Chapter 8 Quiz

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San Jose State University *

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Statistics

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Jun 22, 2024

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1. Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. A skeptical paranormal researcher claims that theproportion of Am ericans that have seen a UFO, p, is less than 2 in every ten thousand. Assuming t hat a hypothesis test of the claim has been conducted andthat the conclusion is f ailure to reject the null hypothesis, state the conclusion in nontechnical terms. a.There is not sufficient evidence to support the claim that the true proportion is l ess than 2 in ten thousand. b. There is not sufficient evidence to support the claim that the true proportion is greater than 2 in ten thousand. c. There is sufficient evidence to support the claim that the true proportion is less than 2 in ten thousand. d. There is sufficient evidence to support the claim that the true proportion is gre ater than 2 in ten thousand. 2. Assume that the data has a normal distribution and the number of observations i s greater than fifty. Find the critical z value used to test a nullhypothesis. α = 0.0 5 for a two-tailed test. Group of answer choices

3. Express the null hypothesis and the alternative hypothesis in symbolic form. An e ntomologist writes an article in a scientific journal which claimsthat fewer than 14 in ten thousand male fireflies are unable to produce light due to a genetic mutati on. Use the appropriate parameter (p or μ) , the trueproportion of fireflies unable to produce light. Group of answer choices a. H0: p = 0.0014 H1: p > 0.0014 b. H0: μ = 0.0014 H1: μ > 0.0014 c. H0: p = 0.0014 H1: p < 0.0014 d. H0: μ = 0.0014 H1: μ < 0.0014 4. Use the given information to find the Pvalue. Also, use a 0.05 significance level a nd state the conclusion about the null hypothesis (reject the nullhypothesis or fail to reject the null hypothesis). The test statistic in a left-tailed test is z = -2.05. Group of an swer choices 5. Assume that the data has a normal distribution and the number of observations i s greater than fifty. Find the critical z value used to test a nullhypothesis. α = 0.05 for a lef t-tailed test.

6. Find the value of the test statistic z using z = ((p) hat - p/square root of ((pq/n))) . A claim is made that the proportion of children who play sportsis less than 0.5, a nd the sample statistics include n = 1469 subjects with 30% saying that they pla y a sport.

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7. The mean height of adult men in the U.S. is 69.7 inches, with a standar d deviation of 3 inches. A sociologist believes that taller men may be m orelikely to be promoted to positions of leadership, so the mean height of male business executives may be greater than the mean height of t he entire malepopulation. A simple random sample of 100 male busine ss executives has a mean height of 69.9 in. Assume that the standard deviation of male executiveheights is = 3 inches. Can we conclude that male business executives are taller on the average than the general m ale population at the = 0.05 level.

Z test statistic= 0.6667, p-value 0.2524, Do not reject the null. 8. Use the given information to find the P-value. Also, use a 0.05 significance level and stat e the conclusion about the null hypothesis (reject the nullhypothesis or fail to reject the n ull hypothesis). With H1: p ≠ 0.501, the test statistic is z = 2.83. a. 0.0023; fail to reject the null hypothesis b. 0.0046; fail to reject the null hypothesis c. 0.0046; reject the null hypothesis

d. 0.0023; reject the null hypothesis 9. Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. If p value = 0.02, then a. the null is rejected at α = 0.05. b. the null is rejected at α = 0.01. c. the null will be rejected at both α = 0.01 and α = 0.05 d. It can not be determined. 10. Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. An entomologist writes an article in a scientificjournal which claims that fewer tha n 4 in ten thousand male fireflies are unable to produce light due to a genetic mutation. A ssuming that a hypothesis test ofthe claim has been conducted and that the conclusion is t o reject the null hypothesis, state the conclusion in nontechnical terms. Group of answer c hoices

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a. There is sufficient evidence to support the claim that the true proportion is less than 4 in t en thousand. b. There is not sufficient evidence to supportthe claim that the true proportion is les s than 4 in ten thousand. c. There is not sufficient evidence to support the claim that the true proportion is g reater than 4 in ten thousand. d. There is sufficient evidence to support the claim that the true proportion is great er than 4 in ten thousand. 11. Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution, or neither.Claim: μ = 119. Sa mple data: n = 11, overbar(x) = 110, s = 15.2. The sample data appear to come from a normally distributed population with unknown μ and σ. a. Student t b. Normal c. Neither 12. Formulate the indicated conclusion in nontechnical terms. Be sure to address the ori ginal claim. Generic drugs are lower-cost substitutes for brand-name drugs. Before a ge neric drug can be sold in the United States, it must be tested and found to perform equi valently to the brand name product. The U.S.Food and Drug Administration is now super vising the testing of a new generic antifungal ointment. The brand-name ointment is kn own to deliver a mean of 3.5micrograms of active ingredient to each square centimeter of skin. As part of the testing, seven subjects apply the ointment. Six hours later, the a mount ofdrug that has been absorbed into the skin is measured. The amounts, in micro grams, are 2.6 3.2 2.1 3.0 3.1 2.9 3.7 How strong is the evidence that the meanamount absorbed differs from 3.5 micrograms? Use the = 0.05 level of significance. DF= 6 , t test -statistic = -2.95, p-value=0.026; Reject the null.

13. Suppose we want to test the claim the majority of adults are in favor of rising the voting age to 21. I the hypothesis test left-tailed, right-tailed, or two tailed? Right tailed.

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Find the P-value for the indicated hypothesis test. 14. A medical school claims that more than 28% of its students plan to go into general practice. It is found that among a random sample of 130 of the school’s students, 32% of them plan to go into general practice. Find the P value for a test of the school’s claim(Use graphing calculator’s function) a. 0.1370 b. 0.3461 c. 0.1935 d. 0.3078 15. Express the null hypothesis and the alternative hypothesis in symbolic form. The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, , of 40 F , ideal for a certain type of German pilsner. The owner of the brewer does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. a. H H b. H H

c. H d. H H 16. Find the P-value for the indicated hypothesis test. In a sample of 88 children selected randomly from one town, it is found that 8 of them suffer from asthma. Find the two-tailed P-value for a test of the claim that the proportion of all children in the town who suffer from asthma is equal to 11%. a. 0.2843 b. 0.5671 c. 0.2157 d. -0.2843