One Sample Hypothesis Testing

A Type I error is when: 

• We reject the null hypothesis when it is actually true
• We obtain the wrong test statistic
• We fail to reject the null hypothesis when it's actually false
• We reject the alternate hypothesis when it's actually true

A car manufacturer advertises that its new subcompact models get 47 mpg. If μ is the mileage of these cars, what could be the null and alternate hypothesis if we wanted to check if the car's mpg is overrated? 

• H₀ = 47
  H_a = 47
• H₀ = 47
  H_a < 47
• H₀ = 47
  H_a > 47
• H₀ = 47
  H_a ≠ 47

In testing hypotheses, which of the following would be strong evidence against the null hypothesis?

• using a small level of significance
• using a large level of significance
• obtaining data with a small p-value
• obtaining data with a low test statistic

You construct a 95% confidence interval for a mean and find it to be 1.1 ± 0.8. Which of the following is true?

• A test of the hypotheses H₀: μ = 1.2, H_a: μ ≠ 1.2 would reject H₀ at the 0.05 level.
• A test of the hypotheses H₀: μ = 1.1, H_a: μ ≠ 1.1 would reject H₀ at the 0.05 level
• A test of the hypotheses H₀: μ = 0, H_a: μ ≠ 0 would reject H₀ at the 0.05 level
• All three tests above would reject H₀ at the 0.05 level.

In their advertisements, a new diet program would like to claim that their methods result in a mean weight loss of more than ten pounds in two weeks. In order to determine if this is a valid claim, they hire an independent testing agency that then selects twenty-five people to be placed on this diet. The agency should be testing the null hypothesis H₀: m = 10 and the alternative hypothesis

• Ha: μ < 10
• Ha: μ > 10
• Ha: μ ≥ 10
• Ha: μ ≤ 10

A tire manufacturer claims that one particular type of tire will last at least 50,000 miles.  A group of angry customers does not believe this is so.  They take a sample of 14 tires to test if the mean mileage of the tires is really less than 50,000.  What set of hypotheses are they interested in testing?

• a) H0: m = 50,000 vs. Ha: m < 50,000
• b)H0: x̅ = 50,000 vs. Ha: x̅ < 50,000
• c)H0: m = 50,000 vs. Ha: m ≠ 50,000
• d)H0: m = 50,000 vs. Ha: m > 50,000

A tire manufacturer claims that one particular type of tire will last at least 50,000 miles.  A group of angry customers does not believe this is so.  They took a sample of 14 tires to test if the mean mileage of the tires is really less than 50,000.  If 0.0100 < P-value < 0.0200, what decision should be made if testing at the a = 0.05 level?

• a)Reject H0 and conclude that the tires were not performing as claimed.
• b)Reject H0 and conclude that the mean tire life really is 50,000 miles.
• c)Do not reject H0 and conclude that the tires were not performing as claimed.
• d)Do not reject H0 and conclude that the mean tire life really is 50,000 miles. 

Tags

CCSS.HSS.IC.B.4

In performing a hypothesis test where the null

hypothesis is that the μ = 6.9. A random sample of 16

items is selected. The sample mean is 7.1 and the sample

standard deviation is 2.4. It can be assumed that the

population is normally distributed at α = .05.

• 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

Tags

CCSS.HSS.IC.B.4

The average yield of a certain crop is 10.1 bushels per plant. A biologist claims that a new fertilizer will result in a greater yield. The appropriate null and alternative hypotheses would be:

• H₀ : µ = 10.8; H_a: µ > 10.8

• H₀ : µ = 10.8; H_a: µ ≠ 10.8

• H₀ : µ = 10.1; H_a: µ > 10.1

• H₀ : µ = 10.1; H_a: µ < 10.1

• H₀ : µ = 10.1; H_a: µ ≠ 10.1

An opinion poll asks a SRS of 200 adults how they feel about voting for an amendment. What hypothesis would test if the proportion is greater than 60%?

• H₀ : p = 0.6; H_a: p > 0.6

• H₀ : p = 0.6; H_a: p ≠ 0.6

• H₀ : p = 0.6; H_a: p < 0.6

• H₀ : p = 0.6; H_a: p = 0.75

• H₀ : p = 0.75; H_a: p < 0.6