Question

1. Bo Derek calculates that she needs a sample size of 200, given the sampling error, population variance and required z-score for 95% confidence. However, she learns later that the true variance is half of what she used in the sample size calculation. Based on this new value of variance, new sample size required will now be ________.

1. 100
2. 800
3. 400
4. 50

1. A college dean wants to determine the average time it takes a student to get from one class to the next. Preliminary studies have shown that it is reasonable to assume that the standard deviation of class travel times is 1.5 minutes. What is the sample size needed if the dean wants to achieve a maximum sampling error at 0.25 minutes in his mean estimate at 95% confidence level?

1. 99
2. 144
3. 240
4. None of the above

Answer 1

n =sample size;

=Variance;

=Standard deviation

1)

Option A. 100 is correct.

We know that the standard error, SE =

Now, since the variance is half, the new variance is: 0.5

Thus, new sample size, n* =0.5 =100

2)

Option D. None of the above is correct.

Standard deviation, =1.5 mins

At 95% confidence level, for a two-tailed case, the critical value of Z =1.96

Maximum sampling error, E =0.25 mins

We know that, E =

n =[1.96*1.5/0.25]2 =138.2976

Rounding to the next integer, n =139

The minimum sample size is required is 139.

However, if we use Z =2 instead of 1.96 (that is, rounding 1.96 to 2), we get n =144.

However, 1.96 is the exact Z value and thus, "none of the above" option is correct.