Question 1

Determine the P-value in a hypothesis test for a population mean with H0: µ = hypothesized value and Ha: µ > hypothesized value.

Accepted Answer

A)  area to the right of the calculated t under the t curve with df = n − 2 
B)  area to the left of the calculated t under the t curve with df = n − 1 
C)  area to the right of the calculated t under the t curve with df = n − 1 
D)  area to the left of the calculated t under the t curve with df = n − 2 
E)  area to the right of the calculated t under the t curve with df = n 
A)  area to the right of the calculated t under the t curve with df = n − 2 
B)  area to the left of the calculated t under the t curve with df = n − 1 
C)  area to the right of the calculated t under the t curve with df = n − 1 
D)  area to the left of the calculated t under the t curve with df = n − 2 
E)  area to the right of the calculated t under the t curve with df = n

Question 2

A journal article summarizes findings of a study on the effect of color on perception of temperature. The article states that experiments involving 32 participants showed an insignificant difference in the effect of orange and violet on subjective feeling of cold. On average, it was 0.3° warmer in the orange room than in the violet one, when participants started to complain about being cold. The sample standard deviation of the differences was s = 0.7. Does this provide convincing evidence that there is no significant difference in the effect of orange and violet on subjective feeling of cold in general? Test the relevant hypotheses using a α = 0.05. ​

Accepted Answer

A)  P-value  0.05, there is convincing evidence that there is no significant difference in the effect of orange and violet on subjective feeling of cold in general. 
D)  P-value < 0.05, there is no convincing evidence that there is no significant difference in the effect of orange and violet on subjective feeling of cold in general. But the mean difference is too small to have a practical importance. 
E)  There is no enough information to make a conclusion. 
A)  P-value  0.05, there is convincing evidence that there is no significant difference in the effect of orange and violet on subjective feeling of cold in general. 
D)  P-value < 0.05, there is no convincing evidence that there is no significant difference in the effect of orange and violet on subjective feeling of cold in general. But the mean difference is too small to have a practical importance. 
E)  There is no enough information to make a conclusion.

Question 3

If the null hypothesis is not rejected, there is strong statistical evidence that the null hypothesis is true.

Accepted Answer

A) True 
 B)False

Question 4

The choice of the alternative hypothesis depends on the objectives of the study.

Accepted Answer

A) True 
 B)False

Question 5

Explain in your own words what a hypothesis test is.

Accepted Answer

In a hypothesis test, we are u

Question 6

Researchers study how the global warming affects the sea level. They wonder whether the mean of yearly differences of the sea level has increased from 4.4 mm using the level of significance α = 0.05. What does the level of significance mean in the context of the study?

Accepted Answer

A)  The probability of a decision that the mean of differences would be less than 4.4 mm, when in fact the mean is still 4.4 mm. 
B)  The probability of a decision that the mean of differences would stay the same, when in fact it would increase. 
C)  The probability of a decision that the mean of differences would be greater than 4.4 mm, no matter whether it would increase in fact or not. 
D)  The probability of a decision that the mean of differences would stay the same, no matter whether it would increase in fact or not. 
E)  The probability of a decision that the mean of differences would be greater than 4.4 mm, when in fact it is still the same. 
A)  The probability of a decision that the mean of differences would be less than 4.4 mm, when in fact the mean is still 4.4 mm. 
B)  The probability of a decision that the mean of differences would stay the same, when in fact it would increase. 
C)  The probability of a decision that the mean of differences would be greater than 4.4 mm, no matter whether it would increase in fact or not. 
D)  The probability of a decision that the mean of differences would stay the same, no matter whether it would increase in fact or not. 
E)  The probability of a decision that the mean of differences would be greater than 4.4 mm, when in fact it is still the same.

Question 7

A company provides portable walkie-talkies to construction crews. Their batteries last, on average, 55 hours of continuous use. The purchasing manager receives a brochure advertising a new brand of batteries with a lower price, but suspects that the lifetime of the batteries may be shorter than the brand currently in use. To test this, the new brand is installed in 8 randomly selected radios. Here are the results for the lifetime of the batteries (in hours): 45 52 56 55 51 57 48 52 Is there sufficient evidence to conclude that the purchasing manager is correct in his conjecture that the new brand has a shorter average lifetime?

Accepted Answer

​ 1) μ = true mean lifetime of new batte

Question 8

A hypothesis test for a population mean uses t statistic, when the population standard deviation σ is known.

Accepted Answer

A) True 
 B)False

Question 9

In your own words, distinguish between "statistical" and "practical" significance.

Accepted Answer

If observing a difference between a samp

Question 10

In cities and towns on the borders between states there is a significant amount of flight across state lines to avoid high state taxes on gasoline. Some states (such as Iowa) have large rivers for borders and tolls to cross the bridges. Do these tolls impede traffic to other states to get cheaper gasoline? To test this hypothesis, an experimental Toll-Free Week will be instituted at the Farmington Bridge, where currently 50 cars per day drive out of the state. Let μ denote the true average number of border crossings per day at Farmington if there were no toll. 
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 = 50 b) Ha : μ > 50 c) A Type

Question 11

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 mean, and given the raw data, describe how you would check the assumptions.

Accepted Answer

There are 2 conditions that need to be m

Question 12

The local airport authority wants to investigate whether the mean of handled passengers per month has increased from 64,500 to plan maintenance works. Determine the valid null and alternative hypotheses.

Accepted Answer

A)  H0:   > 64,500 versus Ha:   = 64,500 
B)  H0: µ = 64,500 versus Ha: µ > 64,500 
C)  H0:   = 64,500 versus Ha: µ > 64,500 
D)  H0: µ > 64,500 versus Ha: µ = 64,500 
E)  H0:   = 64,500 versus Ha:   > 64,500 
A)  H0:   > 64,500 versus Ha:   = 64,500 
B)  H0: µ = 64,500 versus Ha: µ > 64,500 
C)  H0:   = 64,500 versus Ha: µ > 64,500 
D)  H0: µ > 64,500 versus Ha: µ = 64,500 
E)  H0:   = 64,500 versus Ha:   > 64,500

Question 13

Which information will be comprehensive when summarizing the results of a hypothesis test? ​

Accepted Answer

A)  Hypotheses, test procedure, conclusion in context. 
B)  Hypotheses, test procedure, test statistic, conclusion in context. 
C)  Sample size, hypotheses, conclusion in context. 
D)  Hypotheses, test statistic, boxplot, normal probability plot, conclusion in context. 
E)  Hypotheses, significance level, test power, conclusion in context. 
A)  Hypotheses, test procedure, conclusion in context. 
B)  Hypotheses, test procedure, test statistic, conclusion in context. 
C)  Sample size, hypotheses, conclusion in context. 
D)  Hypotheses, test statistic, boxplot, normal probability plot, conclusion in context. 
E)  Hypotheses, significance level, test power, conclusion in context.

Question 14

The power of a test is the probability of failing to reject the null hypothesis.

Accepted Answer

A) True 
 B)False

Question 15

According to a survey conducted 5 years ago, the proportion of left-handed students at a university was 0.12. Has the proportion increased over the years? A random sample of 50 students was chosen, 9 of whom were left-handed. Use the output from the Shiny app "Randomization Test for One Proportion" to complete an appropriate hypothesis test. ​   ​ Interpret the obtained results, using a significance level of 0.1. ​

Accepted Answer

A)  There is convincing evidence that the proportion of left-handed students has decreased. 
B)  There is convincing evidence that the proportion of left-handed students has increased. 
C)  There is no convincing evidence that the proportion of left-handed students has increased. 
D)  The proportion of left-handed students has certainly remained the same. 
E)  The sample is too small to make a conclusion. 
A)  There is convincing evidence that the proportion of left-handed students has decreased. 
B)  There is convincing evidence that the proportion of left-handed students has increased. 
C)  There is no convincing evidence that the proportion of left-handed students has increased. 
D)  The proportion of left-handed students has certainly remained the same. 
E)  The sample is too small to make a conclusion.

Question 16

The Environmental Protection Agency (EPA) is charged with monitoring the environment. One aspect of this is keeping track of "acid rain," a broad term describing the fall of water through an acidic atmosphere. Acidity is measured on the pH scale, where pure water has a pH of 7.0. Normal rain is slightly acidic because carbon dioxide dissolves into it, and thus has a pH of about 5.5. (A lower pH indicates greater acidity.) Suppose the EPA wishes to determine whether a particular area is subject to acid rain. Let μ denote the true average for pH in this area. 
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 = 5.5 b) Ha : μ < 5.5 c) Type

Question 17

It is customary to say that the result of a hypothesis test is statistically significant when the P-value is smaller than α.

Accepted Answer

A) True 
 B)False

Determine the P-value in a hypothesis test for a population mean with H₀: µ = hypothesized value and Ha: µ > hypothesized value.

If the null hypothesis is not rejected, there is strong statistical evidence that the null hypothesis is true.

The choice of the alternative hypothesis depends on the objectives of the study.

Explain in your own words what a hypothesis test is.

Researchers study how the global warming affects the sea level. They wonder whether the mean of yearly differences of the sea level has increased from 4.4 mm using the level of significance α = 0.05. What does the level of significance mean in the context of the study?

A hypothesis test for a population mean uses t statistic, when the population standard deviation σ is known.

In your own words, distinguish between "statistical" and "practical" significance.

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 mean, and given the raw data, describe how you would check the assumptions.

The local airport authority wants to investigate whether the mean of handled passengers per month has increased from 64,500 to plan maintenance works. Determine the valid null and alternative hypotheses.

Which information will be comprehensive when summarizing the results of a hypothesis test?

The power of a test is the probability of failing to reject the null hypothesis.

It is customary to say that the result of a hypothesis test is statistically significant when the P-value is smaller than α.

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

Determine the P-value in a hypothesis test for a population mean with H0: µ = hypothesized value and Ha: µ > hypothesized value.

If the null hypothesis is not rejected, there is strong statistical evidence that the null hypothesis is true.

The choice of the alternative hypothesis depends on the objectives of the study.

Explain in your own words what a hypothesis test is.

Researchers study how the global warming affects the sea level. They wonder whether the mean of yearly differences of the sea level has increased from 4.4 mm using the level of significance α = 0.05. What does the level of significance mean in the context of the study?

A hypothesis test for a population mean uses t statistic, when the population standard deviation σ is known.

In your own words, distinguish between "statistical" and "practical" significance.

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 mean, and given the raw data, describe how you would check the assumptions.

The local airport authority wants to investigate whether the mean of handled passengers per month has increased from 64,500 to plan maintenance works. Determine the valid null and alternative hypotheses.

Which information will be comprehensive when summarizing the results of a hypothesis test? ​

The power of a test is the probability of failing to reject the null hypothesis.

It is customary to say that the result of a hypothesis test is statistically significant when the P-value is smaller than α.

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

Determine the P-value in a hypothesis test for a population mean with H₀: µ = hypothesized value and Ha: µ > hypothesized value.

Which information will be comprehensive when summarizing the results of a hypothesis test?