Exam 7: Inferences Based on a Single Sample: 355 Tests of Hypotheses

The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion exceeds 25%, then the lab will scale back a proposed enlargement of its facilities. Suppose 200 business students were randomly sampled and 65 have laptops. Find the rejection region for the corresponding test using $\alpha = .01$

(Multiple Choice)

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Question 21

A random sample of $n$ observations, selected from a normal population, is used to test the null hypothesis $H _ { 0 } : \sigma ^ { 2 } = 155$ . Specify the appropriate rejection region. $H _ { \mathrm { a } } : \sigma ^ { 2 } > 155 , n = 25 , \alpha = .10$

(Multiple Choice)

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Question 22

Suppose we wish to test $H _ { 0 } : \mu = 20$ vs. $H _ { \mathrm { a } } : \mu < 20$ . Which of the following possible sample results gives the most evidence to support $H _ { \mathrm { a } }$ (i.e., reject $H _ { 0 }$ )?

(Multiple Choice)

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Question 23

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. A random sample of 350 manufacturing firms is selected, and only 34 of them offer child-care benefits. Specify the rejection region that the union will use when testing at $\alpha = .05$

(Essay)

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Question 24

The alternative hypothesis is accepted as true unless there is overwhelming evidence that it is false.

(True/False)

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Question 25

A rejection region is established in each tail of the sampling distribution for a two-tailed test.

(True/False)

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Question 26

A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but now are beginning to increase in price because of added features. According to the story, the average price of all digital cameras a couple of years ago was $\$ 215.00$ . A random sample of $n = 22$ cameras was recently taken and entered into a spreadsheet. It was desired to test to determine if that average price of all digital cameras is now more than $\$ 215.00$ . Find a rejection region appropriate for this test if we are using $\alpha = 0.05$ .

(Multiple Choice)

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Question 27

It is desired to test $H _ { 0 } : \mu = 40$ against $H _ { \mathrm { a } } : \mu < 40$ using $\alpha = .10$ . The population in question is uniformly distributed with a standard deviation of 10 . A random sample of 36 will be drawn from this population. If $\mu$ is really equal to 35 , what is the probability that the hypothesis test would lead the investigator to commit a Type II error?

(Multiple Choice)

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Question 28

The State Association of Retired Teachers has recently taken flak from some of its members regarding the poor choice of the association's name. The association's by-laws require that more than 60 percent of the association must approve a name change. Rather than convene a meeting, it Is first desired to use a sample to determine if meeting is necessary. Suppose the association decided to conduct a test of hypothesis using the following null and alternative hypotheses: :=0.6 :>0.6 Define a Type I Error in the context of this problem.

(Multiple Choice)

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Question 29

How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 40 tissues during a cold. Suppose a random sample of 10,000 people yielded the following data on the number of tissues used during a cold: $\bar { x } = 31 , s = 18$ using the sample information provided, set up the calculation for the test statistic for the relevant hypothesis test, but do not simplify.

(Multiple Choice)

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Question 30

A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 238 students and asked each to provide the amount of time they spent traveling to campus. This variable, travel time, was then used conduct a test of hypothesis. The goal was to determine if the average travel time of all the university's students differed from 20 minutes. Suppose the large-sample test statistic was calculated to be z $z = 2.14$ 4. Find the p-value for this test of hypothesis.

(Multiple Choice)

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Question 31

A revenue department is under orders to reduce the time small business owners spend filling out pension form ABC-5500. Previously the average time spent on the form was 53 hours. In order to test whether the time to fill out the form has been reduced, a sample of 82 small business owners who annually complete the form was randomly chosen and their completion times recorded. The mean completion time for the sample was 52.8 hours with a standard deviation of 28 hours. State the rejection region for the desired test at ? = .05.

(Essay)

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Question 32

I want to test $H _ { 0 } : p = .7 \text { vs. } H _ { \mathrm { a } } : p \neq .7$ using a test of hypothesis. This test would be called a(n) ____________ test.

(Multiple Choice)

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Question 33

Type I errors and Type II errors are complementary events so that $\alpha = P$ (Type I error) $=$ $1 - P$ (Type II error) $= 1 - \beta$ .

(True/False)

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Question 34

A small private college is interested in determining the percentage of its students who live off campus and drive to class. Specifically, it was desired to determine if less than $20 \%$ of their curren students live off campus and drive to class. Suppose a sample of 108 students produced a test statistic of $z = - 1.35$ . Find the $p$ -value for the test of interest to the college.

(Multiple Choice)

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Question 35

Given $H _ { 0 } : \mu = 25 , H _ { \mathrm { a } } : \mu \neq 25$ , and $p = 0.029$ . Do you reject or fail to reject $H _ { 0 }$ at the $.01$ level of significance?

(Multiple Choice)

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Question 36

A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 238 students and asked each to provide the amount of time they spent traveling to campus. This variable, travel time, was then used conduct a test of hypothesis. The goal was to determine if the average travel time of all the university's students differed from 20 minutes. Suppose the sample mean and sample standard deviation were calculated to be 23.2 and 20.26 minutes, respectively. Calculate the value of the test statistic to be used in the test.

(Multiple Choice)

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Question 37

A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but are now beginning to increase in price because of added features. According to the story, the average price of all digital cameras a couple of years ago was $215.00. A random sample of cameras was recently taken and entered into a spreadsheet. It was desired to test to determine if that average price of all digital cameras is now more than $215.00. What null and alternative hypothesis should be tested?

(Multiple Choice)

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Question 38

State University uses thousands of fluorescent light bulbs each year. The brand of bulb it currently uses has a mean life of 800 hours. A competitor claims that its bulbs, which cost the same as the brand the university currently uses, have a mean life of more than 800 hours. The university has decided to purchase the new brand if, when tested, the evidence supports the manufacturer's claim at the $.05$ significance level. Suppose 121 bulbs were tested with the following results: $\bar { x } = 830$ hours, $s = 110$ hours. Conduct the test using $\alpha = .05$ .

(Essay)

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Question 39

In a test of hypothesis, the sampling distribution of the test statistic is calculated under the assumption that the alternative hypothesis is true.

(True/False)

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Question 40

Showing 21 - 40 of 144

A random sample of $n$ observations, selected from a normal population, is used to test the null hypothesis $H _ { 0 } : \sigma ^ { 2 } = 155$ . Specify the appropriate rejection region. $H _ { \mathrm { a } } : \sigma ^ { 2 } > 155 , n = 25 , \alpha = .10$

Suppose we wish to test $H _ { 0 } : \mu = 20$ vs. $H _ { \mathrm { a } } : \mu < 20$ . Which of the following possible sample results gives the most evidence to support $H _ { \mathrm { a } }$ (i.e., reject $H _ { 0 }$ )?

The alternative hypothesis is accepted as true unless there is overwhelming evidence that it is false.

A rejection region is established in each tail of the sampling distribution for a two-tailed test.

I want to test $H _ { 0 } : p = .7 \text { vs. } H _ { \mathrm { a } } : p \neq .7$ using a test of hypothesis. This test would be called a(n) ____________ test.

Type I errors and Type II errors are complementary events so that $\alpha = P$ (Type I error) $=$ $1 - P$ (Type II error) $= 1 - \beta$ .

Given $H _ { 0 } : \mu = 25 , H _ { \mathrm { a } } : \mu \neq 25$ , and $p = 0.029$ . Do you reject or fail to reject $H _ { 0 }$ at the $.01$ level of significance?

In a test of hypothesis, the sampling distribution of the test statistic is calculated under the assumption that the alternative hypothesis is true.

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Random Variables and Probability Distributions

Sampling Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Design of Experiments and Analysis of Variance

Categorical Data Analysis

Simple Linear Regression

Multiple Regression and Model Building

Methods for Quality Improvement: Statistical Process Control Available on CD

Time Series: Descriptive Analyses, Models, and Forecasting Available on CD

Nonparametric Statistics Available on CD

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Exam 7: Inferences Based on a Single Sample: 355 Tests of Hypotheses

Suppose we wish to test H0:μ=20H _ { 0 } : \mu = 20H0​:μ=20 vs. Ha:μ<20H _ { \mathrm { a } } : \mu < 20Ha​:μ<20 . Which of the following possible sample results gives the most evidence to support HaH _ { \mathrm { a } }Ha​ (i.e., reject H0H _ { 0 }H0​ )?

The alternative hypothesis is accepted as true unless there is overwhelming evidence that it is false.

A rejection region is established in each tail of the sampling distribution for a two-tailed test.

I want to test H0:p=.7 vs. Ha:p≠.7H _ { 0 } : p = .7 \text { vs. } H _ { \mathrm { a } } : p \neq .7H0​:p=.7 vs. Ha​:p=.7 using a test of hypothesis. This test would be called a(n) ____________ test.

Type I errors and Type II errors are complementary events so that α=P\alpha = Pα=P (Type I error) === 1−P1 - P1−P (Type II error) =1−β= 1 - \beta=1−β .

Given H0:μ=25,Ha:μ≠25H _ { 0 } : \mu = 25 , H _ { \mathrm { a } } : \mu \neq 25H0​:μ=25,Ha​:μ=25 , and p=0.029p = 0.029p=0.029 . Do you reject or fail to reject H0H _ { 0 }H0​ at the .01.01.01 level of significance?

In a test of hypothesis, the sampling distribution of the test statistic is calculated under the assumption that the alternative hypothesis is true.

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Random Variables and Probability Distributions

Sampling Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Design of Experiments and Analysis of Variance

Categorical Data Analysis

Simple Linear Regression

Multiple Regression and Model Building

Methods for Quality Improvement: Statistical Process Control Available on CD

Time Series: Descriptive Analyses, Models, and Forecasting Available on CD

Nonparametric Statistics Available on CD

Filters

Suppose we wish to test $H _ { 0 } : \mu = 20$ vs. $H _ { \mathrm { a } } : \mu < 20$ . Which of the following possible sample results gives the most evidence to support $H _ { \mathrm { a } }$ (i.e., reject $H _ { 0 }$ )?

I want to test $H _ { 0 } : p = .7 \text { vs. } H _ { \mathrm { a } } : p \neq .7$ using a test of hypothesis. This test would be called a(n) ____________ test.

Type I errors and Type II errors are complementary events so that $\alpha = P$ (Type I error) $=$ $1 - P$ (Type II error) $= 1 - \beta$ .

Given $H _ { 0 } : \mu = 25 , H _ { \mathrm { a } } : \mu \neq 25$ , and $p = 0.029$ . Do you reject or fail to reject $H _ { 0 }$ at the $.01$ level of significance?