Question 1

Small P-values indicate that the observed sample is inconsistent with the null hypothesis.

Accepted Answer

A) True 
 B)False  True

Question 2

The university conducts a study designed to find out the proportion of students who have conversational fluency in two or more foreign languages. The previous study provided the result of 7%. The test is carried out using data from a random sample of n = 72. In this sample, the number of students who speak two or more foreign languages is 10. Complete an appropriate hypothesis test with α = 0.05 and make a conclusion using the output from the Shiny app "Exact Binomial Test for One Proportion". ​   ​

Accepted Answer

A)  The proportion of students who speak two or more foreign languages has certainly remained the same. 
B)  There is convincing evidence that the proportion of students who speak two or more foreign languages has decreased. 
C)  There is no convincing evidence that the proportion of students who speak two or more foreign languages has increased. 
D)  There is convincing evidence that the proportion of students who speak two or more foreign languages has increased. 
E)  The sample is too small to make a conclusion. 
A)  The proportion of students who speak two or more foreign languages has certainly remained the same. 
B)  There is convincing evidence that the proportion of students who speak two or more foreign languages has decreased. 
C)  There is no convincing evidence that the proportion of students who speak two or more foreign languages has increased. 
D)  There is convincing evidence that the proportion of students who speak two or more foreign languages has increased. 
E)  The sample is too small to make a conclusion. D

Question 3

For tests of hypotheses about μ, β decreases as the sample size increases if the level of significance stays the same.

Accepted Answer

A) True 
 B)False  True

Question 4

The level of significance of a test is the probability of making a type I error, given that the null hypothesis is true.

Accepted Answer

A) True 
 B)False

Question 5

The statement s2 = 100 is a statistical hypothesis.

Accepted Answer

A) True 
 B)False

Question 6

β is called the observed significance level.

Accepted Answer

A) True 
 B)False

Question 7

One of the early decisions that must be made when performing a hypothesis test is the choice of significance level. Briefly describe the considerations that go into making this decision.

Accepted Answer

To decide on the significance level, the

Question 8

Explain in your own words the distinction between a null and alternative hypothesis.

Accepted Answer

The null hypothesis is the cla

Question 9

Psychologists have noted that people tend make classifications based on their "typicality." For example, a dog is more readily classified as a mammal than is a whale, because dogs are "more typical" of mammals than are whales. Previous large-scale studies have established the following for songbirds such as robins: when young children are shown a picture of a songbird and asked if it is a bird they respond "yes" in an average of 750 milliseconds. Do children regard chickens as representative of birds? If so, are they more representative or less representative of birds than are songbirds? Let μ represent the mean time it takes children to respond to a question about whether a chicken is a bird. The investigators wish to determine whether the classification time differs from the time needed to classify songbirds. 
a) What is the appropriate null hypothesis? 
b) What is the appropriate alternative hypothesis? 
c) In your own words, distinguish between a Type I and a Type II error in this context.

Accepted Answer

a) H₀ : μ = 750 b) Ha : μ ≠ 750 c) A Ty

Question 10

Children as young as 2 years of age, upon seeing an object placed under a pillow in a familiar setting at home, will understand to look for it after an interval of time and be able to find it. Investigators believe this capability will be less pronounced in a laboratory situation, where the child is away from the familiar setting of home. Let π denote the proportion of 2-year-olds than have this understanding in the home situation, and suppose that π = .35. The investigators wish to determine whether the proportion that remembers is less when the child is away from home. 
a) What is the appropriate null hypothesis? 
b) What is the appropriate alternative hypothesis? 
c) In your own words, distinguish between a Type I and a Type II error in this context.

Accepted Answer

a) H₀ : π = .35 b) Ha : π < .35 c) A Ty

Question 11

City officials will conduct a study of the proportion of vehicle owners among the neighborhood residents. The study, which was held 5 years ago, provided the result of 50%. Suppose that a random sample of size n = 20 with the obtained proportion 0.45 is used to decide if the proportion has increased for the whole neighborhood. Calculate the P-value using the appropriate test to analyze these data. ​

Accepted Answer

A)  A large-sample z test can be used. 0.04 < P-value < 0.06. 
B)  Both a randomization test for one proportion or a large-sample z test can be used. 0.04 < P-value < 0.06. 
C)  A large-sample z test, a randomization test for one proportion, or an exact binomial test for one proportion can be used. 0.06 < P-value < 0.08. 
D)  Both a randomization test for one proportion or an exact binomial test for one proportion can be used. 0.06 < P-value < 0.08. 
E)  Both a randomization test for one proportion or an exact binomial test for one proportion can be used. 0.09 < P-value < 0.1. 
A)  A large-sample z test can be used. 0.04 < P-value < 0.06. 
B)  Both a randomization test for one proportion or a large-sample z test can be used. 0.04 < P-value < 0.06. 
C)  A large-sample z test, a randomization test for one proportion, or an exact binomial test for one proportion can be used. 0.06 < P-value < 0.08. 
D)  Both a randomization test for one proportion or an exact binomial test for one proportion can be used. 0.06 < P-value < 0.08. 
E)  Both a randomization test for one proportion or an exact binomial test for one proportion can be used. 0.09 < P-value < 0.1.

Question 12

Select the correct statement about the test power.

Accepted Answer

A)  When Ha is false, power = 1 - β. 
B)  When H0 is true, power = 1 - α. 
C)  When H0 is false, power = 1 - β. 
D)  When H0 is false, power = 1 - α. 
E)  When H0 is true, power = 1 - β. 
A)  When Ha is false, power = 1 - β. 
B)  When H0 is true, power = 1 - α. 
C)  When H0 is false, power = 1 - β. 
D)  When H0 is false, power = 1 - α. 
E)  When H0 is true, power = 1 - β.

Question 13

A type II error is made by failing to reject a false null hypothesis.

Accepted Answer

A) True 
 B)False

Question 14

Suppose that a study has been published linking arsenic, which is commonly found in tap water, to increased cancer rates. The study also stated that arsenic levels below 10 ppm could be considered harmless. Suppose that residents of Hacienda Heights, CA, are worried about the arsenic level in the local tap water. 
a) What hypothesis should they test? 
b) Describe a Type I and Type II error in this context.

Accepted Answer

a) H₀ : μ = 10 H_a : μ > 10 b) A Type I err

Question 15

The average wingspan of a crowned eagle is supposed to be 40 in. A random sample of 31 crowned eagles raised in captivity gave the following results:   = 39.5, s = 1.8. Do the data indicate that the wingspan of captive eagles is less than that of those that live in the wild? Use the significance level α = 0.05.

Accepted Answer

A)  P-value  α, thus the null hypothesis is rejected. There is convincing evidence that the wingspan of captive eagles is less than that of those that live in the wild. 
C)  P-value  α, thus the null hypothesis is not rejected. There is no sufficient evidence to conclude that the wingspan of captive eagles is less than that of those that live in the wild. 
A)  P-value  α, thus the null hypothesis is rejected. There is convincing evidence that the wingspan of captive eagles is less than that of those that live in the wild. 
C)  P-value  α, thus the null hypothesis is not rejected. There is no sufficient evidence to conclude that the wingspan of captive eagles is less than that of those that live in the wild.

Question 16

All other things being equal, choosing a smaller value of α will increase the probability of making a type II error.

Accepted Answer

A) True 
 B)False

Question 17

When performing tests of hypotheses, there are assumptions that must be met in order for the test to be appropriate. For the test of a hypothesis about a population proportion, describe how you would check the assumptions.

Accepted Answer

There are 2 conditions which need to be

Question 18

The average sleeping time required for teenagers who experience major physical exertion is about 8 hours. Do the members of the school sport teams sleep enough? Sleeping time for a random sample of 16 sport team members was obtained. ​   ​ Which test is appropriate for this sample? ​

Accepted Answer

A)  A one-sample t test. 
B)  A large-sample z test and a randomization test for a population mean. 
C)  A large-sample z test. 
D)  A randomization test for a population mean and a one-sample t test. 
E)  A randomization test for a population mean. 
A)  A one-sample t test. 
B)  A large-sample z test and a randomization test for a population mean. 
C)  A large-sample z test. 
D)  A randomization test for a population mean and a one-sample t test. 
E)  A randomization test for a population mean.

Question 19

A cooler bag producing company claims that their coolers keep products cold for 12 hours. A test of hypotheses H0: µ = 12 versus Ha: µ < 12 is based on a sample of size n = 33. Suppose that σ is known to be 0.6 and a significance level of 0.05 will be used. Determine the power of the test and interpret the result when µ = 11.75.

Accepted Answer

A)  The power of the test is 0.23, which means that 23% of the samples will result in a conclusion to reject H0: µ = 12 when the true µ is 11.75. 
B)  The power of the test is 0.01, which means that 1% of the samples will result in a conclusion to reject H0: µ = 12 when the true µ is 11.75. 
C)  The power of the test is 0.77, which means that 77% of the samples will result in a conclusion to reject H0: µ = 12 when the true µ is 11.75. 
D)  The power of the test is 0.99, which means that 99% of the samples will result in a conclusion to reject H0: µ = 12 when the true µ is 11.75. 
E)  The power of the test is 0.67, which means that 67% of the samples will result in a conclusion to reject H0: µ = 12 when the true µ is 11.75. 
A)  The power of the test is 0.23, which means that 23% of the samples will result in a conclusion to reject H0: µ = 12 when the true µ is 11.75. 
B)  The power of the test is 0.01, which means that 1% of the samples will result in a conclusion to reject H0: µ = 12 when the true µ is 11.75. 
C)  The power of the test is 0.77, which means that 77% of the samples will result in a conclusion to reject H0: µ = 12 when the true µ is 11.75. 
D)  The power of the test is 0.99, which means that 99% of the samples will result in a conclusion to reject H0: µ = 12 when the true µ is 11.75. 
E)  The power of the test is 0.67, which means that 67% of the samples will result in a conclusion to reject H0: µ = 12 when the true µ is 11.75.

Question 20

Do the students in the campus spend less on food than an average American resident does? To answer this question, expenses of 25 students were calculated. ​   ​ Food expenses of an average American person are $220. Interpret the output of the Shiny app "Randomization test for a population mean" using a significance level of 0.05. ​   ​

Accepted Answer

A)  There is convincing evidence that students' expenses are less than the national average. 
B)  There is no convincing evidence that students' expenses are less than the national average. 
C)  There is convincing evidence that students' expenses are equal to the national average. 
D)  Students' expenses are certainly equal to the national average. 
E)  The population is too large to make a conclusion. 
A)  There is convincing evidence that students' expenses are less than the national average. 
B)  There is no convincing evidence that students' expenses are less than the national average. 
C)  There is convincing evidence that students' expenses are equal to the national average. 
D)  Students' expenses are certainly equal to the national average. 
E)  The population is too large to make a conclusion.

Small P-values indicate that the observed sample is inconsistent with the null hypothesis.

For tests of hypotheses about μ, β decreases as the sample size increases if the level of significance stays the same.

The level of significance of a test is the probability of making a type I error, given that the null hypothesis is true.

The statement s² = 100 is a statistical hypothesis.

β is called the observed significance level.

One of the early decisions that must be made when performing a hypothesis test is the choice of significance level. Briefly describe the considerations that go into making this decision.

Explain in your own words the distinction between a null and alternative hypothesis.

Select the correct statement about the test power.

A type II error is made by failing to reject a false null hypothesis.

All other things being equal, choosing a smaller value of α will increase the probability of making a type II error.

When performing tests of hypotheses, there are assumptions that must be met in order for the test to be appropriate. For the test of a hypothesis about a population proportion, describe how you would check the assumptions.

The average sleeping time required for teenagers who experience major physical exertion is about 8 hours. Do the members of the school sport teams sleep enough? Sleeping time for a random sample of 16 sport team members was obtained. Which test is appropriate for this sample?

The Role of Statistics and the Data Analysis Process

Collecting Data Sensibly

Graphical Methods for Describing Data

Numerical Methods for Describing Data

Summarizing Bivariate Data

Probability

Random Variables and Probability Distributions

Sampling Variability and Sampling Distributions

Estimation Using a Single Sample

Comparing Two Populations or Treatments

The Analysis of Categorical Data and Goodness-Of-Fit Tests

Simple Linear Regression and Correlation: Inferential Methods

Multiple Regression Analysis

Analysis of Variance

Nonparametric Distribution-Free Statistical Methods

Filters

Exam 10: Hypothesis Testing Using a Single Sample

Small P-values indicate that the observed sample is inconsistent with the null hypothesis.

For tests of hypotheses about μ, β decreases as the sample size increases if the level of significance stays the same.

The level of significance of a test is the probability of making a type I error, given that the null hypothesis is true.

The statement s2 = 100 is a statistical hypothesis.

β is called the observed significance level.

One of the early decisions that must be made when performing a hypothesis test is the choice of significance level. Briefly describe the considerations that go into making this decision.

Explain in your own words the distinction between a null and alternative hypothesis.

Select the correct statement about the test power.

A type II error is made by failing to reject a false null hypothesis.

All other things being equal, choosing a smaller value of α will increase the probability of making a type II error.

When performing tests of hypotheses, there are assumptions that must be met in order for the test to be appropriate. For the test of a hypothesis about a population proportion, describe how you would check the assumptions.

The average sleeping time required for teenagers who experience major physical exertion is about 8 hours. Do the members of the school sport teams sleep enough? Sleeping time for a random sample of 16 sport team members was obtained. ​ ​ Which test is appropriate for this sample? ​

The Role of Statistics and the Data Analysis Process

Collecting Data Sensibly

Graphical Methods for Describing Data

Numerical Methods for Describing Data

Summarizing Bivariate Data

Probability

Random Variables and Probability Distributions

Sampling Variability and Sampling Distributions

Estimation Using a Single Sample

Comparing Two Populations or Treatments

The Analysis of Categorical Data and Goodness-Of-Fit Tests

Simple Linear Regression and Correlation: Inferential Methods

Multiple Regression Analysis

Analysis of Variance

Nonparametric Distribution-Free Statistical Methods

Filters

The statement s² = 100 is a statistical hypothesis.

The average sleeping time required for teenagers who experience major physical exertion is about 8 hours. Do the members of the school sport teams sleep enough? Sleeping time for a random sample of 16 sport team members was obtained. Which test is appropriate for this sample?