Self-test help

#1
Hey guys. I have two questions I need answered to finish an independent test.

1. In sampling without replacement from a population of 900, it's found that the standard error of the mean is only two-thirds as large as it would have been if the population were infinite in size. What is the approximate sample size?

2. In a simple random sample from a pop. that's approximately normally distriubuted, the following data values were collected:

68, 79, 70, 98, 74, 79, 50, 102, 92, 96

Based on this information, the confidence level would be 90% that the pop. mean is somewhere between:

a) 71.36 and 90.24 b) 69.15 and 92.45 c) 65.33 and 95.33 d) 73.36 and 88.24

I used the t-distribution table for this one. I came out with

80.8 plus/minus 1.833 * 28.43/sqrt10. My answer comes close but does not match any of the answers.
 

JohnM

TS Contributor
#2
Try to re-compute your standard deviation - you should get 16.274, and that would push you toward choice A.
 
#3
Hi John. I'm confused on recomputing my standard deviation. Also, how would your answer push me towards answer A? What should I do for question #1 as well? Thanks so much for your help.
 

JohnM

TS Contributor
#4
On question 2, it looks like you're using 28.43 as the std dev, and it should be 16.274.

Sorry, but I passed right by question #1.

The adjustment to the standard error of the mean for finite populations is the formula:

(N - n) / (N - 1)

Set this equal to 2/3, plug in N=900, and solve for n (sample size).