(ACT:1) Hypothesis Testing for the Mean (Small Samples)

A used car dealer says that the mean price of a 2008 Honda CR-V is at least $20,500. You suspect this claim is incorrect and find that a random sample of 14 similar vehicles has a mean price of $19,850 and a standard deviation of $1084. Is there enough evidence to reject the dealer’s claim at α = 0.05? Assume the population is normally distributed. 

State the hypothesis of the given problem.

• Ho:  µ  $\ge$  20,500
  H1:  µ $<$  20,500

• Ho:  µ  $\le$  20,500
  H1:  µ $>$  20,500

• Ho:  µ  $>$  20,500
  H1:  µ $\le$  20,500

• Ho:  µ  $<$  20,500
  H1:  µ $\ge$  20,500

A used car dealer says that the mean price of a 2008 Honda CR-V is at least $20,500. You suspect this claim is incorrect and find that a random sample of 14 similar vehicles has a mean price of $19,850 and a standard deviation of $1084. Is there enough evidence to reject the dealer’s claim at α = 0.05? Assume the population is normally distributed. 

What is the value of the critical region?

• Critical region = −1.771

• Critical region = 1.771

• Critical region = −2.160

• Critical region = 2.160

A used car dealer says that the mean price of a 2008 Honda CR-V is at least $20,500. You suspect this claim is incorrect and find that a random sample of 14 similar vehicles has a mean price of $19,850 and a standard deviation of $1084. Is there enough evidence to reject the dealer’s claim at α = 0.05? Assume the population is normally distributed. 

Find the t-score for the sample.

• t-score = −2.244

• t-score = 2.244

• t-score = 2.255

• t-score = −2.255

A used car dealer says that the mean price of a 2008 Honda CR-V is at least $20,500. You suspect this claim is incorrect and find that a random sample of 14 similar vehicles has a mean price of $19,850 and a standard deviation of $1084. Is there enough evidence to reject the dealer’s claim at α = 0.05? Assume the population is normally distributed. 

What is the decision rule and conclusion on the given problem?

• t value is in the rejection region, therefore we reject H0: there is enough evidence at the 5% significance level to accept the claim.
  

• t value is not in the rejection region, therefore we fail to reject H0: there is no enough evidence at the 5% significance level to reject this claim.

• t value is in the rejection region, therefore we reject H0: there is no enough evidence at the 5% significance level to accept the claim.

• t value is in the rejection region, therefore we fail to reject H0: there is enough evidence at the 5% significance level to reject this claim.

A manufacturer claims that his tires last at least 40,000

miles. A test on 25 tires reveals that the mean life of a tire is 39,750 miles, with a standard deviation of 387 miles. Test the Manufacturer’s claim at α = .01.

What is the statement of the hypothesis of the given problem?

• Ho: µ $\ge$ 40,000
  H1: µ $<$ 40,000

• Ho: µ $>$ 40,000
  H1: µ $\le$ 40,000

• Ho: µ $<$ 40,000
  H1: µ $\ge$ 40,000

• Ho: µ $\le$ 40,000
  H1: µ $>$ 40,000

A manufacturer claims that his tires last at least 40,000 miles. A test on 25 tires reveals that the mean life of a tire is 39,750 miles, with a standard deviation of 387 miles.

Test the Manufacturer’s claim at α = .01.

What is the critical region?

• Critical region = -2.492

• Critical region = 2.492

• Critical region = -2.797

• Critical region = 2.797

A manufacturer claims that his tires last at least 40,000 miles. A test on 25 tires reveals that the mean life of a tire is 39,750 miles, with a standard deviation of 387 miles.

Test the Manufacturer’s claim at α = .01.

What is the t score for the sample?

• t-score = 461.88

• t-score = -461.88

• t-score = -461.86

• t-score = 461.86

A manufacturer claims that his tires last at least 40,000

miles. A test on 25 tires reveals that the mean life of a tire

is 39,750 miles, with a standard deviation of 387 miles.

Test the Manufacturer’s claim at α = .01.

What is the decision rule and conclusion.

• t value is in the rejection region, therefore we reject H0: there is enough evidence at the 2% significance level to accept the claim.

• t value is not in the rejection region, therefore we fail to reject H0: there is no enough evidence at the 2% significance level to reject this claim.

• t value is in the rejection region, therefore we fail reject H0: there is no enough evidence at the 2% significance level to accept the claim.

• t value is not in the rejection region, therefore we reject H0: there is enough no evidence at the 2% significance level to reject this claim.

A one sample t-test is conducted on Ho : μ = 81.6. The

sample has a sample mean = 84.1 , s = 3.1, n = 25, and α = .01.

• Reject Ho

• Reject Ha

• Fail to reject Ho

• Fail to reject Ha

A one sample t-test is conducted on Ho : μ = 81.6. The

sample has a sample mean = 84.1 , s = 3.1, n = 25, and α =

.01.

• There is enough evidence to reject the claim

• There is not enough evidence to reject the claim

• There is enough evidence to support the claim

• There is not enough evidence to support the claim