4. A new population of Dalmatians has been discovered; µ, the unknown population

Question

4. A new population of Dalmatians has been discovered; µ, the unknown population mean number of spots for these new Dalmatians, may be different from 120, the mean number of spots on regular Dalmatians. You will use the mean number of spots from a sample of these new Dalmatians to make inferences about µ. Somehow, you know that for these new Dalmatians, the population standard deviation = 30.

a) Complete the table below with the six margins of error that would be part of confidence intervals for µ for the confidence levels assigned to you using samples of the specified sizes. Note: This table should include only margins of error. You should be sure that the relative sizes of the margins of error in each row and column make sense.

b) Suppose that you took a random sample of 9 new Dalmatians and found the sample mean number of spots shown in the last column of your assigned line in the table above. For your Confidence Level #2, give the confidence interval for µ expressed both as “sample mean ± margin of error” AND as the range of values covered (e.g., “from __ to __” in which the blanks are replaced by the sample mean – margin of error and sample mean + margin of error, respectively).

c) The confidence interval that you constructed in part b provides the information necessary to conduct a test of H0: µ = 120 vs. Ha: µ 120 at some level of . (1) What is the level of ? (2) With that level of , using this confidence interval, should H0: µ = 120 be rejected? Why or why not?

d) Suppose that you took a random sample of 100 new Dalmatians and found the sample mean number of spots shown in the last column of your assigned line in the table above. For your Confidence Level #2, give the confidence interval for µ expressed both as “sample mean ± margin of error” AND as the range of values covered (e.g., “from __ to __” in which the blanks are filled in by sample mean – margin of error and sample mean + margin of error, respectively).

e) The confidence interval that you constructed in part d provides the information necessary to conduct a test of H0: µ = 120 vs. Ha: µ 120 at the same level of as in part c. With that level of , given your sample mean (see table), should H0: µ = 120 be rejected? Why or why not?

CD#1 CD#2 CD#3 SAMPLE MEAN (FOR PART B AND D) 90% 96% 99% 105

Explanation / Answer

Part A, B and D

part C

alpha = 0.04
CI = (84.4625 , 125.5375 )
No, Null Hypothesis cannot be rejected as 120 lies in the CI

part E
alpha = 0.04
CI = (98.8388 , 111.1612 )
Reject the null hypothesis as 120 does not lie in the CI

CI = 90% and n = 9 CI = 90% and n = 100 CI for 90% 90% n 9 100 mean 105 105 z-value of 90% CI 1.6449 1.6449 std. dev. 30 30 SE = std.dev./sqrt(n) 10.00000 3.00000 ME = z*SE 16.44854 4.93456 Lower Limit = Mean - ME 88.55146 100.06544 Upper Limit = Mean + ME 121.44854 109.93456 90% CI (88.5515 , 121.4485 ) (100.0654 , 109.9346 )

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.