Question 1

An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose,on average,more than 10 pounds.A consumer activist decides to test the authenticity of the claim.She follows the progress of 18 women who recently joined the weight-reduction program.She calculates the mean weight loss of these participants as 10.8 pounds with a standard deviation of 2.4 pounds.Which of the following is an appropriate hypotheses to test the advertisement's claim? A) H_o:μ < 10,H_A:μ ≥ 10 B) H_o:μ ≥ 10,H_A:μ < 10 C) H_o:μ ≤ 10,H_A:μ > 10 D) H_o:μ = 10,H_A:μ ≠ 10

Accepted Answer

The appropriate hypothesis to test the claim is to determine if the true mean weight loss of participants in the weight-reduction program is greater than 10 pounds as claimed by the advertisement. Therefore, the null hypothesis (H_o) should state that the true mean weight loss is less than or equal to 10 pounds, and the alternative hypothesis (H_A) should state that the true mean weight loss is greater than 10 pounds. Thus, the correct hypothesis testing notation is H_o:μ ≤ 10 versus H_A:μ > 10. Option C is the closest match to this notation, so it is the best choice.

Question 2

George W.Bush famously claimed in his 2003 State of the Union address that the United States had uncovered evidence that Iraq had developed weapons of mass destruction under Saddam Hussein.Consider the null hypothesis,"Iraq does not possess weapons of mass destruction." After deciding that Iraq did possess weapons of mass destruction and invading this country,the United States found no evidence of said weapons.Is this a Type I or a Type II error on the part of the United States? Explain.

Accepted Answer

The answer of George W.Bush famously claimed in his 2003...

Question 3

Massachusetts Institute of Technology grants pirate certificates to those students who successfully complete courses in archery,fencing,sailing,and pistol shooting ("MIT Awards Pirate Certificates to Undergraduates," Boston Globe,March 3,2012).Sheila claims that those students who go on to earn pirate certificates are able to hit a higher proportion of bull's-eyes during the archery final exam than the course average of 0.15.Specify the null and alternative hypotheses to test her claim.

Accepted Answer

The answer of Massachusetts Institute of Technology grants pirate certificates...

Question 4

Construct the null and alternative hypotheses for the following claims.
a."The school's mean GPA differs from 2.50 GPA."
b."The school's mean GPA is less than 2.50 GPA."

Accepted Answer

The answer of Construct the null and alternative hypotheses for...

Question 5

A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night.If this is to happen,it will have to move one of its most viewed shows to another slot.The network conducts a survey asking its viewers which show they would rather watch.The network receives 827 responses,of which 428 indicate that they would like to see the new show in the lineup.At the 1% significance level,the rejection region(s)for this hypothesis would be ________.
A) 2.330
B) 2.030
C) 1.960
D) 1.645

Accepted Answer

The rejection region for a hypothesis test at the 1% significance level (two-tailed) corresponds to a critical z-value of approximately ±2.576. However, since the options provided are for a one-tailed test, the closest critical z-value for a 1% significance level (one-tailed) is 2.330.

Question 6

Vermont-based Green Mountain Coffee Roasters dominates the market for single-serve coffee in the United States,with its subsidiary Keurig accounting for approximately 70% of sales ("Rivals Try to Loosen Keurig's Grip on Single-Serve Coffee Market," Chicago Tribune,February 26,2011).But Keurig's patent on K-cups,the plastic pods used to brew the coffee,is expected to expire in 2012,allowing other companies to better compete.Suppose a potential competitor has been conducting blind taste tests on its blend and finds that 47% of consumers strongly prefer its French Roast to that of Green Mountain Coffee Roasters.After tweaking its recipe,the competitor conducts a test with 144 tasters,of which 72 prefer its blend.The competitor claims that its new blend is preferred by more than 47% of consumers to Green Mountain Coffee Roasters' French Roast.What critical value should be used to test this claim at the 1% significance level?
A) 2.33
B) 2.36
C) 2.58
D) 2.61

Accepted Answer

The critical value for a one-tailed test at the 1% significance level with 143 degrees of freedom is 2.33.

Question 7

A company has developed a new diet that it claims will lower one's weight by more than 10 pounds.Health officials decide to conduct a test to validate this claim.The consumers should be _____________________________________.
A) more concerned about Type I error
B) more concerned about Type II error
C) concerned about both Type I and Type II errors
D) is not concerned at all

Accepted Answer

The answer of A company has developed a new diet...

Question 8

An engineer is designing an experiment to test if airplane engines are faulty and unsafe to fly.The engineer expects 0.0001% of engines to be unsafe.The null hypothesis is that the probability of an unsafe engine is less than or equal to 0.0001% and the alternative hypothesis is that the probability the engine is unsafe is greater than 0.0001%.
a.Describe the consequences of Type I and Type II errors.
b.Should the engineer design the test with a higher alpha or a higher beta? Explain.

Accepted Answer

The answer of An engineer is designing an experiment to...

Question 9

Expedia would like to test if the average round-trip airfare between Philadelphia and Dublin is less than $1,200.Which of the following hypothesis tests should be performed?
A) Left-tailed
B) Right-tailed
C) Two-tailed
D) There is not enough information to answer.

Accepted Answer

A left-tailed test is appropriate when the hypothesis is testing if a parameter is less than a certain value. In this case, Expedia wants to test if the average round-trip airfare is less than $1,200, which fits the criteria for a left-tailed test.

Question 10

A company has developed a new diet that it claims will lower one's weight by more than 10 pounds.Health officials decide to conduct a test to validate this claim.The manager of the company _____________________________________.
A) is more concerned about Type I error
B) is more concerned about Type II error
C) is concerned about both Type I and Type II errors
D) is not concerned at all

Accepted Answer

The manager of the company is more concerned about a Type II error because this type of error would involve failing to detect the diet's effectiveness when it actually does work, potentially harming the company's reputation and sales.

Question 11

An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose,on average,more than 10 pounds.A consumer activist decides to test the authenticity of the claim.She follows the progress of 18 women who recently joined the weight-reduction program.She calculates the mean weight loss of these participants as 10.8 pounds with a standard deviation of 2.4 pounds.At the 5% significance level,the critical value would be ______.
A) 1.960
B) 1.645
C) 2.030
D) 1.740

Accepted Answer

The answer of An advertisement for a popular weight-loss clinic...

Question 12

A company decided to test the hypothesis that the average time a company's employees are spending to check their private e-mails at work is more than 6 minutes.A random sample of 40 employees were selected and they averaged 6.6 minutes.It is believed that the population standard deviation is 1.7 minutes.The α is set to 0.05.The critical value for this hypothesis test would be ______.
A) 6.0
B) 7.4
C) 6.4
D) 7.9

Accepted Answer

The hypothesis test uses a t-distribution since the population standard deviation is unknown and the sample size is less than 30. The null hypothesis is that the average time spent checking private emails is 6 minutes or less (H0: μ ≤ 6), while the alternative hypothesis is that it is more than 6 minutes (Ha: μ > 6). The significance level α is 0.05, so the critical value can be found using a t-distribution with 39 degrees of freedom (40 employees minus 1). Using a t-table or a calculator, the critical value is 1.684. The test statistic can be calculated using the formula:

t = (x̄ - μ) / (s / √n)

where x̄ is the sample mean (6.6 minutes), μ is the hypothesized population mean (6 minutes), s is the sample standard deviation (1.7 minutes), and n is the sample size (40 employees). Plugging in the values, we get:

t = (6.6 - 6) / (1.7 / √40) ≈ 2.16

The calculated t-statistic is greater than the critical value of 1.684, so we reject the null hypothesis and conclude that there is evidence to support the claim that the average time spent checking private emails is more than 6 minutes. Therefore, the critical value for this hypothesis test would be the t-value at 0.05 level of significance with 39 degrees of freedom, which is approximately 1.684. The closest option is C) 6.4.

Question 13

Expedia would like to test if the average round-trip airfare between Philadelphia and Dublin is less than $1,200.The correct hypothesis statement would be __________________________.
A) 
B) 
C) 
D)

Accepted Answer

The correct hypothesis statement for testing if the average round-trip airfare between Philadelphia and Dublin is less than $1,200 would be:
Null hypothesis (H0): The average round-trip airfare between Philadelphia and Dublin is $1,200 or more.
Alternative hypothesis (Ha): The average round-trip airfare between Philadelphia and Dublin is less than $1,200.
Option C is the correct statement for this choice which states Ha: The average round-trip airfare between Philadelphia and Dublin is less than $1,200.

Question 14

A company decided to test the hypothesis that the average time a company's employees are spending to check their private e-mails at work is more than 6 minutes.A random sample of 40 employees were selected and they averaged 6.6 minutes.It is believed that the population standard deviation is 1.7 minutes.The α is set to 0.05.The p-value for this hypothesis test would be ______.
A) 0.0644
B) 0.0129
C) 0.0268
D) 0.0395

Accepted Answer

We need to conduct a one-sample t-test since we don't know the population standard deviation and the sample size is less than 30.

Null hypothesis: H0: μ ≤ 6 (the average time spent checking private e-mails is less than or equal to 6 minutes)

Alternative hypothesis: H1: μ > 6 (the average time spent checking private e-mails is more than 6 minutes)

The test statistic can be calculated as:

t=(x̄-μ)/(s/√n)=(6.6-6)/(1.7/√40)=2.35

Degrees of freedom= n-1 = 40-1 = 39

Using a t-distribution table or calculator with 39 degrees of freedom and α=0.05, the critical value is 1.684.

The p-value is the probability of obtaining a test statistic as extreme as t=2.35 or more extreme, assuming the null hypothesis is true.

The p-value can be calculated as P(T>2.35)=0.0129

Since the p-value (0.0129) is less than the level of significance (0.05), we reject the null hypothesis. Therefore, we can conclude that the average time employees spend checking their private emails is more than 6 minutes.

Question 15

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 α is set to 0.05.The confidence interval for this hypothesis test would be __________________.
A) [$14,118.9,$19,881.2]
B) [$14,839.1,$19,160.9]
C) [$16,279.7,$17,720.3]
D) [$15,588.2,$18,411.8]

Accepted Answer

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

Question 16

A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night.If this is to happen,it will have to move one of its most viewed shows to another slot.The network conducts a survey asking its viewers which show they would rather watch.The network receives 827 responses,of which 428 indicate they would like to see the new show in the lineup.Which of the following is an appropriate hypotheses to test if the television network should give its newest show a spot during prime time at night? A) H_o:p < 0.50,H_A:p ≥ 0.50 B) H_o:p ≥ 0.50,H_A:p < 0.50 C) H_o:p ≤ 0.50,H_A:p > 0.50 D) H_o:p = 0.50,H_A:p ≠ 0.50

Accepted Answer

We need to test whether the proportion of viewers who prefer the new show is greater than 50% or not, as this will determine whether the network should give the new show a spot during prime time or not. 
Let HS1U1B1O represent the null hypothesis that the proportion of viewers who prefer the new show is less than or equal to 50% (i.e., p ≤ 0.5), and HS1U1B1A represent the alternative hypothesis that the proportion of viewers who prefer the new show is greater than 50% (i.e., p > 0.5). 
Therefore, the appropriate hypotheses to test in this case are: 
HS1U1B1O: p ≤ 0.5
HS1U1B1A: p > 0.5 
Hence, the answer is C.

Question 17

Vermont-based Green Mountain Coffee Roasters dominates the market for single-serve coffee in the United States,with its subsidiary Keurig accounting for approximately 70% of sales ("Rivals Try to Loosen Keurig's Grip on Single-Serve Coffee Market," Chicago Tribune,February 26,2011).But Keurig's patent on K-cups,the plastic pods used to brew the coffee,is expected to expire in 2012,allowing other companies to better compete.Suppose a potential competitor has been conducting blind taste tests on its blend and finds that 47% of consumers strongly prefer its French Roast to that of Green Mountain Coffee Roasters.After tweaking its recipe,the competitor conducts a test with 144 tasters,of which 72 prefer its blend.The competitor claims that its new blend is preferred by more than 47% of consumers to Green Mountain Coffee Roasters' French Roast.At the 1% significance level,does the evidence support the claim?
A) No,because the value of the test statistic is less than the critical value.
B) Yes,because the value of the test statistic is less than the critical value.
C) No,because the value of the test statistic is greater than the critical value.
D) Yes,because the value of the test statistic is greater than the critical value.

Accepted Answer

We are given that the competitor claims that its new blend is preferred by more than 47% of consumers to Green Mountain Coffee Roasters' French Roast. This is a one-tailed test: the competitor is claiming superiority of its blend, compared to Green Mountain's blend. The null hypothesis is that the competitor's blend is not preferred by more than 47% of consumers. The alternative hypothesis is that the competitor's blend is preferred by more than 47% of consumers.

We can use a z-test for proportions to test this claim. The test statistic is calculated as:

z = (p - P) / sqrt(P * (1 - P) / n)

where p is the proportion of tasters who preferred the competitor's blend (72/144 = 0.5), P is the hypothesized proportion under the null (0.47), and n is the sample size (144).

Plugging in the values, we get:

z = (0.5 - 0.47) / sqrt(0.47 * 0.53 / 144) = 1.16

At the 1% significance level, the critical value for a one-tailed z-test is 2.33. Since our calculated test statistic (1.16) is less than the critical value (2.33), we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to support the claim that the competitor's blend is preferred by more than 47% of consumers compared to Green Mountain Coffee Roasters' French Roast.

Question 18

A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night.If this is to happen,it will have to move one of its most viewed shows to another slot.The network conducts a survey asking its viewers which show they would rather watch.The network receives 827 responses,of which 428 indicate that they would like to see the new show in the lineup.The test statistic for this hypothesis would be _______.
A) 1.35
B) 1.05
C) 1.25
D) 1.15

Accepted Answer

The answer of A television network is deciding whether or...

Question 19

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 α is set to 0.05.The p-value for this hypothesis test would be ______.
A) 0.1310
B) 0.0950
C) 0.0475
D) 0.0219

Accepted Answer

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

Question 20

An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose,on average,more than 10 pounds.A consumer activist decides to test the authenticity of the claim.She follows the progress of 18 women who recently joined the weight-reduction program.She calculates the mean weight loss of these participants as 10.8 pounds with a standard deviation of 2.4 pounds.The test statistic for this hypothesis would be _______.
A) 1.41
B) −1.41
C) 1.74
D) −1.74

Accepted Answer

The answer of An advertisement for a popular weight-loss clinic...

Quiz 9: Hypothesis Testing

Construct the null and alternative hypotheses for the following claims. a."The school's mean GPA differs from 2.50 GPA." b."The school's mean GPA is less than 2.50 GPA."

A company has developed a new diet that it claims will lower one's weight by more than 10 pounds.Health officials decide to conduct a test to validate this claim.The consumers should be _____________________________________.

Expedia would like to test if the average round-trip airfare between Philadelphia and Dublin is less than $1,200.Which of the following hypothesis tests should be performed?

A company has developed a new diet that it claims will lower one's weight by more than 10 pounds.Health officials decide to conduct a test to validate this claim.The manager of the company _____________________________________.

Expedia would like to test if the average round-trip airfare between Philadelphia and Dublin is less than $1,200.The correct hypothesis statement would be __________________________.