Question 1

Many hotel chains that offer free Wi- Fi service to their customers have experienced increasing demand for Internet bandwidth and increasing costs. Marriott International would like to test the hypothesis that the proportion of customers that are carrying two Wi- Fi devices exceeds 0.60. A random sample of 120 Marriott customers found that 78 have two Wi- Fi devices. Marriott International would like to set α = 0.01. The test statistic for this hypothesis test would be --------. A)z_p = 2.03 B)z_p =1.80 C)z_p = 1.58 D)z_p = 1.12

Accepted Answer

The test statistic for this hypothesis test is calculated using the formula for a one-sample z-test for proportions: $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$, where $\hat{p}$ is the sample proportion, $p_0$ is the hypothesized population proportion, and $n$ is the sample size. Here, $\hat{p} = \frac{78}{120} = 0.65$, $p_0 = 0.60$, and $n = 120$. Plugging these values into the formula gives a z-value of approximately 2.03, which corresponds to choice A.

Question 2

Many franchisers favor owners who operate multiple stores by providing them with preferential treatment. Suppose the Small Business Administration would like to perform a hypothesis test to investigate if 80% of franchisees own only one location using α = 0.05. A random sample of 120 franchisees found that 85 owned only one store. The test statistic for this hypothesis test would be . A)z_p = - 1.17 B)z_p = 2.52 C)z_p = 1.46 D)z_p = - 1.82

Accepted Answer

B

Question 3

YouTube would like to test the hypothesis that the average length of an online video watched by a user is more than 8 minutes. A random sample of 37 people watched online videos that averaged 8.7 minutes in length. It is believed that the population standard deviation for the length of online videos is 2.5 minutes. YouTube would like to set ? = 0.02. The test statistic for this hypothesis test would be --------- .
A)$$t \bar { x }$$ = 1.89
B)$$z \bar { x }$$= 2.23
C)$$z \bar { x }$$= 1.70
D)$$t \bar { x }$$ = 2.06

Accepted Answer

C

Question 4

A professor would like to test the hypothesis that the average number of minutes that a student needs to complete a statistics exam is equal to 45 minutes. A Type II error would occur if the professor concludes that the average exam time is ___________.
A)equal to 45 minutes when, in reality, the average time is not equal to 45 minutes.
B)not equal to 45 minutes when, in reality, the average time is greater than 45 minutes.
C)not equal to 45 minutes when, in reality, the average time is equal to 45 minutes.
D)equal to 45 minutes when, in reality, the average time is less than 45 minutes.

Accepted Answer

A Type II error occurs when the null hypothesis is not rejected when it is false. In this context, it means failing to detect that the average time is not 45 minutes when it actually isn't.

Question 5

Many franchisers favor owners who operate multiple stores by providing them with preferential treatment. Suppose the Small Business Administration would like to perform a hypothesis test to investigate if 80% of franchisees own only one location using α = 0.05. A random sample of 120 franchisees found that 85 owned only one store. The p- value for this hypothesis test would be------ .
A)0.0118
B)0.0759
C)0.1236
D)0.0320

Accepted Answer

The p-value of 0.0118 indicates that there is a statistically significant difference from the hypothesized proportion of 80% (or 0.80) of franchisees owning only one location, given that the sample proportion is 85/120 = 0.7083 and the significance level is α = 0.05. This p-value is calculated using a hypothesis test for a proportion, comparing the observed sample proportion to the hypothesized proportion.

Question 6

The Department of Education would like to test the hypothesis that the average debt load of graduating students with a Bachelor's degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The Department of Education would like to set α = 0.05. The conclusion for this hypothesis test would be that because the absolute value of the test statistic is______
A)less than the absolute value of the critical value, we cannot conclude that the average student debt load is not equal to $17,000.
B)more than the absolute value of the critical value, we can conclude that the average student debt load is not equal to $17,000.
C)more than the absolute value of the critical value, we cannot conclude that the average student debt load is not equal to $17,000.
D)less than the absolute value of the critical value, we can conclude that the average student debt load is not equal to $17,000.

Accepted Answer

The answer of The Department of Education would like to...

Question 7

YouTube would like to test the hypothesis that the average length of an online video watched by a user is more than 8 minutes. A random sample of 37 people watched online videos that averaged 8.7 minutes in length. It is believed that the population standard deviation for the length of online videos is 2.5 minutes. YouTube would like to set α = 0.02. The p- value for this hypothesis test would be -------.
A)0.0245
B)0.0719
C)0.0150
D)0.0446

Accepted Answer

The answer of YouTube would like to test the hypothesis...

Question 8

The National Association of Realtors reported that 26% of home buyers in the state of Florida are foreigners. When testing the validity of this report, a Type II error would occur if it was concluded that the proportion of foreign buyers was __________ .
A)equal to 26% when, in reality, the proportion was not equal to 26%.
B)not equal to 26% when, in reality, the proportion was equal to 26%.
C)more than 26% when, in reality, the proportion was 26% or less.
D)26% or less when, in reality, the proportion was more than 26%.

Accepted Answer

A Type II error occurs when the null hypothesis is not rejected when it is false. In this context, the null hypothesis likely states that the proportion of foreign buyers is equal to 26%. A Type II error would happen if it was concluded that the proportion is equal to 26% (failing to reject the null hypothesis) when in reality, the proportion is not equal to 26%.

Question 9

Zappos is an online retailer based in Nevada and employs 1,300 employees. One of their competitors, Amazon.com, would like to test the hypothesis that the average age of a Zappos employee is less than 36 years old. A random sample of 22 Zappos employees was found to have an average age of 33.9 years. The standard deviation for this sample was 4.1 years. Amazon would like to set α = 0.025. The conclusion for this hypothesis test would be that because the test statistic is ----
A)less than the critical value, we cannot conclude that the average age of Zappos employees is less than 36 years old.
B)more than the critical value, we cannot conclude that the average age of Zappos employees is less than 36 years old.
C)less than the critical value, we can conclude that the average age of Zappos employees is less than 36 years old.
D)more than the critical value, we can conclude that the average age of Zappos employees is less than 36 years old.

Accepted Answer

The test statistic is calculated and compared to the critical value for a one-tailed test at α = 0.025. If the test statistic is less than the critical value, it supports the hypothesis that the average age is less than 36 years.

Question 10

A Type I error occurs in hypothesis testing when we _______.
A)fail to reject the alternative hypothesis and the alternative hypothesis is false
B)reject the alternative hypothesis and the alternative hypothesis is true
C)reject the null hypothesis and the null hypothesis is true
D)fail to reject the null hypothesis and the null hypothesis is false

Accepted Answer

A Type I error occurs when we incorrectly reject the null hypothesis when it is actually true.

Question 11

A golfer claims that his average golf score at the course he plays regularly is less than 90. The correct hypothesis statement for this golfer to prove his claim would be
A)H0: µ = 90; H1: µ × 90.
B)H0: µ × 90; H1: µ = 90.
C)H0: µ c 90; H1: µ < 90.
D)H0: µ c 90; H1: µ c 90.

Accepted Answer

The correct hypothesis statement for proving the golfer's claim that his average score is less than 90 is to set the null hypothesis (H0) as the average score being equal to or greater than 90 (µ ≥ 90) and the alternative hypothesis (H1) as the average score being less than 90 (µ < 90). Option C correctly represents this with "H0: µ ≥ 90; H1: µ < 90," though it uses "c" to indicate "≥" which might be a typographical error.

Question 12

A golfer claims that his average golf score at the course he plays regularly is less than 90. A random sample of 35 rounds of golf was selected and the scores were recorded. Assume that the standard deviation for the population of scores for this golfer is 3.4 and the true population mean for scores for this golfer is 88.2. Using α = 0.05, beta equals -----.
A)0.0694
B)0.1292
C)0.1895
D)0.0944

Accepted Answer

The power of the test is 1 - beta. Given the population mean is 88.2, which is less than 90, the null hypothesis is false. The power is calculated using the z-test for means, and the beta value corresponding to the power is 0.0694.

Question 13

The critical value for a hypothesis test ______________.
A)represents the number of standard deviations between the sample mean and the population mean according to the alternative hypothesis
B)determines the observed level of significance
C)represents the number of standard deviations between the sample mean and the population mean according to the null hypothesis
D)is based on the significance level and determines the boundary for the rejection region

Accepted Answer

The critical value is determined by the significance level and is used to define the boundary of the rejection region in hypothesis testing.

Question 14

Many franchisers favor owners who operate multiple stores by providing them with preferential treatment. Suppose the Small Business Administration would like to perform a hypothesis test to investigate if 80% of franchisees own only one location using α = 0.05. A random sample of 120 franchisees found that 85 owned only one store. The conclusion for this hypothesis test would be that because the absolute value of the test statistic is-----
A)more than the absolute value of the critical value, we can conclude that the proportion of franchisees that own only one store equals 0.80.
B)less than the absolute value of the critical value, we cannot conclude that the proportion of franchisees that own only one store does not equal 0.80.
C)more than the absolute value of the critical value, we can conclude that the proportion of franchisees that own only one store does not equal 0.80.
D)less than the absolute value of the critical value, we can conclude that the proportion of franchisees that own only one store does not equal 0.80.

Accepted Answer

The correct conclusion is that if the absolute value of the test statistic is more than the absolute value of the critical value, it indicates that the observed data are significantly different from what was expected under the null hypothesis. In this context, it means we can conclude that the proportion of franchisees that own only one store does not equal 0.80, rejecting the null hypothesis.

Question 15

Breyers is a major producer of ice cream and would like to test the hypothesis that the average American consumes more than 17 ounces if ice cream per month. A random sample of 15 Americans was found to consume an average of 18.2 ounces of ice cream last month. The standard deviation for this sample was 3.9 ounces. Breyers would like to set α = 0.10. The p-value for this hypothesis test would be between _______ .
A)0.02 and 0.05
B)0.10 and 0.20
C)0.05 and 0.10
D)0.01 and 0.02

Accepted Answer

The answer of Breyers is a major producer of ice...

Question 16

The National Center for Education Statistics would like to test the hypothesis that the proportion of Bachelor's degrees that were earned by women equals 0.60. A random sample of 140 college graduates with Bachelor degrees found that 75 were women. The National Center for Education Statistics would like to set α = 0.10. The test statistic for this hypothesis test would be _______ .
A)zp = 2.17
B)zp = 1.36
C)zp = - 1.55
D)zp = - 1.21

Accepted Answer

The answer of The National Center for Education Statistics would...

Question 17

The Department of Education would like to test the hypothesis that the average debt load of graduating students with a Bachelor's degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The Department of Education would like to set α = 0.05. Which one of the following statements is true?
A)Because the p-value is less than α, we fail to reject the null hypothesis and conclude that the average debt load is not equal to $17,000.
B)Because the p-value is greater than α, we fail to reject the null hypothesis and cannot conclude that the average debt load is not equal to $17,000.
C)Because the p-value is greater than α, we fail to reject the null hypothesis and conclude that the average debt load is equal to $17,000.
D)Because the p-value is less than α, we reject the null hypothesis and conclude that the average debt load is equal to $17,000.

Accepted Answer

B) is correct because when the p-value is greater than the significance level (α), the decision is to fail to reject the null hypothesis. This means there is not enough evidence to conclude a difference from the hypothesized mean, but it does not prove the null hypothesis to be true.

Question 18

The Department of Education would like to test the hypothesis that the average debt load of graduating students with a Bachelor's degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The Department of Education would like to set α = 0.05. The critical value for this hypothesis test would be _____ .
A)2.33
B)1.645
C)1.28
D)1.96

Accepted Answer

Given that the population standard deviation is known and a significance level (α) of 0.05 is set for a two-tailed test, the critical value corresponds to the Z-score for a 95% confidence interval, which is 1.96.

Question 19

Recently, Experian reported that the average credit score for a new- car loan was 753. Suppose Ally Financial, a bank holding company that finances car loans, would like to test the hypothesis that the average credit score has increased since the Experian report. A random sample of 20 new- car loans had an average credit score of 764.2 with a sample standard deviation of 34.5. Ally Financial would like to set α = 0.05. The test statistic for this hypothesis test would be ----- .
A)t x = 2.31
B)t x = 1.45
C)z x = 2.04
D)z x = 1.25

Accepted Answer

The test statistic for this hypothesis test is calculated using the formula for a t-test because the population standard deviation is unknown and the sample size is small (n < 30). The formula is $t = \frac{\bar{x} - \mu}{(s/\sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $s$ is the sample standard deviation, and $n$ is the sample size. Plugging in the given values: $t = \frac{764.2 - 753}{(34.5/\sqrt{20})}$ results in a t-value close to 1.45, making option B the correct choice.

Question 20

Zappos is an online retailer based in Nevada and employs 1,300 employees. One of their competitors, Amazon.com, would like to test the hypothesis that the average age of a Zappos employee is less than 36 years old. A random sample of 22 Zappos employees was found to have an average age of 33.9 years. The standard deviation for this sample was 4.1 years. Amazon would like to set α = 0.025. The correct hypothesis statement for this hypothesis test would be ____ A)H₀: µ = 36; H1: µ × 36. B)H₀: µ c 36; H1: µ < 36. C)H₀: µ c 36; H1: µ > 36. D)H₀: µ = 33.9; H1: µ × 33.9.

Accepted Answer

The correct hypothesis statement for testing if the average age is less than a certain value involves setting the null hypothesis (H0) as the population mean (µ) being equal to the value under consideration (in this case, 36 years), and the alternative hypothesis (H1) as the population mean being less than this value. Therefore, the correct formulation is H0: µ = 36; H1: µ < 36.

Quiz 9: Weight Management and Body Image

A professor would like to test the hypothesis that the average number of minutes that a student needs to complete a statistics exam is equal to 45 minutes. A Type II error would occur if the professor concludes that the average exam time is ___________.

The National Association of Realtors reported that 26% of home buyers in the state of Florida are foreigners. When testing the validity of this report, a Type II error would occur if it was concluded that the proportion of foreign buyers was __________ .

A Type I error occurs in hypothesis testing when we _______.

A golfer claims that his average golf score at the course he plays regularly is less than 90. The correct hypothesis statement for this golfer to prove his claim would be

The critical value for a hypothesis test ______________.