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 current Students live off campus and drive to class. A sample of 108 students was randomly selected and the following printout was obtained: Hypothesis Test - One Proportion $\begin{array}{ll} \text { Sample Size } & 108 \\ \text { Successes } & 16 \\ \text { Proportion } & 0.14815 \end{array}$ Null Hypothesis: $\quad \mathrm { P } = 0.2$ Alternative Hyp: $\quad \mathrm { P } < 0.2$ $\begin{array}{lccc} \text { Difference } & -0.05185 & & \\ \text { Standard Error } & 0.03418 & \\ Z & -1.35 & \text { p-value } & 0.0885 \end{array}$ Based on the information contained in the printout, what conclusion would be correct when testing at $\alpha = 0.05$.

A) Accept $\mathrm { H } _ { 0 }$ B) Fail to reject $\mathrm { H } _ { 0 }$ C) Accept $\mathrm { H } _ { \mathrm { A } }$ D) Reject $\mathrm { H } _ { 0 }$ A) Accept $\mathrm { H } _ { 0 }$ B) Fail to reject $\mathrm { H } _ { 0 }$ C) Accept $\mathrm { H } _ { \mathrm { A } }$ D) Reject $\mathrm { H } _ { 0 }$

A test of hypothesis was performed to determine if the true proportion of college students who preferred a particular brand of soda differs from .50. The ASP printout is supplied below. Note: All data refer to the proportion of students who preferred the brand of soda. $\text { HYPOTHESIS: PROPORTION X }=\mathrm{x}$ $X=\operatorname{drink}-(\operatorname{soda}=1)$ $\begin{array}{llcc} \text { SAMPLE PROPORTION OF X } &=.407186\\ \text { SAMPLE SIZE OF X } &=167 \\ \text { HYPOTHESIZED VALUE (x) } &=.5 \\ \end{array}$ $\text { SAMPLEPROPORTION } x-x=-.092814$ $\begin{aligned} \mathrm{Z} & =-2.39884 \\ \text { P-VALUE } & =.0164 \\ \text { P-VALUE } / 2 & =.0082 \\ \text { SD. } \text { ERROR } & =.0386912 \end{aligned}$ State the proper conclusion if the test was conducted at \[\alpha = , 10\]

A) There is insufficient evidence to indicate the true proportion of college students who prefer the brand of soda is less than .50. B) There is sufficient evidence to indicate the true proportion of college students who prefer the brand of soda is less than .50. C) There is insufficient evidence to indicate the true proportion of college students who prefer the brand of soda differs from .50. D) There is sufficient evidence to indicate the true proportion of college students who prefer the brand of soda differs from .50. A) There is insufficient evidence to indicate the true proportion of college students who prefer the brand of soda is less than .50. B) There is sufficient evidence to indicate the true proportion of college students who prefer the brand of soda is less than .50. C) There is insufficient evidence to indicate the true proportion of college students who prefer the brand of soda differs from .50. D) There is sufficient evidence to indicate the true proportion of college students who prefer the brand of soda differs from .50.

Data were collected from the sale of 25 properties by a local real estate agent. The following printout concentrated on the land value variable from the sampled properties. HYPOTHESIS: MEAN X $= x$ $\begin{array}{rl} \text {X}&=\text { land} -\text { value }\\ \\ \text { SAMPLE MEAN OF X }&=50,740\\ \text { SAMPLE VARIANCE OF X }&=273,643,254\\ \text { SAMPLE SIZE OF X }&=25\\ x&=46,297\\ \\ \text { MEANX- } \mathrm{x} & =4443 \\ \mathrm{t} & =1.34293 \\ \text { D.F. } & =24 \\ \text { P-VALUE } & =0.1918585 \\ \text {P -VALUE } / 2 & =0.0959288 \\ \text { SD. ERROR } & =3308.43 \end{array}$ Find the $p$-value for testing whether the mean land value differs from $\$ 46,297$.

A) $p = 0.1918585$ B) $p = 0.808142$ C) $p = 0.308142$ D) $p = 0.0959288$ A) $p = 0.1918585$ B) $p = 0.808142$ C) $p = 0.308142$ D) $p = 0.0959288$

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

A method currently used by doctors to screen women for possible breast cancer fails to detect cancer in 20% of women who actually have the disease. A new method has been developed that researchers hope will be able to detect cancer more accurately. A random sample of 80 women known to have breast cancer were screened using the new method. Of these, the new method failed to detect cancer in 9. Is the sample size sufficiently large to conduct this test of hypothesis? Explain.

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Question 61

Consider the following printout. HYPOTHESIS: VARIANCE $X = x$ $X = g p a$ SAMPLE MEAN OF X $= 2.2602$ SAMPLE VARIANCE OF $X = .19000$ SAMPLE SIZE OF X $= 198$ HYPOTHESIZED VALUE $( x ) = 2.4$ VARIANCE $X - x = - .1398$ $z = - 4.51298$ State the proper conclusion when testing $H _ { 0 } : \mu = 2.4$ vs. $H _ { \mathrm { a } } : \mu < 2.4$ at $\alpha = .05$ .

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Question 62

The null distribution is the distribution of the test statistic assuming the null hypothesis is true; it mound shaped and symmetric about the null mean $\mu _0$ .

(True/False)

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Question 63

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 current Students live off campus and drive to class. A sample of 108 students was randomly selected and the following printout was obtained: Hypothesis Test - One Proportion Sample Size 108 Successes 16 Proportion 0.14815 Null Hypothesis: $\quad \mathrm { P } = 0.2$ Alternative Hyp: $\quad \mathrm { P } < 0.2$ Difference -0.05185 Standard Error 0.03418 Z -1.35 p-value 0.0885 Based on the information contained in the printout, what conclusion would be correct when testing at $\alpha = 0.05$ .

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Question 64

The rejection region refers to the values of the test statistic for which we will reject the alternative hypothesis.

(True/False)

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Question 65

The smaller the p-value in a test of hypothesis, the more significant the results are.

(True/False)

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Question 66

The owner of Get-A-Away Travel has recently surveyed a random sample of 183 customers to determine whether the mean age of the agency's customers is over 32 . The appropriate hypotheses are $H _ { 0 } : \mu = 32 , H _ { \mathrm { a } } : \mu > 32$ . If he concludes the mean age is over 32 when it is not, he makes a ____error. If he concludes the mean age is not over 32 when it is, he makes a _error.

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Question 67

Find the rejection region for the specified hypothesis test. -Consider a test of $\mathrm { H } _ { 0 } : \mu = 9$ . For the following case, give the rejection region for the test in terms of the $z$ -statistic: $\mathrm { H } _ { \mathrm { a } } : \mu > 9 , \alpha = 0.01$

(Multiple Choice)

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Question 68

A test of hypothesis was performed to determine if the true proportion of college students who preferred a particular brand of soda differs from .50. The ASP printout is supplied below. Note: All data refer to the proportion of students who preferred the brand of soda. $\text { HYPOTHESIS: PROPORTION X }=\mathrm{x}$ $X=\operatorname{drink}-(\operatorname{soda}=1)$ SAMPLE PROPORTION OF X =.407186 SAMPLE SIZE OF X =167 HYPOTHESIZED VALUE (x) =.5 $\text { SAMPLEPROPORTION } x-x=-.092814$ =-2.39884 P-VALUE =.0164 P-VALUE /2 =.0082 SD. ERROR =.0386912 State the proper conclusion if the test was conducted at $\alpha = , 10$

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Question 69

A random sample of $n = 15$ observations is selected from a normal population to test $H _ { 0 } : \mu = 2.89$ against $H _ { \mathrm { a } } : \mu < 2.89$ at $\alpha = .01$ . Specify the rejection region.

(Essay)

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Question 70

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 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. The information was entered into a spreadsheet and the following printout was obtained: One-Sample T Test Null Hypothesis: $\mu = 215$ Alternative Hyp: $\mu > 215$ $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 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 $215.00. The information was entered into a spreadsheet and the following printout was obtained: One-Sample T Test Null Hypothesis: \mu = 215 Alternative Hyp: \mu > 215 Cases Included 22 Is a sample size n = 22 large enough to utilize the central limit theorem in this inferential procedure?$ Cases Included 22 Is a sample size $n = 22$ large enough to utilize the central limit theorem in this inferential procedure?

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Question 71

How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 41 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: $\bar { x } = 35 , s = 18$ . Identify the null and alternative hypothesis for a test to determine if the mean number of tissues used during a cold is less than $41 .$

(Multiple Choice)

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Question 72

A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 51 students and asked each to provide the amount of time they spent traveling to campus. The sample results found that the sample mean was $23.243$ minutes and the sample standard deviation was $20.40$ minutes. It is desired to determine if the population standard deviation exceeds 20 minutes. Calculate the test statistic for this test of hypothesis.

(Multiple Choice)

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Question 73

Data were collected from the sale of 25 properties by a local real estate agent. The following printout concentrated on the land value variable from the sampled properties. HYPOTHESIS: MEAN X $= x$ X = land - value SAMPLE MEAN OF X =50,740 SAMPLE VARIANCE OF X =273,643,254 SAMPLE SIZE OF X =25 x =46,297 MEANX- =4443 =1.34293 D.F. =24 P-VALUE =0.1918585 P -VALUE /2 =0.0959288 SD. ERROR =3308.43 Find the $p$ -value for testing whether the mean land value differs from $\$ 46,297$ .

(Multiple Choice)

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Question 74

We never conclude "Accept $\mathrm { H } _ { 0 }$ " in a test of hypothesis. This is because:

(Multiple Choice)

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Question 75

Based on the information in the screen below, what would you conclude in the test of $H _ { 0 } : \mu \leq 14 , H _ { \mathrm { a } } : \mu > 14 \text {. Use } \alpha = .01 \text {. }$ $Based on the information in the screen below, what would you conclude in the test of H _ { 0 } : \mu \leq 14 , H _ { \mathrm { a } } : \mu > 14 \text {. Use } \alpha = .01 \text {. }$

(Essay)

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Question 76

The hypotheses for $H _ { 0 } : \mu = 125.4 \text { and } H _ { \mathrm { a } } : \mu \neq 125.4 \text { are tested at } \alpha = .10 \text {. Sketch the }$ appropriate rejection region.

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Question 77

A supermarket sells rotisserie chicken at a fixed price per chicken rather than by the weight of the chicken. The store advertises that the average weight of their chickens is 4.6 pounds. A random sample of 30 of the store's chickens yielded the weights (in pounds) shown below. 4.4 4.7 4.6 4.4 4.5 4.3 4.6 4.5 4.6 4.9 4.6 4.8 4.3 4.4 4.7 4.5 4.2 4.3 4.1 4.0 4.5 4.6 4.2 4.4 4.7 4.8 5.0 4.2 4.1 4.5 Test whether the population mean weight of the chickens is less than 4.6 pounds. Use $\alpha = .05 .$

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Question 78

Under the assumption that $\mu = \mu _ { \mathrm { a } }$ , where $\mu _ { \mathrm { a } }$ is the alternative mean, the distribution of $\bar { x }$ is mound shaped and symmetric about $\mu _ { \mathrm { a } }$ .

(True/False)

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Question 79

It is desired to test H0: µ = 50 against HA: µ ? 50 using ? = 0.10. The population in question is uniformly distributed with a standard deviation of 15. A random sample of 49 will be drawn from this population. If µ is really equal to 48, 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 80

Showing 61 - 80 of 144

The null distribution is the distribution of the test statistic assuming the null hypothesis is true; it mound shaped and symmetric about the null mean $\mu _0$ .

The rejection region refers to the values of the test statistic for which we will reject the alternative hypothesis.

The smaller the p-value in a test of hypothesis, the more significant the results are.

Find the rejection region for the specified hypothesis test. -Consider a test of $\mathrm { H } _ { 0 } : \mu = 9$ . For the following case, give the rejection region for the test in terms of the $z$ -statistic: $\mathrm { H } _ { \mathrm { a } } : \mu > 9 , \alpha = 0.01$

A random sample of $n = 15$ observations is selected from a normal population to test $H _ { 0 } : \mu = 2.89$ against $H _ { \mathrm { a } } : \mu < 2.89$ at $\alpha = .01$ . Specify the rejection region.

We never conclude "Accept $\mathrm { H } _ { 0 }$ " in a test of hypothesis. This is because:

The hypotheses for $H _ { 0 } : \mu = 125.4 \text { and } H _ { \mathrm { a } } : \mu \neq 125.4 \text { are tested at } \alpha = .10 \text {. Sketch the }$ appropriate rejection region.

Under the assumption that $\mu = \mu _ { \mathrm { a } }$ , where $\mu _ { \mathrm { a } }$ is the alternative mean, the distribution of $\bar { x }$ is mound shaped and symmetric about $\mu _ { \mathrm { a } }$ .

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

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

The null distribution is the distribution of the test statistic assuming the null hypothesis is true; it mound shaped and symmetric about the null mean μ0\mu _0μ0​ .

The rejection region refers to the values of the test statistic for which we will reject the alternative hypothesis.

The smaller the p-value in a test of hypothesis, the more significant the results are.

A random sample of n=15n = 15n=15 observations is selected from a normal population to test H0:μ=2.89H _ { 0 } : \mu = 2.89H0​:μ=2.89 against Ha:μ<2.89H _ { \mathrm { a } } : \mu < 2.89Ha​:μ<2.89 at α=.01\alpha = .01α=.01 . Specify the rejection region.

We never conclude "Accept H0\mathrm { H } _ { 0 }H0​ " in a test of hypothesis. This is because:

Based on the information in the screen below, what would you conclude in the test of H0:μ≤14,Ha:μ>14. Use α=.01. H _ { 0 } : \mu \leq 14 , H _ { \mathrm { a } } : \mu > 14 \text {. Use } \alpha = .01 \text {. }H0​:μ≤14,Ha​:μ>14. Use α=.01.

Under the assumption that μ=μa\mu = \mu _ { \mathrm { a } }μ=μa​ , where μa\mu _ { \mathrm { a } }μa​ is the alternative mean, the distribution of xˉ\bar { x }xˉ is mound shaped and symmetric about μa\mu _ { \mathrm { a } }μa​ .

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

The null distribution is the distribution of the test statistic assuming the null hypothesis is true; it mound shaped and symmetric about the null mean $\mu _0$ .

A random sample of $n = 15$ observations is selected from a normal population to test $H _ { 0 } : \mu = 2.89$ against $H _ { \mathrm { a } } : \mu < 2.89$ at $\alpha = .01$ . Specify the rejection region.

We never conclude "Accept $\mathrm { H } _ { 0 }$ " in a test of hypothesis. This is because:

Under the assumption that $\mu = \mu _ { \mathrm { a } }$ , where $\mu _ { \mathrm { a } }$ is the alternative mean, the distribution of $\bar { x }$ is mound shaped and symmetric about $\mu _ { \mathrm { a } }$ .