Suppose that a simple random sample is taken from a normal population having a s
ID: 3230033 • Letter: S
Question
Suppose that a simple random sample is taken from a normal population having a standard deviation of 13 for the purpose of obtaining a 95% confidence interval for the mean of the population. Complete parts (a) through (c) below The sample size is 9, obtain the mat gin of error The margin of error for a sample size of 9 is (Round to two decimal places as needed) Repeat pan (a) for a sample size of 36. The margin of error for a sample size of 36 is (Round to two decimal places as needed) c Can you guess the margin of error for a sample size or 144? Explain your reasoning The margin error for a sample size of 144 is (Round to two decimal places as needed) Explain your reasoning Because the sample size____ by a factor of___ from part b to part (c) the margin of error was by (Type whole numbers)Explanation / Answer
Given population Standard deviation(SD) is 13 and Significance level is 95%.
(a) Sample size is 9. Sincen is < 30, we use the tcritical for alpha=0.05 for degrees of freedom = n-1 = 9-1 = 8
The tcritical,0.05,8 = 2.306 for
ME = tcritical * SD/SQRT(n) = 2.306*13/SQRT(9) = 9.99
(b) Sample size is 36. Since n is > 30, we use the zcritical values for alpha=0.05 which is 1.96
ME =zcritical * SD/SQRT(n) = 1.96*13/SQRT(36) = 4.25
(c) Sample size is 144. Therefore the ME is = 2.12 WHY?
The sample size has increased 4 times from (b) which is 36 * 4.
Now ME = zcritical * SD/SQRT(n)
Therefore 1.96*13/ Sqrt(144)
= 1.96*13/SQRT(36*4) ....Since SQRT (A*B) = SQRT(A) * SQRT(B)
= 1.96*13/ [SQRT(36) * SQRT(4)] ...But we have calculated 1.96*13/SQRT(36) as 4.25 in (b).
Therefore, the equation becomes = 4.25/SQRT(4) = 4.25/2 = 2.12
In The last line enter the following:
Because the sample size increased by a factor of 4 from part (b) to part (c) The ME was divided/4.25 by 2. Please choose between divided or 4.25 as am not aware what will pop up as the options.
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