Question

An article reports that the average initial rate of absorption (in g/min·cm2) for a sample of five clay bricks with fine glass particles added was 1299.8 with a standard deviation of 329.8, and the average for another sample of fifteen bricks without glass particles added was 4500.8 with a standard deviation of 271.6. Let μX represent the population mean without glass particles and let μY represent the population mean with glass particles. Find a 98% confidence interval for the difference μX−μY . Round down the degrees of freedom to the nearest integer and round the answers to three decimal places.

The 98% confidence interval is

Answer 1

Confidence interval is :-

( X̅1 - X̅2 ) ± t( α/2 , n1+n2-2) SP √( (1/n1) + (1/n2))

t(α/2, n1 + n1 - 2) = t( 0.02/2, 5 + 15 - 2) = 2.552
( 1299.8 - 4500.8 ) ± t(0.02/2 , 5 + 15 -2) 285.5603 √ ( (1/5) + (1/15))
Lower Limit = ( 1299.8 - 4500.8 ) - t(0.02/2 , 5 + 15 -2) 285.5603 √( (1/5) + (1/15))
Lower Limit = -3577.325
Upper Limit = ( 1299.8 - 4500.8 ) + t(0.02/2 , 5 + 15 -2) 285.5603 √( (1/5) + (1/15))
Upper Limit = -2824.675
98% Confidence Interval is ( -3577.325 , -2824.675 )