91Ó°ÊÓ

Which of the following are true? If false, explain briefly. a. AP-value of 0.01 means that the null hypothesis is false. b. AP-value of 0.01 means that the null hypothesis has a 0.01 chance of being true. c. AP-value of 0.01 is evidence against the null hypothesis. d. AP-value of 0.01 means we should definitely reject the null hypothesis.

Which of the following are true? If false, explain briefly. a. If the null hypothesis is true, you'll get a high P-value. b. If the null hypothesis is true, a P-value of 0.01 will occur about \(1 \%\) of the time. c. A P-value of 0.90 means that the null hypothesis has a good chance of being true. d. AP-value of 0.90 is strong evidence that the null hypothesis is true.

Which of the following are true? If false, explain briefly. a. A very high P-value is strong evidence that the null hypothesis is false. b. A very low P-value proves that the null hypothesis is false. c. A high P-value shows that the null hypothesis is true. d. A P-value below 0.05 is always considered sufficient evidence to reject a null hypothesis.

Which of the following are true? If false, explain briefly. a. A very low P-value provides evidence against the null hypothesis. b. A high P-value is strong evidence in favor of the null hypothesis. c. AP-value above 0.10 shows that the null hypothesis is true. d. If the null hypothesis is true, you can't get a P-value below 0.01

Which of the following statements are true? If false, explain briefly. a. Using an alpha level of \(0.05,\) a P-value of 0.04 results in rejecting the null hypothesis. b. The alpha level depends on the sample size. C. With an alpha level of \(0.01,\) a \(P\) -value of 0.10 results in rejecting the null hypothesis. d. Using an alpha level of \(0.05,\) a P-value of 0.06 means the null hypothesis is true.

Which of the following statements are true? If false, explain briefly. a. It is better to use an alpha level of 0.05 than an alpha level of 0.01 . b. If we use an alpha level of 0.01 , then a P-value of 0.001 is statistically significant. c. If we use an alpha level of \(0.01,\) then we reject the null hypothesis if the \(\mathrm{P}\) -value is 0.001 d. If the P-value is 0.01 , we reject the null hypothesis for any alpha level greater than 0.01 .

A new reading program may reduce the number of elementary school students who read below grade level. The company that developed this program supplied materials and teacher training for a large-scale test involving nearly 8500 children in several different school districts. Statistical analysis of the results showed that the percentage of students who did not meet the grade- level goal was reduced from \(15.9 \%\) to \(15.1 \%\). The hypothesis that the new reading program produced no improvement was rejected with a P-value of 0.023 . a. Explain what the P-value means in this context. b. Even though this reading method has been shown to be significantly better, why might you not recommend that your local school adopt it?

For each of the following situations, state whether a Type I, a Type II, or neither error has been made. Explain briefly. a. A bank wants to know if the enrollment on their website is above \(30 \%\) based on a small sample of customers. They test \(\mathrm{H}_{0}: p=0.3\) vs. \(\mathrm{H}_{\mathrm{A}}: p>0.3\) and reject the null hypothesis. Later they find out that actually \(28 \%\) of all customers enrolled. b. A student tests 100 students to determine whether other students on her campus prefer Coke or Pepsi and finds no evidence that preference for Coke is not 0.5 . Later, a marketing company tests all students on campus and finds no difference. c. A human resource analyst wants to know if the applicants this year score, on average, higher on their placement exam than the 52.5 points the candidates averaged last year. She samples 50 recent tests and finds the average to be 54.1 points. She fails to reject the null hypothesis that the mean is 52.5 points. At the end of the year, they find that the candidates this year had a mean of 55.3 points. d. A pharmaceutical company tests whether a drug lifts the headache relief rate from the \(25 \%\) achieved by the placebo. They fail to reject the null hypothesis because the P-value is \(0.465 .\) Further testing shows that the drug actually relieves headaches in \(38 \%\) of people.

For each of the following situations, state whether a Type I, a Type II, or neither error has been made. a. A test of \(\mathrm{H}_{0}: \mu=25\) vs. \(\mathrm{H}_{\mathrm{A}}: \mu>25\) rejects the null hypothesis. Later it is discovered that \(\mu=24.9\). b. A test of \(\mathrm{H}_{0}: p=0.8\) vs. \(\mathrm{H}_{\mathrm{A}}: p<0.8\) fails to reject the null hypothesis. Later it is discovered that \(p=0.9\). c. A test of \(\mathrm{H}_{0}: p=0.5\) vs. \(\mathrm{H}_{\mathrm{A}}: p \neq 0.5\) rejects the null hypothesis. Later it is discovered that \(p=0.65\). d. A test of \(\mathrm{H}_{0}: p=0.7\) vs. \(\mathrm{H}_{\mathrm{A}}: p<0.7\) fails to reject the null hypothesis. Later it is discovered that \(p=0.6\).

A medical researcher tested a new treatment for poison ivy against the traditional ointment. He concluded that the new treatment is more effective. Explain what the P-value of 0.047 means in this context.