STATISTICS: STA 2023 Chapter 8 Questions 1 – 7 are based on the following: Is Fa

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STATISTICS: STA 2023 Chapter 8 Questions 1 – 7 are based on the following: Is Facebook the most popular social media app among the North Camus student population? In a recent survey of 70 North Campus students, 56 indicated that Facebook was their number one choice in terms of social media apps. Use a 0.05 significance level to test the claim that the proportion of North campus students who choose Facebook as their number one choice is greater than 75%. Questions 8 – 14 are based on the following: What proportion of the North campus student population own a pet? In a survey of 50 randomly selected students, 30 indicated that they own a pet. Using these results, conduct a hypothesis test at the .05 significance level to test the claim that the proportion of North Campus students who own a pet is equal to 50 percent. 8. State the claim in symbolic form. (a) P £ .50(b) P ³ .50 (c) p > .50(d) p < .50 (e) p = .50 9. Identify the null and alternative hypotheses: (A) Ho: p ³ .50 H1: p < .50(b) Ho: p < .50H1: p ³ .50 (c) Ho: p > .50H1: p £ .50(d) Ho: p £ .50H1: p > .50 (e) Ho: p = .50H1: p .50 10. What type of hypothesis test is it? (a) left-tail(b) right-tailed(c) two-tailed 11. What is the value of the test statistic? (a) -1.41(b) 1.58(c) -1.58(d) 1.41(e) 23.62 12. What is the P-value? (a) 0.9207(b) 0.0793(c) 1.841(d) .1586(e) .0002 13. What is your conclusion? (a) Reject the null(b) Fail to reject the null 14. State the final conclusion in simple non-technical terms. Be sure to address the original claim (hint: see figure 8-7 on page 403) (a) There is not sufficient sample evidence to support the claim that that the proportion of North Campus students who own a pet is equal to 50 percent. (b) There is sufficient sample evidence to warrant rejection of the claim that the proportion of North Campus students who own a pet is equal to 50 percent. (c) There is not sufficient evidence to warrant rejection of the claim that the proportion of North Campus students who own a pet is equal to 50 percent. (d) The sample data support the claim that the proportion of North Campus students who own a pet is equal to 50 percent. (e) There is sufficient evidence to support the claim that the proportion of North Campus students who own a pet is equal to 50 percent. Questions 15 – 20 are based on the following: The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. In a sample of 100 bears, the mean weight was found to be 185 lbs. Assume that (population standard deviation) is known to be 125 lbs, use a 0.03 significance level to test the claim that the population mean weight of bears is equal to 210 lbs. 15. State the claim in symbolic form. (a) µ £ .210(b) µ ³ .185 (c) µ = 185(d) µ = 210 16. Identify the null and alternative hypotheses: (A) Ho: µ ³ 210 H1: µ < 210(b) Ho: µ = 210 H1: µ 210 (c) Ho: µ 210H1: µ = 210(d) Ho: µ £ 185 H1: µ > 185 17. What type of hypothesis test is this? (a) left-tail(b) right-tailed(c) two-tailed 18. What is the value of the test statistic? (a) 2.00(b) 0.0228(c) -2.00(d) .0456 19. What is the P-value? (a) 0.0228(b) 0.456(c) -2.00(d) 0.0456 20. State the final conclusion in simple non-technical terms. Be sure to address the original claim (hint: see figure 8-7 on page 403). (a) There is not sufficient sample evidence to support the claim that the population mean weight of bears is equal to 210 lbs. (b) There is sufficient sample evidence to warrant rejection of the claim that the population mean weight of bears is equal to 210 lbs. (c) There is not sufficient evidence to warrant rejection of the claim that the population mean weight of bears is equal to 210 lbs. (d) The sample data support the claim that more than 80% of adults believe that the population mean weight of bears is equal to 210 lbs. Are you smarter than a fifth-grader? A random sample of 60 fifth-graders in a certain school district are given a standardized mathematics skills test. The sample mean score is = 52. Assume the standard deviation of test scores is = 15. The nationwide average score on this test is 50. The school superintendent wants to know whether the fifth-graders in her school district have greater math skills than the nationwide average. Use a 0.01 level of significance to test the claim that the fifth-graders in her school district have higher math skills than the nationwide average. 21. State the claim in symbolic form. (a) µ £ 50(b) µ ³ 52 (c) µ > 50(d) µ = 50 (e) µ > 52 22. Identify the null and alternative hypotheses: (A) Ho: µ ³ 50 H1: µ < 50(b) Ho: µ = 52 H1: µ 52 (c) Ho: µ 52H1: µ = 52(d) Ho: µ £ 50 H1: µ > 50 23. What type of hypothesis test is this? (a) left-tail(b) right-tailed(c) two-tailed 24. What is the value of the test statistic? (a) -1.03(b) 0.8485(c) 1.03(d) .1515(e) 1.63 25. What is the P-value? (a) 0.8485(b) 1.03(c) 1.63(d) 0.1515(e) -1.03 26. State the final conclusion in simple non-technical terms. Be sure to address the original claim (hint: see figure 8-7 on page 403). (a) There is not sufficient sample evidence to support the claim that the fifth-graders have higher math skills than the nationwide average. (b) There is sufficient sample evidence to warrant rejection of the claim that the fifth-graders have higher math skills than the nationwide average. (c) There is not sufficient evidence to warrant rejection of the claim that the fifth-graders have higher math skills than the nationwide average. (d) The sample data support the claim that the fifth-graders have higher math skills than the nationwide average. 27. On a separate sheet of paper answer the following questions and turn in with your scantron. Show all your workings and calculations. Is it true that the mean age of students at North Campus is 25 year old? In a survey of 70 students at North Campus, the sample mean age was found to be 24.96, with a standard deviation s = 8.04. Using a .03 significance level, test the claim that mean age of students at North Campus is equal to 25. Show all steps in the hypothesis testing procedure. Clearly enumerate the null and alternative hypotheses. Show calculation of test statistic and p-vale. Give wording of the final conclusion using figure 8-7 on page 403 of your textbook. 28. Is it true that the majority of North campus students text while driving? In a survey of 60 students at North Campus, 45 indicated that they often text while driving. Using a .05 significance level, test the claim that the proportion of students at North Campus who text while driving is greater than 50%. Show all steps in the hypothesis testing procedure. Clearly enumerate the null and alternative hypotheses. Show calculation of test statistic and p-vale. Give wording of the final conclusion using figure 8-7 on page 403 of your textbook. STATISTICS: STA 2023 Chapter 8 Questions 1 – 7 are based on the following: Is Facebook the most popular social media app among the North Camus student population? In a recent survey of 70 North Campus students, 56 indicated that Facebook was their number one choice in terms of social media apps. Use a 0.05 significance level to test the claim that the proportion of North campus students who choose Facebook as their number one choice is greater than 75%. Questions 8 – 14 are based on the following: What proportion of the North campus student population own a pet? In a survey of 50 randomly selected students, 30 indicated that they own a pet. Using these results, conduct a hypothesis test at the .05 significance level to test the claim that the proportion of North Campus students who own a pet is equal to 50 percent. 8. State the claim in symbolic form. (a) P £ .50(b) P ³ .50 (c) p > .50(d) p < .50 (e) p = .50 9. Identify the null and alternative hypotheses: (A) Ho: p ³ .50 H1: p < .50(b) Ho: p < .50H1: p ³ .50 (c) Ho: p > .50H1: p £ .50(d) Ho: p £ .50H1: p > .50 (e) Ho: p = .50H1: p .50 10. What type of hypothesis test is it? (a) left-tail(b) right-tailed(c) two-tailed 11. What is the value of the test statistic? (a) -1.41(b) 1.58(c) -1.58(d) 1.41(e) 23.62 12. What is the P-value? (a) 0.9207(b) 0.0793(c) 1.841(d) .1586(e) .0002 13. What is your conclusion? (a) Reject the null(b) Fail to reject the null 14. State the final conclusion in simple non-technical terms. Be sure to address the original claim (hint: see figure 8-7 on page 403) (a) There is not sufficient sample evidence to support the claim that that the proportion of North Campus students who own a pet is equal to 50 percent. (b) There is sufficient sample evidence to warrant rejection of the claim that the proportion of North Campus students who own a pet is equal to 50 percent. (c) There is not sufficient evidence to warrant rejection of the claim that the proportion of North Campus students who own a pet is equal to 50 percent. (d) The sample data support the claim that the proportion of North Campus students who own a pet is equal to 50 percent. (e) There is sufficient evidence to support the claim that the proportion of North Campus students who own a pet is equal to 50 percent. Questions 15 – 20 are based on the following: The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. In a sample of 100 bears, the mean weight was found to be 185 lbs. Assume that (population standard deviation) is known to be 125 lbs, use a 0.03 significance level to test the claim that the population mean weight of bears is equal to 210 lbs. 15. State the claim in symbolic form. (a) µ £ .210(b) µ ³ .185 (c) µ = 185(d) µ = 210 16. Identify the null and alternative hypotheses: (A) Ho: µ ³ 210 H1: µ < 210(b) Ho: µ = 210 H1: µ 210 (c) Ho: µ 210H1: µ = 210(d) Ho: µ £ 185 H1: µ > 185 17. What type of hypothesis test is this? (a) left-tail(b) right-tailed(c) two-tailed 18. What is the value of the test statistic? (a) 2.00(b) 0.0228(c) -2.00(d) .0456 19. What is the P-value? (a) 0.0228(b) 0.456(c) -2.00(d) 0.0456 20. State the final conclusion in simple non-technical terms. Be sure to address the original claim (hint: see figure 8-7 on page 403). (a) There is not sufficient sample evidence to support the claim that the population mean weight of bears is equal to 210 lbs. (b) There is sufficient sample evidence to warrant rejection of the claim that the population mean weight of bears is equal to 210 lbs. (c) There is not sufficient evidence to warrant rejection of the claim that the population mean weight of bears is equal to 210 lbs. (d) The sample data support the claim that more than 80% of adults believe that the population mean weight of bears is equal to 210 lbs. Are you smarter than a fifth-grader? A random sample of 60 fifth-graders in a certain school district are given a standardized mathematics skills test. The sample mean score is = 52. Assume the standard deviation of test scores is = 15. The nationwide average score on this test is 50. The school superintendent wants to know whether the fifth-graders in her school district have greater math skills than the nationwide average. Use a 0.01 level of significance to test the claim that the fifth-graders in her school district have higher math skills than the nationwide average. 21. State the claim in symbolic form. (a) µ £ 50(b) µ ³ 52 (c) µ > 50(d) µ = 50 (e) µ > 52 22. Identify the null and alternative hypotheses: (A) Ho: µ ³ 50 H1: µ < 50(b) Ho: µ = 52 H1: µ 52 (c) Ho: µ 52H1: µ = 52(d) Ho: µ £ 50 H1: µ > 50 23. What type of hypothesis test is this? (a) left-tail(b) right-tailed(c) two-tailed 24. What is the value of the test statistic? (a) -1.03(b) 0.8485(c) 1.03(d) .1515(e) 1.63 25. What is the P-value? (a) 0.8485(b) 1.03(c) 1.63(d) 0.1515(e) -1.03 26. State the final conclusion in simple non-technical terms. Be sure to address the original claim (hint: see figure 8-7 on page 403). (a) There is not sufficient sample evidence to support the claim that the fifth-graders have higher math skills than the nationwide average. (b) There is sufficient sample evidence to warrant rejection of the claim that the fifth-graders have higher math skills than the nationwide average. (c) There is not sufficient evidence to warrant rejection of the claim that the fifth-graders have higher math skills than the nationwide average. (d) The sample data support the claim that the fifth-graders have higher math skills than the nationwide average. 27. On a separate sheet of paper answer the following questions and turn in with your scantron. Show all your workings and calculations. Is it true that the mean age of students at North Campus is 25 year old? In a survey of 70 students at North Campus, the sample mean age was found to be 24.96, with a standard deviation s = 8.04. Using a .03 significance level, test the claim that mean age of students at North Campus is equal to 25. Show all steps in the hypothesis testing procedure. Clearly enumerate the null and alternative hypotheses. Show calculation of test statistic and p-vale. Give wording of the final conclusion using figure 8-7 on page 403 of your textbook. 28. Is it true that the majority of North campus students text while driving? In a survey of 60 students at North Campus, 45 indicated that they often text while driving. Using a .05 significance level, test the claim that the proportion of students at North Campus who text while driving is greater than 50%. Show all steps in the hypothesis testing procedure. Clearly enumerate the null and alternative hypotheses. Show calculation of test statistic and p-vale. Give wording of the final conclusion using figure 8-7 on page 403 of your textbook. STATISTICS: STA 2023 Chapter 8 Questions 1 – 7 are based on the following: Is Facebook the most popular social media app among the North Camus student population? In a recent survey of 70 North Campus students, 56 indicated that Facebook was their number one choice in terms of social media apps. Use a 0.05 significance level to test the claim that the proportion of North campus students who choose Facebook as their number one choice is greater than 75%. Questions 8 – 14 are based on the following: What proportion of the North campus student population own a pet? In a survey of 50 randomly selected students, 30 indicated that they own a pet. Using these results, conduct a hypothesis test at the .05 significance level to test the claim that the proportion of North Campus students who own a pet is equal to 50 percent. 8. State the claim in symbolic form. (a) P £ .50(b) P ³ .50 (c) p > .50(d) p < .50 (e) p = .50 9. Identify the null and alternative hypotheses: (A) Ho: p ³ .50 H1: p < .50(b) Ho: p < .50H1: p ³ .50 (c) Ho: p > .50H1: p £ .50(d) Ho: p £ .50H1: p > .50 (e) Ho: p = .50H1: p .50 10. What type of hypothesis test is it? (a) left-tail(b) right-tailed(c) two-tailed 11. What is the value of the test statistic? (a) -1.41(b) 1.58(c) -1.58(d) 1.41(e) 23.62 12. What is the P-value? (a) 0.9207(b) 0.0793(c) 1.841(d) .1586(e) .0002 13. What is your conclusion? (a) Reject the null(b) Fail to reject the null 14. State the final conclusion in simple non-technical terms. Be sure to address the original claim (hint: see figure 8-7 on page 403) (a) There is not sufficient sample evidence to support the claim that that the proportion of North Campus students who own a pet is equal to 50 percent. (b) There is sufficient sample evidence to warrant rejection of the claim that the proportion of North Campus students who own a pet is equal to 50 percent. (c) There is not sufficient evidence to warrant rejection of the claim that the proportion of North Campus students who own a pet is equal to 50 percent. (d) The sample data support the claim that the proportion of North Campus students who own a pet is equal to 50 percent. (e) There is sufficient evidence to support the claim that the proportion of North Campus students who own a pet is equal to 50 percent. Questions 15 – 20 are based on the following: The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. In a sample of 100 bears, the mean weight was found to be 185 lbs. Assume that (population standard deviation) is known to be 125 lbs, use a 0.03 significance level to test the claim that the population mean weight of bears is equal to 210 lbs. 15. State the claim in symbolic form. (a) µ £ .210(b) µ ³ .185 (c) µ = 185(d) µ = 210 16. Identify the null and alternative hypotheses: (A) Ho: µ ³ 210 H1: µ < 210(b) Ho: µ = 210 H1: µ 210 (c) Ho: µ 210H1: µ = 210(d) Ho: µ £ 185 H1: µ > 185 17. What type of hypothesis test is this? (a) left-tail(b) right-tailed(c) two-tailed 18. What is the value of the test statistic? (a) 2.00(b) 0.0228(c) -2.00(d) .0456 19. What is the P-value? (a) 0.0228(b) 0.456(c) -2.00(d) 0.0456 20. State the final conclusion in simple non-technical terms. Be sure to address the original claim (hint: see figure 8-7 on page 403). (a) There is not sufficient sample evidence to support the claim that the population mean weight of bears is equal to 210 lbs. (b) There is sufficient sample evidence to warrant rejection of the claim that the population mean weight of bears is equal to 210 lbs. (c) There is not sufficient evidence to warrant rejection of the claim that the population mean weight of bears is equal to 210 lbs. (d) The sample data support the claim that more than 80% of adults believe that the population mean weight of bears is equal to 210 lbs. Are you smarter than a fifth-grader? A random sample of 60 fifth-graders in a certain school district are given a standardized mathematics skills test. The sample mean score is = 52. Assume the standard deviation of test scores is = 15. The nationwide average score on this test is 50. The school superintendent wants to know whether the fifth-graders in her school district have greater math skills than the nationwide average. Use a 0.01 level of significance to test the claim that the fifth-graders in her school district have higher math skills than the nationwide average. 21. State the claim in symbolic form. (a) µ £ 50(b) µ ³ 52 (c) µ > 50(d) µ = 50 (e) µ > 52 22. Identify the null and alternative hypotheses: (A) Ho: µ ³ 50 H1: µ < 50(b) Ho: µ = 52 H1: µ 52 (c) Ho: µ 52H1: µ = 52(d) Ho: µ £ 50 H1: µ > 50 23. What type of hypothesis test is this? (a) left-tail(b) right-tailed(c) two-tailed 24. What is the value of the test statistic? (a) -1.03(b) 0.8485(c) 1.03(d) .1515(e) 1.63 25. What is the P-value? (a) 0.8485(b) 1.03(c) 1.63(d) 0.1515(e) -1.03 26. State the final conclusion in simple non-technical terms. Be sure to address the original claim (hint: see figure 8-7 on page 403). (a) There is not sufficient sample evidence to support the claim that the fifth-graders have higher math skills than the nationwide average. (b) There is sufficient sample evidence to warrant rejection of the claim that the fifth-graders have higher math skills than the nationwide average. (c) There is not sufficient evidence to warrant rejection of the claim that the fifth-graders have higher math skills than the nationwide average. (d) The sample data support the claim that the fifth-graders have higher math skills than the nationwide average. 27. On a separate sheet of paper answer the following questions and turn in with your scantron. Show all your workings and calculations. Is it true that the mean age of students at North Campus is 25 year old? In a survey of 70 students at North Campus, the sample mean age was found to be 24.96, with a standard deviation s = 8.04. Using a .03 significance level, test the claim that mean age of students at North Campus is equal to 25. Show all steps in the hypothesis testing procedure. Clearly enumerate the null and alternative hypotheses. Show calculation of test statistic and p-vale. Give wording of the final conclusion using figure 8-7 on page 403 of your textbook. 28. Is it true that the majority of North campus students text while driving? In a survey of 60 students at North Campus, 45 indicated that they often text while driving. Using a .05 significance level, test the claim that the proportion of students at North Campus who text while driving is greater than 50%. Show all steps in the hypothesis testing procedure. Clearly enumerate the null and alternative hypotheses. Show calculation of test statistic and p-vale. Give wording of the final conclusion using figure 8-7 on page 403 of your textbook.

Explanation / Answer

The statistical software output for problem 8 - 14 is:

One sample proportion hypothesis test:
p : Proportion of successes
H0 : p = 0.5
HA : p 0.5

Hypothesis test results:

Hence,

8. Option E

9. Option E

10. Option C

11. Option D

12. Option D

13. Option B

14. Option C

Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value p 30 50 0.6 0.070710678 1.4142136 0.1573

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