Hypothesis Testing for Small Samples and Proportions

A mayor is concerned about the percentage of city residents who express disapproval of his job performance. His political committee pays for a newspaper ad, hoping to keep his disapproval rating below 21%. They will use a follow up poll to access effectiveness. What are the correct null and alternative hypotheses?

• Ho: μ > 21

  Ha: μ < 21

• Ho: p > .20

  Ha: p < .20

• Ho: p < .21

  Ha: p > .21

• Ho: p > .21

  Ha: p < .21

A random sample of students at a college shows that 54 of 200 students had part-time jobs. We want to see if the proportion of all college students with part time jobs is greater than the national average.

• 1 sample t-test

• 1 prop t-test

• 1 prop z-test

• 1 sample z-test

The alternative hypothesis for a test of the difference between two population proportions is:

• The proportions are equal

• The proportions are both greater than 1

• The proportions are both less than 1

• The proportions are not equal

To test a claim about a mean, when the population standard deviation is unknown we use:

• z procedures

• Pythagorean Theorem

• t procedures

• np > 10 and n(1-p) > 10

Lumber companies dry freshly cut wood in kilns before selling it. A certain percentage of boards develop cracks on their ends during drying. The current drying procedure is known to produce cracks in 16% of boards. The drying supervisor wants to try a new method that she believes will result in a proportion of cracked boards that is less than 16%. Write the appropriate hypotheses.

• Ho: p = 0.16

  Ha: p = 0.16

• Ho: p = 0.16

  Ha: p =/= 0.16

• Ho: p = 0.16

  Ha: p > 0.16

• Ho: p = 0.16

  Ha: p < 0.16

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.

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.

A random sample of 425 citizens of Naboo found that 34% support the Galactic Republic. A sample of 585 citizens of Tatooine found that 38% support the Galactic Republic. What test would you use to determine if the the proportions are different?

• 2 sample z-test for mean 

• 2 sample t-test for mean

• matched-pairs dependent sample t-test for mean

• 2 - proportion z test

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.

Which of the following represents the appropriate null & alternative hypotheses?
The mean height of women is greater than 64"

• H₀: μ > 64
  Hₐ: μ ≠ 64

• H₀: μ = 64
  Hₐ: μ > 64

• H₀: p > 64
  Hₐ: p ≠ 64

• H₀: p = 64
  Hₐ: p > 64