Question 1

A long-distance telephone company claims that the mean duration of long-distance telephone calls originating in one town was greater than 9.4 minutes, which is the average for the state. Determine the conclusion of the hypothesis test assuming that the results of the sampling do not lead to rejection of the null hypothesis.

Accepted Answer

If the null hypothesis is not rejected, it means there is not enough evidence to support the claim that the mean duration is greater than 9.4 minutes.

Question 2

A poll of 1068 adult Americans reveals that 52% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 significance level, test the claim that more than half of all voters prefer the Democrat.

Accepted Answer

The answer of A poll of 1068 adult Americans reveals...

Question 3

$ \mathrm{H}_{\mathrm{a}}: \mu>21.1, \bar{x}=21.5, \sigma=6, \mathrm{n}=100 $; Without computing a P-value, determine whether the alternate hypothesis is supported and give a reason for your conclusion.

Accepted Answer

The sample mean $\bar{x}$ is only 0.4 standard deviations above the claimed mean, which is not enough to support the alternate hypothesis.

Question 4

A two-tailed test is conducted at the 5% significance level. What is the left tail percentile required to reject the null hypothesis?

Accepted Answer

In a two-tailed test at the 5% significance level, the significance is split between the two tails, so each tail has 2.5%.

Question 5

A consumer advocacy group claims that the mean amount of juice in a 16 ounce bottled drink is not 16 ounces, as stated by the bottler. Determine the null and alternative hypotheses for the test
Described.

Accepted Answer

The null hypothesis ($ \mathrm{H}_{0} $) assumes the mean is as stated, 16 ounces. The alternative hypothesis ($ \mathrm{H}_{a} $) suggests the mean is different from 16 ounces, aligning with the claim that it is not 16 ounces.

Question 6

A study of a brand of "in the shell peanuts" gives the following results: $$\begin{array} { c | r } 
\begin{array} { l } 
\text { Number of } \
\text { Peanuts per bag }
\end{array} & \text { Probability } \
\hline 25 & 0.003 \
30 & 0.020 \
35 & 0.090 \
40 & 0.150 \
45 & 0.350 \
50 & 0.217 \
55 & 0.170
\end{array}$$ A significant event at the 0.01 level is a fan getting a bag with how many peanuts?

Accepted Answer

A significant event at the 0.01 level means an event with a probability less than or equal to 0.01. The probability of getting 25 peanuts is 0.003, which is less than 0.01.

Question 7

$$\mathrm { z } = 0.5 \text { for } \mathrm { H } _ { \mathrm { a } } : \mu < \text { claimed value. What is the } \mathrm { P } \text {-value for the test? }$$

Accepted Answer

The P-value is the area under the standard normal distribution curve that is to the left of the test statistic. In this case, the test statistic is z = 0.5, so the P-value is the area under the standard normal distribution curve that is to the left of z = 0.5. This area is equal to 0.6915.

Question 8

A two-tailed test is conducted at the 0.10 significance level. What is the P-value required to reject the null hypothesis?

Accepted Answer

The answer of A two-tailed test is conducted at the...

Question 9

An airline claims that the no-show rate for passengers booked on its flights is less than 6%. Of 380 randomly selected reservations, 18 were no-shows. Use Table 5.1 to find the best estimate of the P- value for a test of the airline's claim.

Accepted Answer

The answer of An airline claims that the no-show rate...

Question 10

In 1990, the average math SAT score for students at one school was 495. Five years later, a teacher wants to perform a hypothesis test to determine whether the average SAT score of students at the
School has changed from the 1990 mean of 495. The hypotheses are: $$\begin{array} { l } 
\mathrm { H } _ { 0 } : \mu = 495 \
\mathrm { H } _ { \mathrm { a } } : \mu \neq 495
\end{array}$$
Explain the meaning of a Type II error.

Accepted Answer

A Type II error occurs when we fail to reject the null hypothesis when it is actually false. In this context, it means failing to reject the hypothesis that the average SAT score is 495 when it is actually different from 495.

Question 11

At one school, the average amount of time that tenth-graders spend watching television each week is 21.6 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average
Amount of time spent watching television per week has decreased. The hypotheses are: 
$\begin{array}{l}
\mathrm{H}_{0}: \mu=21.6 \text { hours } \
\mathrm{H}_{\mathrm{a}}: \mu<21.6 \text { hours }
\end{array}
$
Explain the meaning of a correct decision.

Accepted Answer

A correct decision in hypothesis testing is either failing to reject the null hypothesis when it is true or rejecting the null hypothesis when the alternative hypothesis is true.

Question 12

A psychologist claims that more than 19 percent of the population suffers from professional problems due to extreme shyness. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of
The test apply.

Accepted Answer

The description of the study does not provide enough information to identify the specific population to which the results apply.

Question 13

The principal of a middle school claims that annual incomes of the families of the seventh-graders at his school vary more than the annual incomes of the families of the seventh-graders at a neighboring school, which have variation described by $\sigma = \$ 13,700$ . Assume that a hypothesis test of the claim has
Been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply.

Accepted Answer

The hypothesis test was conducted on the families of the seventh-graders at the principal's school, so the results apply to all of the families of the class of seventh graders at the principal's school.

Question 14

In 1990, the average duration of long-distance telephone calls originating in one town was 9.3 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.3 minutes.
Formulate the null and alternative hypotheses for the study described.

Accepted Answer

The null hypothesis states that the mean duration has not changed, while the alternative hypothesis states that the mean duration is different from 9.3 minutes, indicating a change.

Question 15

A manufacturer claims that the mean amount of juice in its 16 ounce bottles is $ 16.1 $ ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The mean volume of juice for a random sample of 70 bottles was $ 15.94 $ ounces. Do the data provide sufficient evidence to conclude that the mean amount of juice for all 16ounce bottles, $ \mu $, is less than $ 16.1 $ ounces? Perform the appropriate hypothesis test using a significance level of $ 0.10 $. Assume that $ \sigma=0.9 $ ounces.

Accepted Answer

The z-score of -1.49 is less than -1.645, the critical value for a significance level of 0.10, so we reject the null hypothesis and conclude that the mean amount of juice is less than 16.1 ounces.

Question 16

A two-tailed test is conducted at the 5% significance level. Which of the z-scores below is the smallest one that leads to rejection of the null hypothesis?

Accepted Answer

In a two-tailed test at the 5% significance level, the critical z-scores are approximately ±1.96. A z-score of 2.15 is beyond this critical value, leading to rejection of the null hypothesis.

Question 17

A psychologist claims that more than 29 percent of the professional population suffers from problems due to extreme shyness. 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 non-technical terms.

Accepted Answer

The failure to reject the null hypothesis indicates that there is not enough evidence to support the claim that the proportion is greater than 29 percent.

Question 18

A researcher wants to check the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 35 such cases from court files and finds that $\bar{x}$= 16.7 months. Assume that the population standard deviation is 7 months. Test the null hypothesis that µ = 18.7 at the 0.05 significance level.

Accepted Answer

The p-value is greater than 0.05, so we fail to reject the null hypothesis.

Question 19

A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The hypotheses are: 
$ \mathrm{H}_{0}: \mu=16.1 $ ounces
$\mathrm{H}_{\mathrm{a}}: \mu<16.1 \text { ounces }
$
 Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean amount of juice, ?, is less than 16.1 ounces.

Accepted Answer

If the mean amount of juice is less than 16.1 ounces, and the null hypothesis is rejected, then the conclusion is a correct decision.

Question 20

The owner of a football team claims that the mean attendance at games is greater than 83,900. State the null hypothesis and the alternative hypothesis for a test of significance.

Accepted Answer

The null hypothesis ($ \mathrm{H}_{0} $) represents the status quo or a statement of no effect, which is that the mean attendance is 83,900. The alternative hypothesis ($ \mathrm{H}_{a} $) represents the claim being tested, which is that the mean attendance is greater than 83,900.

Quiz 9: Hypothesis Testing

A poll of 1068 adult Americans reveals that 52% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 significance level, test the claim that more than half of all voters prefer the Democrat.

$\mathrm{H}_{\mathrm{a}}: \mu>21.1, \bar{x}=21.5, \sigma=6, \mathrm{n}=100$ ; Without computing a P-value, determine whether the alternate hypothesis is supported and give a reason for your conclusion.

A two-tailed test is conducted at the 5% significance level. What is the left tail percentile required to reject the null hypothesis?

A consumer advocacy group claims that the mean amount of juice in a 16 ounce bottled drink is not 16 ounces, as stated by the bottler. Determine the null and alternative hypotheses for the test Described.

$\mathrm { z } = 0.5 \text { for } \mathrm { H } _ { \mathrm { a } } : \mu < \text { claimed value. What is the } \mathrm { P } \text {-value for the test? }$

A two-tailed test is conducted at the 0.10 significance level. What is the P-value required to reject the null hypothesis?

An airline claims that the no-show rate for passengers booked on its flights is less than 6%. Of 380 randomly selected reservations, 18 were no-shows. Use Table 5.1 to find the best estimate of the P- value for a test of the airline's claim.

A two-tailed test is conducted at the 5% significance level. Which of the z-scores below is the smallest one that leads to rejection of the null hypothesis?

A psychologist claims that more than 29 percent of the professional population suffers from problems due to extreme shyness. 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 non-technical terms.

The owner of a football team claims that the mean attendance at games is greater than 83,900. State the null hypothesis and the alternative hypothesis for a test of significance.

Quiz 9: Hypothesis Testing

A poll of 1068 adult Americans reveals that 52% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 significance level, test the claim that more than half of all voters prefer the Democrat.

Ha:μ>21.1,xˉ=21.5,σ=6,n=100 \mathrm{H}_{\mathrm{a}}: \mu>21.1, \bar{x}=21.5, \sigma=6, \mathrm{n}=100 Ha​:μ>21.1,xˉ=21.5,σ=6,n=100 ; Without computing a P-value, determine whether the alternate hypothesis is supported and give a reason for your conclusion.

A two-tailed test is conducted at the 5% significance level. What is the left tail percentile required to reject the null hypothesis?

A consumer advocacy group claims that the mean amount of juice in a 16 ounce bottled drink is not 16 ounces, as stated by the bottler. Determine the null and alternative hypotheses for the test Described.

z=0.5 for Ha:μ< claimed value. What is the P-value for the test? \mathrm { z } = 0.5 \text { for } \mathrm { H } _ { \mathrm { a } } : \mu < \text { claimed value. What is the } \mathrm { P } \text {-value for the test? }z=0.5 for Ha​:μ< claimed value. What is the P-value for the test?

A two-tailed test is conducted at the 0.10 significance level. What is the P-value required to reject the null hypothesis?

An airline claims that the no-show rate for passengers booked on its flights is less than 6%. Of 380 randomly selected reservations, 18 were no-shows. Use Table 5.1 to find the best estimate of the P- value for a test of the airline's claim.

A two-tailed test is conducted at the 5% significance level. Which of the z-scores below is the smallest one that leads to rejection of the null hypothesis?

A psychologist claims that more than 29 percent of the professional population suffers from problems due to extreme shyness. 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 non-technical terms.

The owner of a football team claims that the mean attendance at games is greater than 83,900. State the null hypothesis and the alternative hypothesis for a test of significance.

$\mathrm{H}_{\mathrm{a}}: \mu>21.1, \bar{x}=21.5, \sigma=6, \mathrm{n}=100$ ; Without computing a P-value, determine whether the alternate hypothesis is supported and give a reason for your conclusion.

$\mathrm { z } = 0.5 \text { for } \mathrm { H } _ { \mathrm { a } } : \mu < \text { claimed value. What is the } \mathrm { P } \text {-value for the test? }$