16.)The mean height of women in a country (ages 2029) is 63.6 inches. A random sample of 60 women in this age group is selected. What is the probability that the mean height for the sample is greater than 64 inches? Assume =2.94. The probability that the mean height for the sample is greater than 64 inches is enter your response here. (Round to four decimal places as needed.) 17.)In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The responses were normally distributed, with a mean of 4.7 and a standard deviation of 2.5. Answer parts (a)-(d) below. (a) Find the probability that a randomly selected study participant's response was less than 4. The probability that a randomly selected study participant's response was less than 4 is enter your response here. (Round to four decimal places as needed.) (b) Find the probability that a randomly selected study participant's response was between 4 and 6. The probability that a randomly selected study participant's response was between 4 and 6 is enter your response here. (Round to four decimal places as needed.) (c) Find the probability that a randomly selected study participant's response was more than 8. The probability that a randomly selected study participant's response was more than 8 is enter your response here. (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. A. The event in part (a) is unusual because its probability is less than 0.05. B. The events in parts (a) and (c) are unusual because their probabilities are less than 0.05. C. There are no unusual events because all the probabilities are greater than 0.05. D. The events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05. 18.)Find the indicated area under the standard normal curve. To the left of z=0.26 Click here to view page 1 of the standard normal table. LOADING... Click here to view page 2 of the standard normal table. LOADING... The area to the left of z=0.26 under the standard normal curve is enter your response here. (Round to four decimal places as needed.) 19.)Find the indicated z-score shown in the graph to the right. z Area=0.2546z=? 0 A normal curve is over a horizontal z-axis and is centered on 0. A vertical line segment extends from the curve to the horizontal axis at a point labeled z = ?. The area under the curve and to the left of the vertical line segment is shaded and labeled Area = 0.2546. The z-score is enter your response here. (Round to two decimal places as needed.) 20.)Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded area of the graph. Assume the variable x is normally distributed. SAT Critical Reading Scores 200 800 475 Score =506=1222001160 Ha: 1160 B. H0: 1160 Ha: >1160 C. H0: >1192.96 Ha: 1192.96 D. H0: 1192.96 Ha: <1192.96 E. H0: 1160 Ha: <1160 f. h0: 1192.96 ha:>1192.96 Calculate the standardized test statistic. The standardized test statistic is enter your response here. (Round to two decimal places as needed.) Determine the P-value. P=enter your response here (Round to three decimal places as needed.) Determine the outcome and conclusion of the test. Fail to reject Reject H0. At the 7% significance level, there is is not enough evidence to support reject the claim. 22.)A random sample of 85 eighth grade students' scores on a national mathematics assessment test has a mean score of 287. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 280. Assume that the population standard deviation is 34. At =0.13, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify H0 and Ha. Choose the correct answer below. A. H0: 280 (claim) Ha: >280 B. H0: =280 (claim) Ha: >280 C. H0: <280 ha: 280 (claim) d. h0: <280 e.>280 (claim) F. H0: =280 Ha: >280 (claim) (b) Find the standardized test statistic z, and its corresponding area. z=enter your response here (Round to two decimal places as needed.) (c) Find the P-value. P-value=enter your response here (Round to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. Fail to reject H0 Reject H0 (e) Interpret your decision in the context of the original claim. At the 13% significance level, there is is not enough evidence to support reject the administrator's claim that the mean score for the state's eighth graders on the exam is more than 280. 23.)A nutritionist claims that the mean tuna consumption by a person is 3.1 pounds per year. A sample of 70 people shows that the mean tuna consumption by a person is 2.9 pounds per year. Assume the population standard deviation is 1.22 pounds. At =0.02, can you reject the claim? (a) Identify the null hypothesis and alternative hypothesis. A. H0: 2.9 Ha: =2.9 B. H0: >3.1 Ha: 3.1 C. H0: >2.9 Ha: 2.9 D. H0: 3.1 Ha: >3.1 E. H0: 2.9 Ha: >2.9 F. H0: =3.1 Ha: 3.1 (b) Identify the standardized test statistic. z=enter your response here (Round to two decimal places as needed.) (c) Find the P-value. enter your response here (Round to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. A. Reject H0. There is sufficient evidence to reject the claim that mean tuna consumption is equal to 3.1 pounds. B. Fail to reject H0. There is not sufficient evidence to reject the claim that mean tuna consumption is equal to 3.1 pounds. C. Reject H0. There is not sufficient evidence to reject the claim that mean tuna consumption is equal to 3.1 pounds. D. Fail to reject H0. There is sufficient evidence to reject the claim that mean tuna consumption is equal to 3.1 pounds. 24.)A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 55 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 55.6 milligrams. Assume the population is normally distributed and the population standard deviation is 7.9 milligrams. At =0.10, can you reject the company's claim? Complete parts (a) through (e). (a) Identify H0 and Ha. Choose the correct answer below. A. H0: 55.6 Ha: =55.6 B. H0: 55 Ha: <55 c. h0: ha: 55.6 d. 55 e. <55.6 f. (b) find the critical value(s). select correct choice below and fill in answer box within your choice. (round to two decimal places as needed.) a. values are enter response here. b. value is identify rejection region(s). choose below. -4 0 4 z reject h0.reject h0.fail h0. a normal curve over horizontal axis labeled from negative increments of 1 centered on 0. vertical line segments extend left right curve. area under segment lines shaded h@sub{0}. between fail extends (c) standardized test statistic. here (d) decide whether or null hypothesis. since region, not (e) interpret decision context original claim. at 10% significance level, there enough evidence support company's claim that mean caffeine content per 12-ounce bottle cola equal greater than different less milligrams. 25.)a fast food restaurant estimates sodium one its breakfast sandwiches no more 918 random sample 60 has 913 assume population standard deviation 23 do you have restaurant's claim? complete parts (a) through (e). hypothesis alternative <913 (claim)>918 C. H0: <913 (claim) ha: 913 d. h0: 918 e. f.>918 Ha: 918 (claim) (b) Identify the critical value(s). Use technology. z0=enter your response here (Use a comma to separate answers as needed. Round to two decimal places as needed.) Identify the rejection region(s). Select the correct choice below. A. The rejection region is z>1.28. B. The rejection regions are z>1.28 and z<1.28. C. The rejection region is z<1.28. (c) Identify the standardized test statistic. Use technology. z=enter your response here (Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. A. Reject H0. There is not sufficient evidence to reject the claim that mean sodium content is no more than 918 milligrams. B. Reject H0. There is sufficient evidence to reject the claim that mean sodium content is no more than 918 milligrams. C. Fail to reject H0. There is sufficient evidence to reject the claim that mean sodium content is no more than 918 milligrams. D. Fail to reject H0. There is not sufficient evidence to reject the claim that mean sodium content is no more than 918 milligrams. 26.)Use technology to help you test the claim about the population mean, , at the given level of significance, , using the given sample statistics. Assume the population is normally distributed. Claim: >1240; =0.03; =213.07. Sample statistics: x=1257.23, n=300 Identify the null and alternative hypotheses. Choose the correct answer below. A. H0: 1257.23 Ha: <1257.23 B. H0: 1257.23 Ha: >1257.23 C. H0: 1240 Ha: <1240 d. h0: 1240 ha:>1240 E. H0: >1257.23 Ha: 1257.23 F. H0: >1240 Ha: 1240 Calculate the standardized test statistic. The standardized test statistic is enter your response here. (Round to two decimal places as needed.) Determine the P-value. P=enter your response here (Round to three decimal places as needed.) Determine the outcome and conclusion of the test. Fail to reject Reject H0. At the 3% significance level, there is is not enough evidence to reject support the claim. 27.) A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 764 hours. A random sample of 23 light bulbs has a mean life of 744 hours. Assume the population is normally distributed and the population standard deviation is 61 hours. At =0.08, do you have enough evidence to reject the manufacturer's claim? Complete parts (a) through (e). (a) Identify the null hypothesis and alternative hypothesis. A. H0: >764 Ha: 764 (claim) B. H0: =744 Ha: 744 (claim) C. H0: 764(claim) Ha: =764 D. H0: 764 (claim) Ha: <764 e. h0: 744 ha:>744 (claim) F. H0: <744 (claim) ha: 744 (b) identify the critical value(s). use technology. z0=enter your response here (use a comma to separate answers as needed. round two decimal places needed.) rejection region(s). choose correct answer below. a. -4 0 4 z reject h0.fail h0. normal curve is over horizontal z-axis labeled from negative in increments of 1 and centered on 0. vertical line segment extends axis at 1.4. area under right 1.4 shaded one color upper h left another fail b. h0.reject segments extend are both 0.the between c. (c) standardized test statistic. (round (d) decide whether or null hypothesis, (e) interpret decision context original claim. there sufficient evidence claim that mean bulb life least 764 hours. not d. 28.)a scientist estimates nitrogen dioxide level city greater than 33 parts per billion. this estimate, you determine levels for 31 randomly selected days. results (in billion) listed right. assume population standard deviation 7. can support scientist's estimate? complete (a) through (e). 20 23 41 17 39 38 28 19 26 22 29 40 44 21 34 36 32 16 18 25 write mathematically h0 ha. following. h0: <33>33 D. H0: 33 Ha: >33 (claim) E. H0: =33 Ha: >33 (claim) F. H0: =33 (claim) Ha: >33 (b) Find the critical value and identify the rejection region. z0=enter your response here (Round to two decimal places as needed.) Rejection region: z greater than> less than< enter your response here (c) Find the standardized test statistic. z=enter your response here (Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. Reject H0 Fail to reject H0 (e) Interpret the decision in the context of the original claim. At the 11% significance level, there is not is enough evidence to support reject the scientist's claim that the mean nitrogen dioxide level in the city is greater than 33 parts per billion