Question

9. Match problems to procedures

a. Given weights of 31, 29, 26, 33, 40, 28, 30, and 25, at α = 0.05 test that the population mean is 35.

b. Test size C battery mean life is at least 25 hours.

c. An effective vaccine would reduce the proportion of exposed persons contracting a disease. A pharmaceutical company wants to test the effectiveness of a new vaccine in preventing a certain disease. It is expected that 40% of unvaccinated exposed people will contract the disease. A group of 48 exposed persons volunteered to be vaccinated. Later, two of the volunteers contracted the disease. Test H0: π >/= 0.0 (vaccine ineffective) at α 0.01

d. Testing that a gasoline additive increases mileage, we compute mpg with additive minus mpg without additive for each car. If the mean of the differences is positive enough, action will be required to implement the additive.

e. Run times (msec) of a new phone app developed by GotYourGP and established competitor WeTrackYou.Inc. are logged in a data file. At α = 0.05, are the run times of GotYourGP and WeTrackYou.Inc comparable?

                (1) 1-tailed test of proportion with negative critical value

                (2) 2-tailed test of mean with both negative and positive critical values

                (3) 1-tailed test of mean with negative critical values

                (4) 1-tailed test of paired-data with positive critical value

                (5) 2-tailed test of means of 2 independent populations

Answer 1

a. Given weights of 31, 29, 26, 33, 40, 28, 30, and 25, at α = 0.05 test that the population mean is 35

H₀ : µ = 35 vs H_a : µ ≠ 35

2-tailed test of mean with both negative and positive critical values.

b. Test size C battery mean life is at least 25 hours.

H₀ : µ ≥ 25 vs H_a : µ < 25  

1-tailed test of mean with negative critical values.

c. An effective vaccine would reduce the proportion of exposed persons contracting a disease. A pharmaceutical company wants to test the effectiveness of a new vaccine in preventing a certain disease. It is expected that 40% of unvaccinated exposed people will contract the disease. A group of 48 exposed persons volunteered to be vaccinated. Later, two of the volunteers contracted the disease. Test H0: π >/= 0.0 (vaccine ineffective) at α 0.01

H₀: π ≥ 0.0  H_a : π < 0.0

1-tailed test of proportion with negative critical value

d. Testing that a gasoline additive increases mileage, we compute mpg with additive minus mpg without additive for each car. If the mean of the differences is positive enough, action will be required to implement the additive.

H₀: µ_d= 0 vs H_a: µ_d > 0

1-tailed test of paired-data with positive critical value

e. Run times (msec) of a new phone app developed by GotYourGP and established competitor WeTrackYou.Inc. are logged in a data file. At α = 0.05, are the run times of GotYourGP and WeTrackYou.Inc comparable?

H₀: µ₁ = µ₂    vs H_a: µ₁ ≠ µ₂   

2-tailed test of means of 2 independent populations.