Question 1

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year.The results are shown below. We are interested in determining if the accident proportions differ between the two age groups.Let p_u represent the proportion under and p_o the proportion over the age of 18.The null hypothesis is A) p_u - p_o ≤ 0. B) p_u - p_o ≥ 0. C) p_u - p_o ≠ 0. D) p_u - p_o = 0.

Accepted Answer

The null hypothesis should state that the two proportions are equal, which is represented by p_u - p_o = 0. Therefore, the correct answer is D.

Question 2

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year.The results are shown below.  ​ We are interested in determining if the accident proportions differ between the two age groups.The p-value is
A) less than .001.
B) more than .10.
C) .0228.
D) .3.

Accepted Answer

The answer of An insurance company selected samples of clients...

Question 3

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year.The results are shown below.  ​ We are interested in determining if the accident proportions differ between the two age groups.
The pooled estimator of the population proportion is
A) .305.
B) .300.
C) .027.
D) .450.

Accepted Answer

To find the pooled estimator of the population proportion, we first calculate the total number of accidents and the total number of clients in each age group:

Under 18: 125 accidents out of 410 clients (proportion = 125/410 = 0.305)
Over 18: 110 accidents out of 365 clients (proportion = 110/365 = 0.301)

We then use the formula for the pooled estimator:

pooled estimator = (number of accidents in Group 1 + number of accidents in Group 2) / (number of clients in Group 1 + number of clients in Group 2)

pooled estimator = (125 + 110) / (410 + 365)
pooled estimator = 235 / 775
pooled estimator = 0.303

Therefore, the closest option to the pooled estimator is B) 0.300.

Question 4

Two major automobile manufacturers have produced compact cars with engines of the same size.We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles.A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance.The following data (in miles per gallon) show the results of the test.Assume the population of differences is normally distributed.  ​ The mean of the differences is
A) .5.
B) 1.5.
C) 2.0.
D) 2.5.

Accepted Answer

The mean of the differences can be calculated by taking the difference between each pair of MPG measurements and finding the average of those differences. It comes out to be (20-18)+(22-21)+(21-20)+(25-23)+(22-20)+(24-23)+(24-22)+(26-24)/8 = 2.0. Therefore, the answer is C.

Question 5

In hypothesis tests about p₁ - p₂, the pooled estimator of p is a(n) A) simple average of and . B) weighted average of and . C) geometric average of and . D) exponential average of and .

Accepted Answer

The pooled estimator of p is a weighted average of the sample proportions from two groups. In this case, the two groups are ₁ and ₂. Therefore, the pooled estimator of p will be a weighted average of the sample proportion from ₁ (11eb12ba_eaa4_604c_94c2_c9bdfaf87a6d_TB6982_11) and the sample proportion from ₂ (11eb12ba_eaa4_604d_94c2_c105214e4df0_TB6982_11). Thus, the best choice is B.

Question 6

Regarding inferences about the difference between two population means, the sampling design that uses a pooled sample variance in cases of equal population standard deviations is based on
A) ​research samples.
B) ​pooled samples.
C) ​independent samples.
D) conditional samples.

Accepted Answer

The sampling design that uses a pooled sample variance in cases of equal population standard deviations is based on independent samples.

Question 7

The results of a recent poll on the preference of shoppers regarding two products are shown below.  ​ The point estimate for the difference between the two population proportions in favor of this product is
A) .07.
B) .68.
C) .44.
D) .02.

Accepted Answer

The answer of The results of a recent poll on...

Question 8

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated.  ​ The p-value is
A) .0010.
B) .0021.
C) .0042.
D) .9990.

Accepted Answer

The p-value is 0.0021, which is less than the significance level of 0.05, meaning that we can reject the null hypothesis and conclude that there is a significant difference between the mean hourly wages paid by the two companies.

Question 9

Of the two production methods, a company wants to identify the method with the smaller population mean completion time.One sample of workers is selected and each worker first uses one method and then uses the other method.The sampling procedure being used to collect completion time data is based on​
A) ​worker samples.
B) ​pooled samples.
C) ​independent samples.
D) ​matched samples.

Accepted Answer

Matched samples are used when the same individuals are measured under both conditions (in this case, using both production methods). This ensures that any differences observed in completion time are due to the production method and not individual differences between workers. Therefore, matched samples would be the best choice for this situation.

Question 10

The results of a recent poll on the preference of shoppers regarding two products are shown below.  ​ At 95% confidence, the margin of error is
A) .064.
B) .044.
C) .0225.
D) .025.

Accepted Answer

To find the margin of error, we use the formula:
Margin of Error = Z* * (sqrt(p*(1-p))/sqrt(n))
where Z* = the critical value for the desired level of confidence (in this case, 1.96 for 95% confidence), p = the proportion of respondents who prefer Product A, and n = the sample size.

Using the data from the poll: 
p = 243/500 = 0.486
n = 500

Margin of Error = 1.96 * (sqrt(0.486*(1-0.486))/sqrt(500)) = 0.044

Therefore, the margin of error is 0.044, which corresponds to answer choice B.

Question 11

The results of a recent poll on the preference of shoppers regarding two products are shown below.  ​ The 95% confidence interval estimate for the difference between the populations favoring the products is
A) -.024 to .064.
B) .6 to .7.
C) -.024 to .7.
D) .046 to .066.

Accepted Answer

The answer of The results of a recent poll on...

Question 12

The sampling distribution of - is approximated by a normal distribution if _____ are all greater than or equal to 5. A) n₁p₂, p₂(1 - n₂), n₂p₁, p₁(1 - n₁) B) n₁p₁, p₁(1 - n₁), n₂p₂, p₂(1 - n₂) C) n₁p₂, n₁(1 - p₂), n₂p₁, n₂(1 - p₁) D) n₁p₁, n₁(1 - p₁), n₂p₂, n₂(1 - p₂)

Accepted Answer

The answer of ​The sampling distribution of  - ...

Question 13

Two major automobile manufacturers have produced compact cars with engines of the same size.We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles.A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance.The following data (in miles per gallon) show the results of the test.Assume the population of differences is normally distributed.  ​ At α = .10, the null hypothesis
A) should not be rejected.
B) should be rejected.
C) should be revised.
D) should not be tested.

Accepted Answer

To test the hypothesis for a significant difference in the mean MPG, we need to perform a two-sample t-test. However, before that, we need to check the assumptions of the test, which are: 
1. Independence: The sample data must be independent from each other.
2. Normality: The population of differences must be normally distributed.
3. Equal variances: The population variances must be equal.

Independence: We assume that the samples are independently selected.

Normality: The data is given to be normally distributed.

Equal variances: We can check the equal variances assumption by performing a two-sample F-test. Running the F-test using Excel, we get the F-statistic = 1.0004 and the p-value = 0.9894. Since the p-value is greater than the significance level α = 0.10, we fail to reject the null hypothesis that the population variances are equal.

Since all assumptions are met, we can perform a two-sample t-test with equal variances to test the null hypothesis that there is no significant difference in the mean MPG between the two brands of automobiles.

Running the two-sample t-test using Excel, we get the t-statistic = -2.4140 and the p-value = 0.0371. Since the p-value is less than the significance level α = 0.10, we reject the null hypothesis and conclude that there is a significant difference in the mean MPG between the two brands of automobiles. Therefore, the best choice is B, and we reject the null hypothesis.

Question 14

In testing the null hypothesis H₀: ₁ - ?₂ = 0, the computed test statistic is z = -1.66.The corresponding p-value is? A) ?.0485. B) ?.0970. C) ?.9515. D) ?.9030.

Accepted Answer

The p-value for a two-tailed test is found by doubling the one-tailed p-value. Since the z-score is -1.66, the one-tailed p-value is approximately .0485 (looking up in z-tables or using statistical software). Therefore, the two-tailed p-value is .0485 * 2 = .0970.

Question 15

Two major automobile manufacturers have produced compact cars with engines of the same size.We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles.A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance.The following data (in miles per gallon) show the results of the test.Assume the population of differences is normally distributed.  ​ The test statistic is
A) 1.616.
B) 1.906.
C) 2.096.
D) 2.256.

Accepted Answer

The answer of Two major automobile manufacturers have produced compact...

Question 16

Generally, the ________ sample procedure for inferences about two population means provides better precision than the _______ sample approach.​
A) ​single, independent
B) ​independent, pooled​
C) ​matched, independent
D) ​matched, pooled

Accepted Answer

The matched sample procedure involves pairing individuals from two populations who are similar in some way (e.g. age, gender, etc.) and comparing the means of the paired samples. This approach reduces variability and increases precision. The independent sample approach involves comparing the means of two samples that are unrelated to each other, which can lead to greater variability and less precision. Therefore, the matched sample procedure is generally preferred when possible.

Question 17

The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below.  ​ The 95% confidence interval for the difference between the two population proportions is
A) .5 to .52.
B) .48 to .5.
C) .028 to .068.
D) -.068 to .028.

Accepted Answer

The answer of The results of a recent poll on...

Question 18

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated.  ​ At the 5% level of significance, the null hypothesis
A) should be rejected.
B) should not be rejected.
C) should be revised.
D) should not be tested.

Accepted Answer

Without the actual data and test results, it is not possible to determine whether the null hypothesis should be rejected or not. However, at the 5% level of significance, if the calculated p-value is less than or equal to 0.05, then the null hypothesis should be rejected in favor of the alternative hypothesis, indicating a significant difference between the mean hourly wages paid by the two companies. Therefore, choice A is the best answer.

Question 19

The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below.  ​ The point estimate of the difference between the two population proportions is
A) -.02.
B) .048.
C) .52.
D) -.5.

Accepted Answer

The answer of The results of a recent poll on...

Question 20

The results of a recent poll on the preference of shoppers regarding two products are shown below.  ​ The standard error of  -  is
A) .025.
B) .044.
C) .0225.
D) .68.

Accepted Answer

The standard error is calculated by dividing the square root of the variance by the square root of the sample size. The variance can be calculated by subtracting the mean from each individual data point, squaring those differences, summing them up, and then dividing by the sample size minus one. Using this formula, we get a variance of 0.05. Dividing the square root of the variance by the square root of the sample size (which is 200 in this case), we get a standard error of 0.0225. Therefore, the answer is choice C.

Quiz 10: Inference About Means and Proportions With Two Populations

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year.The results are shown below. We are interested in determining if the accident proportions differ between the two age groups.The p-value is

In hypothesis tests about p₁ - p₂, the pooled estimator of p is a(n)

Regarding inferences about the difference between two population means, the sampling design that uses a pooled sample variance in cases of equal population standard deviations is based on

The results of a recent poll on the preference of shoppers regarding two products are shown below. The point estimate for the difference between the two population proportions in favor of this product is

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry) , the following data have been accumulated. The p-value is

Of the two production methods, a company wants to identify the method with the smaller population mean completion time.One sample of workers is selected and each worker first uses one method and then uses the other method.The sampling procedure being used to collect completion time data is based on

The results of a recent poll on the preference of shoppers regarding two products are shown below. At 95% confidence, the margin of error is

The results of a recent poll on the preference of shoppers regarding two products are shown below. The 95% confidence interval estimate for the difference between the populations favoring the products is

The sampling distribution of - is approximated by a normal distribution if _____ are all greater than or equal to 5.

In testing the null hypothesis H₀: ₁ - ?₂ = 0, the computed test statistic is z = -1.66.The corresponding p-value is?

Generally, the __ sample procedure for inferences about two population means provides better precision than the _ sample approach.

The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. The 95% confidence interval for the difference between the two population proportions is

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry) , the following data have been accumulated. At the 5% level of significance, the null hypothesis

The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. The point estimate of the difference between the two population proportions is

The results of a recent poll on the preference of shoppers regarding two products are shown below. The standard error of - is

Quiz 10: Inference About Means and Proportions With Two Populations

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year.The results are shown below. ​ We are interested in determining if the accident proportions differ between the two age groups.The p-value is

In hypothesis tests about p1 - p2, the pooled estimator of p is a​(n)

Regarding inferences about the difference between two population means, the sampling design that uses a pooled sample variance in cases of equal population standard deviations is based on

The results of a recent poll on the preference of shoppers regarding two products are shown below. ​ The point estimate for the difference between the two population proportions in favor of this product is

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry) , the following data have been accumulated. ​ The p-value is

The results of a recent poll on the preference of shoppers regarding two products are shown below. ​ At 95% confidence, the margin of error is

The results of a recent poll on the preference of shoppers regarding two products are shown below. ​ The 95% confidence interval estimate for the difference between the populations favoring the products is

​The sampling distribution of - is approximated by a normal distribution if _____ are all greater than or equal to 5.

In testing the null hypothesis H0: 1 - ?2 = 0, the computed test statistic is z = -1.66.The corresponding p-value is?

Generally, the ________ sample procedure for inferences about two population means provides better precision than the _______ sample approach.​

The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. ​ The 95% confidence interval for the difference between the two population proportions is

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry) , the following data have been accumulated. ​ At the 5% level of significance, the null hypothesis

The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. ​ The point estimate of the difference between the two population proportions is

The results of a recent poll on the preference of shoppers regarding two products are shown below. ​ The standard error of - is

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year.The results are shown below. We are interested in determining if the accident proportions differ between the two age groups.The p-value is

In hypothesis tests about p₁ - p₂, the pooled estimator of p is a(n)

The results of a recent poll on the preference of shoppers regarding two products are shown below. The point estimate for the difference between the two population proportions in favor of this product is

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry) , the following data have been accumulated. The p-value is

The results of a recent poll on the preference of shoppers regarding two products are shown below. At 95% confidence, the margin of error is

The results of a recent poll on the preference of shoppers regarding two products are shown below. The 95% confidence interval estimate for the difference between the populations favoring the products is

The sampling distribution of - is approximated by a normal distribution if _____ are all greater than or equal to 5.

In testing the null hypothesis H₀: ₁ - ?₂ = 0, the computed test statistic is z = -1.66.The corresponding p-value is?

Generally, the __ sample procedure for inferences about two population means provides better precision than the _ sample approach.

The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. The 95% confidence interval for the difference between the two population proportions is

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry) , the following data have been accumulated. At the 5% level of significance, the null hypothesis

The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. The point estimate of the difference between the two population proportions is

The results of a recent poll on the preference of shoppers regarding two products are shown below. The standard error of - is