Find the probability of a type II error,  β\betaβ  , given that the true value of the population proportion
Is 0.72. The sample size is 50 and the significance level is 0.05.

Accepted Answer

A)   0.4129
B)   0.5754
C)   0.7123
D)   0.9706 E) A) and C)
F) A) and D)

Question 8

Suppose we want to test the claim that less than  1/21 / 21/2  of Americans are in favor of raising the voting age to 21. Is the hypothesis test left-tailed, right-tailed, or two-tailed?

Accepted Answer

A)   Left-tailed
B)   Right-tailed
C)   Two-tailed114 D) All of the above
E) B) and C)

Question 9

The p-value is the probability of getting a test statistic at least as extreme as the one representing the sample data, assuming that ______________________________.

Accepted Answer

A)   the null hypothesis is true
B)   the null hypothesis is false
C)   the alternative hypothesis is true
D)   the alternative hypothesis is falseE) A) and B)
F) C) and D)

Question 10

An oil change shop claims that they will change your oil in under 15 minutes. To test this
claim, a consumer advocacy group takes a simple random sample of 10 customers and records
the number of minutes it took to complete oil changes for these customers. Assume that oil
change times are normally distributed. $$\begin{array} { | c | } 
\hline \text { Minutes for Oil Change } \
\hline 8 \
\hline 2 \
\hline 7 \
\hline 12 \
\hline 14 \
\hline 11 \
\hline 25 \
\hline 8 \
\hline 43 \
\hline 15 \
\hline
\end{array}$$ Conduct a hypothesis test for the oil shop's claim about oil change times at the 5% level of
significance.
118

Accepted Answer

\[\begin{array} { l }
H _ { 0 } : \mu =...

Question 11

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. Carter Motor Company claims that its new sedan, the Libra, will average better than 32 miles
Per gallon in the city. Assuming that a hypothesis test of the claim has been conducted and
That the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

Accepted Answer

A)   There is not sufficient evidence to support the claim that the mean is greater than 32 miles per gallon.
B)   There is not sufficient evidence to support the claim that the mean is less than 32 miles per gallon.
C)   There is sufficient evidence to support the claim that the mean is less than 32 miles per gallon.
D)   There is sufficient evidence to support the claim that the mean is greater than 32 miles per gallon.E) None of the above
F) A) and B)

Question 12

A simple random sample of the running time of movies of 70 international movies resulted in
a sample mean length of 112 minutes and a sample standard deviation of 7 minutes. Test the
claim that international movies have a mean running time of more than 110 minutes at the 5%
level of significance. Assume that the lengths of movies are normally distributed.

Accepted Answer

. Reject the null hypothesis. ...

Question 13

Suppose we want to test the claim that the majority of adults are in favor of raising the voting age to 21. Is the hypothesis test left-tailed, right-tailed, or two-tailed?

Accepted Answer

A)   Left-tailed
B)   Right-tailed
C)   Two-tailedD) A) and B)
E) A) and C)

Question 14

The ________________ is the probability of getting a test statistic at least as extreme as the one representing the sample data, assuming that the null hypothesis is true.

Accepted Answer

A)   P-value
B)   sample proportion
C)   critical value
D)   level of significanceE) C) and D)
F) A) and D)

Question 15

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. For randomly selected adults, IQ scores are normally distributed with a standard deviation of 15. The scores of 14 randomly selected college students are listed below. Use a 0.10 significance level to test the claim that the standard deviation of IQ scores of college students is less than 15. Round the sample standard deviation to three decimal places. $$\begin{array} { l l l l l l l } 
115 & 128 & 107 & 109 & 116 & 124 & 135 \
127 & 115 & 104 & 118 & 126 & 129 & 133
\end{array}$$

Accepted Answer

Test statistic: <img  loading="lazy" src="/assets/images/blured-textbook.svg" class="d-inline m-1" alt="blured image" width="139" height="30">. Critical val...

Question 16

Find the critical value or values of  χ2\chi ^ { 2 }χ2  based on the given information.
 H1:σ<0.629n=19α=0.025\begin{array} { l } H _ { 1 } : \sigma < 0.629 \n = 19 \\alpha = 0.025\end{array}H1​:σ<0.629n=19α=0.025​

Accepted Answer

A)    8.2318.2318.231 
B)    31.52631.52631.526 
C)    7.0157.0157.015 
D)    8.9078.9078.907E) B) and C)
F) None of the above

Question 17

Solve the problem. A hypothesis test is performed to test the claim that a population proportion is greater than 0.7. Find the probability of a type II error,  BBB  , given that the true value of the
Population proportion is 0.72. The sample size is 50 and the significance level is 0.05.

Accepted Answer

A)   0.4129
B)   0.7123
C)   0.5754
D)   0.9706 E) A) and C)
F) None of the above

Question 18

Use the given information to find the  PPP -value. Also, use a  0.050.050.05  significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis) . With  H1:p≠0.377H _ { 1 } : p 
eq 0.377H1​:p=0.377 , the test statistic is  z=3.06z = 3.06z=3.06 .

Accepted Answer

A)    0.00110.00110.0011 ; reject the null hypothesis
B)    0.00220.00220.0022 ; fail to reject the null hypothesis
C)    0.00220.00220.0022 ; reject the null hypothesis
D)    0.00110.00110.0011 ; fail to reject the null hypothesis E) B) and C)
F) A) and D)

Question 19

A chi-square hypothesis test is going to be conducted about a population standard deviation. Select the statement that is not true about the Chi-square test

Accepted Answer

A) The sample must be a simple random sample.
B) The population does not have to be a normally distributed population.
C) The alternative hypothesis must contain $< , >$ , or $\neq$ .
D) The sample size must be known.

E) C) and D)
F) None of the above

Correct Answer
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Question 20

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. The owner of a football team claims that the average attendance at games is over 523, and he is
Therefore justified in moving the team to a city with a larger stadium. Assuming that a
Hypothesis test of the claim has been conducted and that the conclusion is failure to reject the
Null hypothesis, state the conclusion in nontechnical terms.

Accepted Answer

A)   There is sufficient evidence to support the claim that the mean attendance is less than 523.
B)   There is not sufficient evidence to support the claim that the mean attendance is less than 523.
C)   There is sufficient evidence to support the claim that the mean attendance is greater than 523.
D)   There is not sufficient evidence to support the claim that the mean attendance is greater than 523.E) B) and D)
F) C) and D)

Exam 8: Hypothesis Testing

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Test statistic: . Critical val...
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Correct Answer
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Correct Answer
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A hypothesis test is performed to test the claim that a population proportion is greater than 0.7. Find the probability of a type II error, $\beta$ , given that the true value of the population proportion Is 0.72. The sample size is 50 and the significance level is 0.05.

Correct Answer
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Find the critical value or values of $\chi ^ { 2 }$ based on the given information. $\begin{array} { l } H _ { 1 } : \sigma < 0.629 \\n = 19 \\\alpha = 0.025\end{array}$

Correct Answer
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Solve the problem. A hypothesis test is performed to test the claim that a population proportion is greater than 0.7. Find the probability of a type II error, $B$ , given that the true value of the Population proportion is 0.72. The sample size is 50 and the significance level is 0.05.

Correct Answer
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Use the given information to find the $P$ -value. Also, use a $0.05$ significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis) . With $H _ { 1 } : p \neq 0.377$ , the test statistic is $z = 3.06$ .

Correct Answer
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Correct Answer
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A chi-square hypothesis test is going to be conducted about a population standard deviation. Select the statement that is not true about the Chi-square test

Correct Answer
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Find the value of the test statistic $z$ using $z = \frac { \hat { p } - p } { \sqrt { \frac { p q } { n } } }$ . A claim is made that the proportion of children who play sports is less than $0.5$ , and the sample statistics include $n = 1320$ subjects with $30 \%$ saying that they play a sport.

Correct Answer
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Suppose we want to test the claim that less than $1 / 2$ of Americans are in favor of raising the voting age to 21. Is the hypothesis test left-tailed, right-tailed, or two-tailed?

Correct Answer
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The p-value is the probability of getting a test statistic at least as extreme as the one representing the sample data, assuming that ______________________________.

Correct Answer
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Correct Answer
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. Reject the null hypothesis. ...
View Answer

Express the original claim in symbolic form. Claim: 20% of adults smoke

Correct Answer
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Correct Answer
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The ________________ is the probability of getting a test statistic at least as extreme as the one representing the sample data, assuming that the null hypothesis is true.

Correct Answer
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Correct Answer
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\[\begin{array} { l }
H _ { 0 } : \mu =...
View Answer

Suppose we want to test the claim that the majority of adults are in favor of raising the voting age to 21. Is the hypothesis test left-tailed, right-tailed, or two-tailed?

Correct Answer
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Correct Answer
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Exam 8: Hypothesis Testing

Correct AnswerverifiedTest statistic: . Critical val...View AnswerShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

A hypothesis test is performed to test the claim that a population proportion is greater than 0.7. Find the probability of a type II error, β\betaβ , given that the true value of the population proportion Is 0.72. The sample size is 50 and the significance level is 0.05.

Correct AnswerverifiedShow Answer

Find the critical value or values of χ2\chi ^ { 2 }χ2 based on the given information. H1:σ<0.629n=19α=0.025\begin{array} { l } H _ { 1 } : \sigma < 0.629 \\n = 19 \\\alpha = 0.025\end{array}H1​:σ<0.629n=19α=0.025​

Correct AnswerverifiedShow Answer

Solve the problem. A hypothesis test is performed to test the claim that a population proportion is greater than 0.7. Find the probability of a type II error, BBB , given that the true value of the Population proportion is 0.72. The sample size is 50 and the significance level is 0.05.

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

A chi-square hypothesis test is going to be conducted about a population standard deviation. Select the statement that is not true about the Chi-square test

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Suppose we want to test the claim that less than 1/21 / 21/2 of Americans are in favor of raising the voting age to 21. Is the hypothesis test left-tailed, right-tailed, or two-tailed?

Correct AnswerverifiedShow Answer

The p-value is the probability of getting a test statistic at least as extreme as the one representing the sample data, assuming that ______________________________.

Correct AnswerverifiedShow Answer

Correct Answerverified. Reject the null hypothesis. ...View AnswerShow Answer

Express the original claim in symbolic form. Claim: 20% of adults smoke

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

The ________________ is the probability of getting a test statistic at least as extreme as the one representing the sample data, assuming that the null hypothesis is true.

Correct AnswerverifiedShow Answer

Correct Answerverified\[\begin{array} { l } H _ { 0 } : \mu =...View AnswerShow Answer

Suppose we want to test the claim that the majority of adults are in favor of raising the voting age to 21. Is the hypothesis test left-tailed, right-tailed, or two-tailed?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct Answer
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Test statistic: . Critical val...
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Correct Answer
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Correct Answer
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A hypothesis test is performed to test the claim that a population proportion is greater than 0.7. Find the probability of a type II error, $\beta$ , given that the true value of the population proportion Is 0.72. The sample size is 50 and the significance level is 0.05.

Correct Answer
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Find the critical value or values of $\chi ^ { 2 }$ based on the given information. $\begin{array} { l } H _ { 1 } : \sigma < 0.629 \\n = 19 \\\alpha = 0.025\end{array}$

Correct Answer
verified

Solve the problem. A hypothesis test is performed to test the claim that a population proportion is greater than 0.7. Find the probability of a type II error, $B$ , given that the true value of the Population proportion is 0.72. The sample size is 50 and the significance level is 0.05.

Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Suppose we want to test the claim that less than $1 / 2$ of Americans are in favor of raising the voting age to 21. Is the hypothesis test left-tailed, right-tailed, or two-tailed?

Correct Answer
verified

Correct Answer
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Correct Answer
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. Reject the null hypothesis. ...
View Answer

Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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\[\begin{array} { l }
H _ { 0 } : \mu =...
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Correct Answer
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Correct Answer
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