Question

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.

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: >_ 0.40 (vaccine Ineffective) at × = 0.01.

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

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

Test size C battery mean life is at 25 hrs.

1. 11-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

Test and CI for One Proportion

Test of p = 0.4 vs p not = 0.4

                                               Exact
Sample X   N Sample p         99% CI           P-Value
    1       2 48 0.041667 (0.002177, 0.179149)    0.000

Since P-value<0.01 so we reject null hypothesis at 1% level of significance and conclude that there is insufficient evidence that 40% of unvaccinated exposed people will contract the disease.

One-Sample T: Weight

Test of mu = 35 vs not = 35

Variable N   Mean StDev SE Mean      95% CI          T      P
Weight    7 31.00   4.55     1.72        (26.80, 35.20) -2.33 0.059

Since P-value>0.05 so we fail to reject null hypothesis at 5% level of significance and conclude that population mean is 35.

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