# Online 12 - Sections 9.1 and 9.2-Doug Ensley

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1 Student: Date: Instructor: Doug Ensley Course: MAT Applied Statistics - Ensley Assignment: Online 12 - Sections 9.1 and Does a P-value of give strong evidence or not especially strong evidence against the null hypothesis? C. The P-value does not give strong evidence B. The P-value gives strong evidence against the null hypothesis because it is D. The P-value does not give strong evidence 2. For (a) and (b), is the statement a null hypothesis or an alternative hypothesis? a. The proportion of adults who favor legalized gambling equals b. The proportion of all college students who are regular smokers is less than 0.28, the value it was ten years ago. c. Introducing notation for a parameter, state the hypotheses in (a) and (b) in terms of the parameter values. a. Is the statement in part (a) the null or alternative hypothesis? Null hypothesis Alternative hypothesis b. Is the statement in part (b) the null or alternative hypothesis? Alternative hypothesis Null hypothesis c. Choose the correct null and alternative hypotheses for part (a). A. H 0 : p > 0.40 H a : p = 0.40 D. H 0 : p < 0.40 H a : p = 0.40 B. H 0 : p = 0.40 H a : p 0.40 E. H 0 : p 0.40 H a : p = 0.40 C. H 0 : p = 0.40 H a : p < 0.40 F. H 0 : p = 0.40 H a : p = 0.40 Choose the correct null and alternative hypotheses for part (b). A. H 0 : p = 0.28 H a : p < 0.28 D. H 0 : p = 0.28 H a : p > 0.28 B. H 0 : p < 0.28 H a : p = 0.28 E. H 0 : p = 0.28 H a : p 0.28 C. H 0 : p > 0.28 H a : p = 0.28 F. H 0 : p 0.28 H a : p = Does a P-value of 0.36 give strong evidence or not especially strong evidence against the null hypothesis? 1 of 9 A. The P-value does not give strong evidence B. The P-value gives strong evidence against the null hypothesis because it is C. The P-value does not give strong evidence D. The P-value gives strong evidence against

2 4. A person who claims to be psychic says that the probability, p, that he can correctly predict the outcome of the astrological sign of a person in another room is greater than 1 / 12, the value that applies with random guessing. If we want to test this claim, we could use the data from an experiment in which he predicts the outcomes for n trials. State hypotheses for a significance test, letting the alternative hypothesis reflect the psychic's claim. Which of the following is the hypothesis test to be conducted? A. H 0 : p = 1 / 12 H a : p < 1 / 12 C. H 0 : p = 1 / 12 H a : p 1 / 12 E. H 0 : p > 1 / 12 H a : p = 1 / 12 B. H 0 : p > 1 / 12 H a : p = 1 / 12 D. H 0 : p 1 / 12 H a : p = 1 / 12 F. H 0 : p = 1 / 12 H a : p > 1 / Does a P-value of give strong evidence or not especially strong evidence against the null hypothesis? C. The P-value does not give strong evidence B. The P-value does not give strong evidence D. The P-value gives strong evidence against the null hypothesis because it is 6. For a test of H 0 : p = 0.50, the sample proportion is 0.36 based on a sample size of 100. Use this information to complete parts (a) through (c) below. a. Find the test statistic z. z = b. Find the P-value for H a : p < P-value = (Round to three decimal places as needed.) c. Does the P-value in (b) give much evidence against H 0? H 0. The P-value indicates that the null hypothesis is plausible. B. The P-value does not give strong evidence against H 0. The P-value indicates that the null hypothesis is not plausible. C. The P-value gives strong evidence against H 0. The P-value indicates that the null hypothesis is not plausible. D. The P-value does not give strong evidence against H 0. The P-value indicates that the null hypothesis is plausible. 2 of 9

3 7. Does a P-value of 0.35 give strong evidence or not especially strong evidence against the null hypothesis? C. The P-value gives strong evidence against the null hypothesis because it is B. The P-value does not give strong evidence D. The P-value does not give strong evidence 3 of 9

4 8. A study considered whether daily consumption of garlic could reduce tick bites. The study used a crossover design where half of the subjects used placebo first and garlic second and half the reverse. The authors described garlic being more effective with 33 subjects and placebo being more effective with 30 subjects. Does this suggest a real difference between garlic and placebo, or are the results consistent with random variation? Complete parts a through d below. a. Identify the relevant variable and parameter. A. The relevant variable is whether garlic or placebo is more effective, and the parameter is the population proportion, p, those for whom placebo is more effective than garlic. B. The relevant variable is the population proportion, p, those for whom garlic is more effective than placebo. The parameter is whether garlic or placebo is more effective. C. The relevant variable is whether garlic or placebo is more effective, and the parameter is the population proportion, p, those for whom garlic is more effective than placebo. b. State hypotheses for a large-sample two sided test. A. H 0 : p = 0.5 H a : p > 0.5 D. H 0 : p = 0.5 H a : p 0.5 B. H 0 : p > 0.5 H a : p = 0.5 E. H 0 : p < 0.5 H a : p = 0.5 C. H 0 : p = 0.5 H a : p < 0.5 F. H 0 : p 0.5 H a : p = 0.5 Check that sample size guidelines are satisfied for that test. No, the sample size was not large enough to make the inference. Yes, the sample size was large enough to make the inference. c. Find the test statistic value. z = (Round to two decimal places as needed.) d. Find the P-value. P-value = (Use the answer from part c to find this answer. Round to two decimal places as needed.) Interpret the P-value and state the conclusion in context. Use a significance level of A. The P-value is greater than the significance level; do not reject the null hypothesis. There is sufficient evidence that the proportion who think garlic more effective than a placebo is greater than 0.5. B. The P-value is less than the significance level; reject the null hypothesis. There is not sufficient evidence that the proportion who think garlic more effective than a placebo is greater than 0.5. C. The P-value is less than the significance level; reject the null hypothesis. There is sufficient evidence that the proportion who think garlic more effective than a placebo is greater than 0.5. D. The P-value is greater than the significance level; do not reject the null hypothesis. There is not sufficient evidence that the proportion who think garlic more effective than a placebo is greater than of 9

5 9. Does a P-value of give strong evidence or not especially strong evidence against the null hypothesis? the null hypothesis because it is C. The P-value gives strong evidence against B. The P-value does not give strong evidence D. The P-value does not give strong evidence 5 of 9

6 10. The 113 students in a class made blinded evaluations of pairs of cola drinks. For the comparison, cola A was preferred 65 times. In the population that this sample represents, is this strong evidence that a majority prefers one of the drinks? Refer to the following MINITAB printout. Test of p = 0.50 vs. not = 0.50 X N Sample p 95% CI Z-Value P-Value (0.483, 0.667) Complete parts (a) through (d) below. a. Explain how to get the test statistic value that MINITAB reports. A. The test statistic is calculated by taking the difference between the sample proportion and the null proportion and dividing it by the standard error. B. The test statistic is calculated by taking the difference between the sample proportion and the standard error and dividing it by the null proportion. C. The test statistic is calculated by taking the difference between the null proportion and the standard error and dividing it by the sample proportion. b. Explain how to get the "P-value". A. Use the value of the test statistic to find the right-tail probability from the standard normal distribution to the right of the test statistic value. B. Use the value of the test statistic to find the two-tail probability from the standard normal distribution to the left and right of the test statistic value. C. Use the value of the test statistic to find the left-tail probability from the standard normal distribution to the left of the test statistic value. Interpret it. A. The P-value tells us that if the alternate hypothesis were true, a proportion of of samples would fall at least as far as the sample data from the null hypothesis. B. The P-value tells us that if the null hypothesis were true, a proportion of of samples would fall at least as far as the sample data from the null hypothesis. C. The P-value tells us that if the null hypothesis were true, a proportion of of samples would fall at least as far as the sample data from the alternative hypothesis. c. Based on the result in (b), does it make sense to "accept H 0 "? Explain. A. Yes, we can "accept H 0 " since there is sufficient evidence that the alternative hypothesis is not true. B. No, but only because there is not enough evidence that H 0 is true. C. It does not make sense to accept the null hypothesis. It is possible that there is a real difference in the population that we are not detecting in our test, and we can never accept a null hypothesis. d. What does the 95% confidence interval tell you that the test does not? A. The significance test tells us a range of plausible values, whereas the 95% confidence interval tells us only that 0.50 is plausible. B. The 95% confidence interval tells us the exact value of the population proportion. C. The 95% confidence interval tells us the range of plausible values, whereas the test merely tells us that 0.50 is plausible. 6 of 9

7 11. Does a P-value of 0.43 give strong evidence or not especially strong evidence against the null hypothesis? the null hypothesis because it is C. The P-value does not give strong evidence B. The P-value does not give strong evidence D. The P-value gives strong evidence against 7 of 9

8 1. A. The P-value gives strong evidence 2. Null hypothesis Alternative hypothesis B. A. H 0 : p = 0.40 H a : p 0.40 H 0 : p = 0.28 H a : p < A. The P-value does not give strong evidence 4. F. H 0 : p = 1 / 12 H a : p > 1 / A. The P-value gives strong evidence C. The P-value gives strong evidence against H 0. The P-value indicates that the null hypothesis is not plausible. 7. B. The P-value does not give strong evidence 8. C. The relevant variable is whether garlic or placebo is more effective, and the parameter is the population proportion, p, those for whom garlic is more effective than placebo. D. H 0 : p = 0.5H a : p 0.5 Yes, the sample size was large enough to make the inference D. The P-value is greater than the significance level; do not reject the null hypothesis. There is not sufficient evidence that the proportion who think garlic more effective than a placebo is greater than C. The P-value gives strong evidence 10. A. The test statistic is calculated by taking the difference between the sample proportion and the null proportion and dividing it by the standard error. 8 of 9 B.

9 Use the value of the test statistic to find the two-tail probability from the standard normal distribution to the left and right of the test statistic value. B. The P-value tells us that if the null hypothesis were true, a proportion of sample data from the null hypothesis of samples would fall at least as far as the C. It does not make sense to accept the null hypothesis. It is possible that there is a real difference in the population that we are not detecting in our test, and we can never accept a null hypothesis. C. The 95% confidence interval tells us the range of plausible values, whereas the test merely tells us that 0.50 is plausible. 11. B. The P-value does not give strong evidence 9 of 9

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