STATISTICS: STA 2023 Chapter 8 Questions 15 – 20 are based on the following: The
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Question
STATISTICS: STA 2023
Chapter 8
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
Solution:-
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
Calculation,
Z Score Calculations
Z = (M - ) / (2 / n)
Z = (185 - 210) / (15625 / 100)
Z = -25 / 12.5
Z = -2
19. What is the P-value?
(a) 0.0228 (b) 0.456 (c) -2.00 (d) 0.0456
If P-value is less than or equal to significance level, then we reject the null hypothesis.
Here 0.456 is greater than 0.03. Therefore we fail to reject the null hypothesis.
20. State the final conclusion in simple non-technical terms.
(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.
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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 52 H1: 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
Z Score Calculations
Z = (M - ) / (2 / n)
Z = (52 - 50) / (225 / 60)
Z = 2 / 1.93649
Z = 1.0328
25. What is the P-value?
(a) 0.8485 (b) 1.03 (c) 1.63 (d) 0.1515 (e) -1.03
The p value is 0.151505. The result is not significant at p < 0.01.
If p-value is greater than significance level, then fail to reject null hypothesis.
26. State the final conclusion in simple non-technical terms.
(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.
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