Answer to Question #262109 in Statistics and Probability for mmm

Question

A random sample of 16 values from a normal population showed a mean 41.5 inches and sum of squares of deviations from this mean equal to 135 square inches. Show that assumption of a mean of 43.5 inches for the population is not reasonable. Obtain 95% and 99% confidence limits for same.

Answer 1

$\bar{x} =41.5 \\ s = \sqrt{\frac{135}{16-1}}=3 \\ n=16$

Confidence interval:

$CI = \bar{x} ±$ Margin of error (E)

Standard error $sx = \frac{s}{\sqrt{n}}$

df= n-1=15

Critical value for 95% confidence interval $t_c=2.49$

$CI = 41.5 ± 2.490 \times 0.75 \\ CI = 41.5 ± 1.8674 \\ CI =(39.632, 43.367)$

Critical value for 99% confidence interval $t_c=3.286$

$CI = 41.5 ± 3.286 \times 0.75 \\ CI = 41.5 ± 2.4645 \\ CI =(39.035, 43.964)$

The assumption of a mean of 43.5 is NOT reasonable at 95% confidence interval as it does not fall within the interval range.

The assumption of a mean of 43.5 is reasonable at 99% confidence interval as it falls within the interval range.