## Question 944:

1## Answer:

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The 95% confidence interval is calculated as the margin of error times about 2 for a 95% level of confidence (1.96 to be more precise).

The margin of error is found as the standard error (SE) times the critical value from the t-distribution for the level of confidence. The critical value can be found using a t-table for 24 degrees of freedom. The attached excel calculator will lookup the value for you, which works out to be 2.06.

The standard error (SE) is the standard deviation divided by the square root of the sample size = 21.90/SQRT(25) = 4.38.

This makes the margin of error = 4.38*2.06 = 9.04 so the 95% confidence interval is 161.040 to 179.120, which is the answer to #1.

Changing the sample size to 46 changes the standard error to 21.90/SQRT(45) = 3.229 and makes the margin of error 6.5. The new 95% confidence interval is 163.577 to 176.583.