Question

1. In a Pew Research Center poll of 745 randomly selected adults, 589 said that it is morally wrong to not report all income on tax returns. Use a 0.01 significance level to test the claim that 75% of adults say that it is morally wrong to not report all income on tax returns.

2. The Hawk-Eye electronic system is used in tennis for displaying an instant replay that shows whether a ball is in bounds or out of bounds. In the first U.S. Open that used the Hawk-Eye system, players could challenge calls made by referees. The Hawk-Eye system was then used to confirm or overturn the referee’s call. Players made 839 challenges, and 327 of those challenges were successful with the call overturned (based on data reported in USA Today). Use a 0.01 significance level to test the claim that the proportion of challenges that are successful is greater than 1 3%.

3. The company Drug Test Success provides a “1-Panel-THC” test for marijuana usage. Among 300 tested subjects, results from 27 subjects were wrong (either a false positive or a false negative). Use a 0.05 significance level to test the claim that less than 10% of the test results are wrong.

4. A simple random sample of 50 adults is obtained, and each person’s red blood cell count (in cells per microliter) is measured. The sample mean is 5.23. The population standard deviation for red blood cell counts is 0.54. Use a 0.01 significance level to test the claim that the sample is from a population with a mean less than 5.4, which is a value often used for the upper limit of the range of normal values.

Answer 1

Question 1:

As we are testing the claim whether 75% of adults say that it is morally wrong to not report all income on tax returns, therefore the test statistic here is computed as:

As this is a two tailed test, the p-value here is computed from the standard normal tables as:

p = 2P( Z > 2.5594) = 2*0.0052 = 0.0104

As the p-value here is 0.0104 > 0.01 which is the level of significance, therefore the test is not significant and we cannot reject the null hypothesis here. Therefore we dont have sufficient evidence here to reject the claim that 75% of the adults say that it is morally wrong to not report all income on tax returns.