Question 1

A random sample of second-round gold scores from a major tournament is listed below. At $\alpha = 0.10$, is there sufficient evidence to conclude that the population variance exceeds
$\begin{array}{llll}
\hline 74 & 82 & 76 & 74 \
78 & 77 & 81 & 82 \
74 & 75 & & \
\hline
\end{array}$

A) There is not enough information to draw a conclusion.
B) No. There is not enough evidence to support the claim that the variance exceeds 9.
C) Yes. There enough evidence to support the claim that the variance exceeds 9.

Accepted Answer

To determine if there is sufficient evidence that the population variance exceeds 9, we perform a chi-square test for variance. Calculating the sample variance and comparing it to the hypothesized variance (9 in this case) using the chi-square distribution and the given alpha level of 0.10, we find that the evidence does not strongly support the claim that the population variance exceeds 9. This conclusion is based on the calculated chi-square statistic and the critical value from the chi-square distribution table.

Question 2

The following display from a TI-84 Plus calculator presents the results of a hypothesis test for a population proportion $p$.

Can $H _ { 0 }$ be rejected at the $0.05$ level?
A) No
B) Yes

Accepted Answer

The answer of The following display from a TI-84 Plus...

Question 3

The following display from a TI-84 Plus calculator presents the results of a hypothesis test for a population proportion $p$.

What is the value of the sample proportion $\hat { p }$ ?
A) 0.219
B) 64
C) 0.29
D) 0.10565

Accepted Answer

The answer of The following display from a TI-84 Plus...

Question 4

$$\text { The } \chi ^ { 2 } \text { critical value for } n = 16 \text { and } \alpha = 0.01 \text { for a left-tailed test is } 5.812 \text {. }$$

Accepted Answer

The given statement is true because the chi-square critical value for n = 16 and α = 0.01 for a left-tailed test is indeed 5.812. This value can be found using a chi-square distribution table or a statistical software package.

Question 5

State the appropriate null and alternative hypothesis and find the critical value for a left-tailed test with $\alpha = 0.10$ and $n = 23$. Use $\sigma ^ { 2 } = 225$. A) $\mathrm { H } _ { \mathrm { O } : } \sigma ^ { 2 } = 225$ $\mathrm { H } _ { 1 : } \sigma ^ { 2 } < 225$ C. $\mathrm { V } . = 14.042$ B) $\mathrm { H } _ { \mathrm { O } } : \sigma ^ { 2 } = 225$ $\mathrm { H } _ { 1 : } \sigma ^ { 2 } < 225$ C. $\mathrm { V } . = 14.848$ C) $\mathrm { H } _ { \mathrm { O } } : \sigma ^ { 2 } = 225$ $\mathrm { H } _ { 1 : } \sigma ^ { 2 } > 225$ C. $\mathrm { V } . = 14.042$ D) $\mathrm { H } _ { \mathrm { O } : } \sigma ^ { 2 } = 225$ $\mathrm { H } _ { 1 : } \sigma ^ { 2 } > 225$ C. $\mathrm { V } . = 14.848$

Accepted Answer

The answer of State the appropriate null and alternative hypothesis...

Question 6

A random sample of 450 shoppers at Quincy Mall found that 125 favored longer
shopping hours. Is this sufficient evidence at the 0.05 level of significance to
conclude that less than 30% of the shoppers at Quincy Mall favor longer hours?

Accepted Answer

The answer of A random sample of 450 shoppers at...

Question 7

A survey by Men's Health magazine stated that $14 \%$ of all men said that they used exercise to relieve stress. A random sample of 100 men was selected, and 9 said that they used exercise to relieve stress. Use the $P$-value method to test the claim. Use $\alpha = 0.10$.
A) There is not enough information to draw a conclusion.
B) Yes. There is not enough evidence to reject the claim that the percentage of men who use exercise to relieve stress is 14%.
C) No. There is enough evidence to reject the claim that the percentage of men who use exercise to relieve stress is 14%.

Accepted Answer

The p-value method involves calculating the probability of observing a sample statistic as extreme as the test statistic, under the assumption that the null hypothesis is true. In this case, the null hypothesis is that the true proportion of men who use exercise to relieve stress is 14% (p = 0.14). The sample proportion is 9 out of 100, or 0.09. Using a significance level of $\alpha = 0.10$, if the calculated p-value is greater than $\alpha$, we do not have enough evidence to reject the null hypothesis. Given the information provided, we do not have the exact p-value, but the correct approach with the given options is to not reject the null hypothesis based on the information provided, implying there is not enough evidence to reject the claim that 14% of men use exercise to relieve stress.

Question 8

Doctors nationally believe that $70 \%$ of a certain type of operation are successful. In a particular hospital, 42 of these operations were observed and 32 of them were successful. At $\alpha = 0.05$ is this hospital's success rate different from the national average?
A) No, because the test value 0.88 is in the noncritical region.
B) Yes, because the test value 0.88 is in the noncritical region.
C) No, because the test value 0.52 is in the noncritical region.
D) Yes, because the test value 0.52 is in the critical region.

Accepted Answer

The test statistic is calculated using the formula for a proportion z-test. The calculated z-value (0.88) falls within the noncritical region, meaning there is not enough evidence to conclude that the hospital's success rate is different from the national average.

Question 9

A political strategist claims that $56 \%$ of voters in Madison County support his candidate. In a poll of 300 randomly selected voters, 150 of them support the strategist's candidate. At $\alpha = 0.05$, is the political strategist's claim warranted?
A) Yes, because the test value -1.23 is in the critical region.
B) No, because the test value -2.72 is in the critical region.
C) Yes, because the test value -2.72 is in the noncritical region.
D) No, because the test value -2.09 is in the critical region.

Accepted Answer

The test value of -2.09 falls in the critical region for a significance level of $\alpha = 0.05$, indicating that the claim is not warranted.

Question 10

Researchers suspect that $17 \%$ of all high school students smoke at least one pack of cigarettes a day. At Wilson High School, a randomly selected sample of 300 students found that 49 students smoke at least one pack of cigarettes a day. At $\alpha = 0.05$, test the claim that less than $17 \%$ of all high school students smoke at least one pack of cigarettes a day. Use the $P$-value method.
A) There is not enough information to draw a conclusion.
B) No. There is not enough evidence to support the claim that the percentage of students who smoke at least one pack of cigarettes a day is less than 17%.
C) Yes. There is enough evidence to support the claim that the percentage of students who smoke at least one pack of cigarettes a day is less than 17%.

Accepted Answer

The sample proportion is 49/300 = 0.1633. The standard deviation of the sample proportion is sqrt(0.17 * 0.83 / 300) = 0.026. The z-score is (0.1633 - 0.17) / 0.026 = -0.254. The P-value is P(Z < -0.254) = 0.398. Since the P-value is greater than 0.05, we fail to reject the null hypothesis. There is not enough evidence to support the claim that the percentage of students who smoke at least one pack of cigarettes a day is less than 17%.

Question 11

A scientist claims that only $65 \%$ of geese in his area fly south for the winter. He tags random geese in the summer and finds that 20 of them do not fly south in the winter. If $\alpha = 0.05$, is the scientist's belief warranted?
A) No, because the test value -0.72 is in the noncritical region.
B) Yes, because the test value 0.72 is in the noncritical region.
C) No, because the test value 0.79 is in the critical region.
D) Yes, because the test value -0.79 is in the noncritical region.

Accepted Answer

The answer of A scientist claims that only $65 \%$...

Question 12

At a certain university, 16% of students fail general chemistry on their first
attempt. Professor Brown teaches at this university and believes that the rate of
first-time failure in his general chemistry classes is 33%. He samples 96 students
from last semester who were first-time enrollees in general chemistry and finds
that 15 of them failed his course. i). State the appropriate null and alternate hypotheses.
ii). Compute the test statistic $\mathrm { z }$.
iii). Using $\alpha = 0.05$, can you conclude that the percentage of failures differs from $33 \%$ ?

Accepted Answer

The answer of At a certain university, 16% of students...

Question 13

The Energy Information Administration reported that $51.5 \%$ of homes in the United States were heated by natural gas. A random sample of 200 homes found that 111 heated by natural gas. Does the evidence support the claim or has the percentage changed? Use $\alpha = 0.05$ and the $P$-value method.
A) Yes. There is not enough evidence to reject the claim that the percentage of homes that are heated by natural gas is 51.5%.
B) No. There is enough evidence to reject the claim that the percentage of homes that are heated by natural gas is 51.5%.
C) There is not enough information to draw a conclusion.

Accepted Answer

To determine if the evidence supports the claim or if the percentage has changed, we perform a hypothesis test for a proportion. The null hypothesis $H_0$ is that the true proportion $p = 0.515$, and the alternative hypothesis $H_a$ is that $p \neq 0.515$. The sample proportion is $\hat{p} = \frac{111}{200} = 0.555$. The test statistic is calculated using the formula $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$, where $p_0 = 0.515$, $\hat{p} = 0.555$, and $n = 200$. Plugging in the values, we calculate the z-value and then find the corresponding P-value. If the P-value is greater than $\alpha = 0.05$, we do not have enough evidence to reject the null hypothesis, meaning the claim that 51.5% of homes are heated by natural gas cannot be rejected based on this sample.

Question 14

It has been claimed that at UCLA at least $40 \%$ of the students live on campus. In a random sample of 250 students, 90 were found to live on campus. Does the evidence support the claim at $\alpha = 0.01$ ?

Accepted Answer

The answer of It has been claimed that at UCLA...

Question 15

In a survey of 702 cigarette smokers, 56 of them reported that they have tried hypnosis therapy to try to quit smoking. Can you conclude that less than one-tenth of smokers have tried hypnosis therapy? Use the $\alpha = 0.05$ level of significance.
A) No conclusion is possible.
B) No
C) Yes

Accepted Answer

The answer of In a survey of 702 cigarette smokers,...

Question 16

About 31% of all burglaries are through an open or unlocked door or window. A sample of 137 burglaries indicated that 88 were not via an open or unlocked door or window. At
The 0.05 level of significance, can it be concluded that this differs from the stated
Proportion?
A) There is not enough information to draw a conclusion.
B) Yes. There is enough evidence to support the claim that the proportion of open or unlocked window or door burglaries differs from 31%.
C) No. There is not enough evidence to support the claim that the proportion of open or unlocked window or door burglaries differs from 31%.

Accepted Answer

Using a hypothesis test for proportions, the sample data does not provide enough evidence to reject the null hypothesis that the proportion of burglaries through an open or unlocked door or window is 31%.

Question 17

The following display from a TI-84 Plus calculator presents the results of a hypothesis test for a population proportion $p$.

State the null and alternate hypotheses.
A) $\mathrm { H } _ { 0 } : p = 0.205 , H _ { 1 } : p = 0.29$
B) $H _ { 0 } : p = 0.054799 , H _ { 1 } : p > 0.054799$
C) $H _ { 0 } : p = 0.29 , H _ { 1 } : p > 0.29$
D) $H _ { 0 } : p = 0.205 , H _ { 1 } : p > 0.205$

Accepted Answer

The answer of The following display from a TI-84 Plus...

Question 18

In a simple random sample of size 100 , there were 60 individuals in the category of interest. It is desired to test $H _ { 0 } : p = 0.69$ versus $H _ { 1 } : p < 0.69$.
i). Compute the sample proportion $\hat { p }$.
ii). It is desired to test $H _ { 0 } : p = 0.69$ versus $H _ { 1 } : p > 0.69$ Compute the test sti
iii). Do you reject $H _ { 0 }$ at the $0.05$ level? tistic

Accepted Answer

The answer of In a simple random sample of size...

Question 19

State the appropriate null and alternative hypothesis and find the critical values for a two-tailed test with $\alpha = 0.10$ and $n = 8$. Use $\sigma ^ { 2 } = 196$.
A) $\mathrm { H } _ { \mathrm { o } } : \sigma ^ { 2 } = 196$
$\mathrm { H } _ { 1 : } \sigma ^ { 2 } \neq 196$
C. V. $= 2.733,15.507$

B) $\mathrm { H } _ { \mathrm { O } } : \sigma ^ { 2 } = 196$
$\mathrm { H } _ { 1 : } \sigma ^ { 2 } \neq 196$
C. V. $= 1.690,16.013$

C) $\mathrm { H } _ { \mathrm { O } } : \sigma ^ { 2 } = 196$
$\mathrm { H } _ { 1 : } \sigma ^ { 2 } \neq 196$
C. V. $= 2.180,17.535$

D) $\mathrm { H } _ { \mathrm { O } : } \sigma ^ { 2 } = 196$
$\mathrm { H } _ { 1 : } : \sigma ^ { 2 } \neq 196$
C. $\mathrm { V } . = 2.167,14.067$

Accepted Answer

The answer of State the appropriate null and alternative hypothesis...

Question 20

State the appropriate null and alternative hypothesis and find the critical value for a right-tailed test with $\alpha = 0.05$ and $n = 18$. Use $\sigma ^ { 2 } = 256$. A) $\mathrm { H } _ { \mathrm { O } } : \sigma 2 = 256$ $\mathrm { H } _ { 1 : } \sigma ^ { 2 } > 256$ C. $\mathrm { V } . = 27.587$ B) $\mathrm { H } _ { \mathrm { O } : } \sigma ^ { 2 } = 256$ $\mathrm { H } _ { 1 : } \sigma ^ { 2 } > 256$ C. $\mathrm { V } . = 28.869$ C) $\mathrm { H } _ { \mathrm { O } } : \sigma 2 = 256$ $\mathrm { H } _ { 1 : } \sigma ^ { 2 } < 256$ C. $\mathrm { V } . = 27.587$ D) $\mathrm { H } _ { \mathrm { O } } : \sigma ^ { 2 } \neq 256$ $\mathrm { H } _ { 1 : } \sigma ^ { 2 } < 256$ C. $\mathrm { V } . = 28.869$

Accepted Answer

The answer of State the appropriate null and alternative hypothesis...

Quiz 8: Hypothesis Testing

A random sample of second-round gold scores from a major tournament is listed below. At $\alpha = 0.10$ , is there sufficient evidence to conclude that the population variance exceeds $\begin{array}{llll}\hline 74 & 82 & 76 & 74 \\78 & 77 & 81 & 82 \\74 & 75 & & \\\hline\end{array}$

$\text { The } \chi ^ { 2 } \text { critical value for } n = 16 \text { and } \alpha = 0.01 \text { for a left-tailed test is } 5.812 \text {. }$

State the appropriate null and alternative hypothesis and find the critical value for a left-tailed test with $\alpha = 0.10$ and $n = 23$ . Use $\sigma ^ { 2 } = 225$ .

A random sample of 450 shoppers at Quincy Mall found that 125 favored longer shopping hours. Is this sufficient evidence at the 0.05 level of significance to conclude that less than 30% of the shoppers at Quincy Mall favor longer hours?

A survey by Men's Health magazine stated that $14 \%$ of all men said that they used exercise to relieve stress. A random sample of 100 men was selected, and 9 said that they used exercise to relieve stress. Use the $P$ -value method to test the claim. Use $\alpha = 0.10$ .

Doctors nationally believe that $70 \%$ of a certain type of operation are successful. In a particular hospital, 42 of these operations were observed and 32 of them were successful. At $\alpha = 0.05$ is this hospital's success rate different from the national average?

A political strategist claims that $56 \%$ of voters in Madison County support his candidate. In a poll of 300 randomly selected voters, 150 of them support the strategist's candidate. At $\alpha = 0.05$ , is the political strategist's claim warranted?

A scientist claims that only $65 \%$ of geese in his area fly south for the winter. He tags random geese in the summer and finds that 20 of them do not fly south in the winter. If $\alpha = 0.05$ , is the scientist's belief warranted?

The Energy Information Administration reported that $51.5 \%$ of homes in the United States were heated by natural gas. A random sample of 200 homes found that 111 heated by natural gas. Does the evidence support the claim or has the percentage changed? Use $\alpha = 0.05$ and the $P$ -value method.

It has been claimed that at UCLA at least $40 \%$ of the students live on campus. In a random sample of 250 students, 90 were found to live on campus. Does the evidence support the claim at $\alpha = 0.01$ ?

In a survey of 702 cigarette smokers, 56 of them reported that they have tried hypnosis therapy to try to quit smoking. Can you conclude that less than one-tenth of smokers have tried hypnosis therapy? Use the $\alpha = 0.05$ level of significance.

About 31% of all burglaries are through an open or unlocked door or window. A sample of 137 burglaries indicated that 88 were not via an open or unlocked door or window. At The 0.05 level of significance, can it be concluded that this differs from the stated Proportion?

State the appropriate null and alternative hypothesis and find the critical values for a two-tailed test with $\alpha = 0.10$ and $n = 8$ . Use $\sigma ^ { 2 } = 196$ .

State the appropriate null and alternative hypothesis and find the critical value for a right-tailed test with $\alpha = 0.05$ and $n = 18$ . Use $\sigma ^ { 2 } = 256$ .

Quiz 8: Hypothesis Testing

The following display from a TI-84 Plus calculator presents the results of a hypothesis test for a population proportion ppp . Can H0H _ { 0 }H0​ be rejected at the 0.050.050.05 level?

The following display from a TI-84 Plus calculator presents the results of a hypothesis test for a population proportion ppp . What is the value of the sample proportion p^\hat { p }p^​ ?

The χ2 critical value for n=16 and α=0.01 for a left-tailed test is 5.812. \text { The } \chi ^ { 2 } \text { critical value for } n = 16 \text { and } \alpha = 0.01 \text { for a left-tailed test is } 5.812 \text {. } The χ2 critical value for n=16 and α=0.01 for a left-tailed test is 5.812.

State the appropriate null and alternative hypothesis and find the critical value for a left-tailed test with α=0.10\alpha = 0.10α=0.10 and n=23n = 23n=23 . Use σ2=225\sigma ^ { 2 } = 225σ2=225 .

A random sample of 450 shoppers at Quincy Mall found that 125 favored longer shopping hours. Is this sufficient evidence at the 0.05 level of significance to conclude that less than 30% of the shoppers at Quincy Mall favor longer hours?

A survey by Men's Health magazine stated that 14%14 \%14% of all men said that they used exercise to relieve stress. A random sample of 100 men was selected, and 9 said that they used exercise to relieve stress. Use the PPP -value method to test the claim. Use α=0.10\alpha = 0.10α=0.10 .

Doctors nationally believe that 70%70 \%70% of a certain type of operation are successful. In a particular hospital, 42 of these operations were observed and 32 of them were successful. At α=0.05\alpha = 0.05α=0.05 is this hospital's success rate different from the national average?

A political strategist claims that 56%56 \%56% of voters in Madison County support his candidate. In a poll of 300 randomly selected voters, 150 of them support the strategist's candidate. At α=0.05\alpha = 0.05α=0.05 , is the political strategist's claim warranted?

A scientist claims that only 65%65 \%65% of geese in his area fly south for the winter. He tags random geese in the summer and finds that 20 of them do not fly south in the winter. If α=0.05\alpha = 0.05α=0.05 , is the scientist's belief warranted?

It has been claimed that at UCLA at least 40%40 \%40% of the students live on campus. In a random sample of 250 students, 90 were found to live on campus. Does the evidence support the claim at α=0.01\alpha = 0.01α=0.01 ?

In a survey of 702 cigarette smokers, 56 of them reported that they have tried hypnosis therapy to try to quit smoking. Can you conclude that less than one-tenth of smokers have tried hypnosis therapy? Use the α=0.05\alpha = 0.05α=0.05 level of significance.

About 31% of all burglaries are through an open or unlocked door or window. A sample of 137 burglaries indicated that 88 were not via an open or unlocked door or window. At The 0.05 level of significance, can it be concluded that this differs from the stated Proportion?

The following display from a TI-84 Plus calculator presents the results of a hypothesis test for a population proportion ppp . State the null and alternate hypotheses.

State the appropriate null and alternative hypothesis and find the critical values for a two-tailed test with α=0.10\alpha = 0.10α=0.10 and n=8n = 8n=8 . Use σ2=196\sigma ^ { 2 } = 196σ2=196 .

State the appropriate null and alternative hypothesis and find the critical value for a right-tailed test with α=0.05\alpha = 0.05α=0.05 and n=18n = 18n=18 . Use σ2=256\sigma ^ { 2 } = 256σ2=256 .

$\text { The } \chi ^ { 2 } \text { critical value for } n = 16 \text { and } \alpha = 0.01 \text { for a left-tailed test is } 5.812 \text {. }$

State the appropriate null and alternative hypothesis and find the critical value for a left-tailed test with $\alpha = 0.10$ and $n = 23$ . Use $\sigma ^ { 2 } = 225$ .

A survey by Men's Health magazine stated that $14 \%$ of all men said that they used exercise to relieve stress. A random sample of 100 men was selected, and 9 said that they used exercise to relieve stress. Use the $P$ -value method to test the claim. Use $\alpha = 0.10$ .

Doctors nationally believe that $70 \%$ of a certain type of operation are successful. In a particular hospital, 42 of these operations were observed and 32 of them were successful. At $\alpha = 0.05$ is this hospital's success rate different from the national average?

A political strategist claims that $56 \%$ of voters in Madison County support his candidate. In a poll of 300 randomly selected voters, 150 of them support the strategist's candidate. At $\alpha = 0.05$ , is the political strategist's claim warranted?

A scientist claims that only $65 \%$ of geese in his area fly south for the winter. He tags random geese in the summer and finds that 20 of them do not fly south in the winter. If $\alpha = 0.05$ , is the scientist's belief warranted?

It has been claimed that at UCLA at least $40 \%$ of the students live on campus. In a random sample of 250 students, 90 were found to live on campus. Does the evidence support the claim at $\alpha = 0.01$ ?

In a survey of 702 cigarette smokers, 56 of them reported that they have tried hypnosis therapy to try to quit smoking. Can you conclude that less than one-tenth of smokers have tried hypnosis therapy? Use the $\alpha = 0.05$ level of significance.

State the appropriate null and alternative hypothesis and find the critical values for a two-tailed test with $\alpha = 0.10$ and $n = 8$ . Use $\sigma ^ { 2 } = 196$ .

State the appropriate null and alternative hypothesis and find the critical value for a right-tailed test with $\alpha = 0.05$ and $n = 18$ . Use $\sigma ^ { 2 } = 256$ .