Hypothesis Testing Two Sample Small Mean

When do you use a t-value instead of a z-value? 

• When n < 30

• When n ≥ 30

• When all of the planets align

• When Ms. O said to

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.

• Reject Ho

• Reject Ha

• Fail to reject Ho

• Fail to reject Ha

H₀: μ = k

H₁: μ ≠ k

• Left-tailed test

• Two-tailed test

• Right-tailed test

A level of significance of 5% means:

• There's a 5% chance we're wrong

• There's a 5% chance we'll be wrong if we fail to reject the null hypothesis

• There's a 5% chance we'll be wrong if we reject the null hypothesis.

• There's a 5% chance you'll get an A on the test.

Two pain relief medicines are tested on volunteer post-operation patients, randomly assigned to one of the two brands of medicine, as to whether or not mean duration of relief are different. Data is recorded in minutes of pain relief. What is the conclusion of the appropriate hypothesis test for this experiment?

• P < .05 so reject Ho.

• P < .05 so fail to reject Ho.

• P > .05 so reject Ho.

• P > .05 so fail to reject Ho.

• 5% significance level is inappropriate for medical decisions.

The U.S. Census Bureau reported that the mean area of U.S. homes built in 2009 was 2,438 square feet.  Assume that a simple random sample of 20 homes built in 2010 had a mean area of 2,514 square feet, with a standard deviation of 225 square feet.  Can you conclude that the mean area of homes built in 2010 is greater than that of homes built in 2009?  Use 0.01 level of significance.

The p-value is ​ (a)   > ​ (b)   ; thus, ​ (c)   the null hypothesis.

​ (d)   evidence to conclude that the mean area of homes built in 2010 is greater than that of homes built in 2009.

• 0.0737

• 0.0654

• we fail to reject

• we reject

• There is not enough

• There is enough

• 0.01

• 0.05

• A) Ho: The mean number of days 9th grade students absent is equal to the mean number of days 12th grade students are absent.
  Ha: The mean number of days 9th grade students absent is less than the mean number of days 12th grade students are absent.
• B) Ho: The mean number of days 12th grade students absent is less than the mean number of days 9th grade students are absent.
  Ha: The mean number of days 12th grade students absent is equal to the mean number of days 9th grade students are absent.
• C) Ho: The mean number of days 12th grade students absent is equal to the mean number of days 9th grade students are absent.
  Ha: The mean number of days 9th grade students absent is greater than the mean number of days 12th grade students are absent. 
• D) Ho: The mean number of days 12th grade students absent is equal to the mean number of days 9th grade students are absent.
  Ha: The mean number of days 12th grade students absent is less than the mean number of days 9th grade students are absent.

A Keebler sales rep claims that there are more chocolate chips in their cookie than in Chips Ahoy cookies.  You take a random sample of 20 Keebler cookies and find an average of 15.8 chips per cookie and a s = 3.7 chips. A random sample of 25 Chips Ahoy yields 14.2 chips per cookie and s = 4.3 chips. What is the conclusion of the test?

• There is enough evidence to reject the claim that there are more chips in Keeblers.

• There is not enough evidence to reject the claim that there are more chips in Keeblers.

• There is enough evidence to support the claim that there are more chips in Keeblers.

• There is not enough evidence to support the claim that there are more chips in Keeblers.

Researchers claim that a blue background enhances creativity based on the average scores below. Test the claim at a 1% significance level.

• P = .0021

  We are more creative with blue.

• P = 0.9979

  We are more creative with blue.

• P = .0021

  We are more creative with red.

• P = 0.9979

  There appears to be no difference.

What type of test?
It is thought that the average penny is older than the average quarter. The average age of a sample of 50 pennies was 8.72 years with a s = 0.73 years and the average age of 50 quarters was 6.78 years with a s = 0.99 years.

• 2 sample z-test for mean

• 2 sample t-test for mean

• matched pairs t-test

• 2 sample z-test for proportion