Question

The birth weights for two groups of babies were compared in a study. In one group the mothers took a zinc supplement during pregnancy. In another group, the mothers took a placebo. A sample of 135 babies in the zinc group had a mean birth weight of 3075 grams. A sample of 141 babies in the placebo group had a mean birth weight of 3002 grams. Assume that the population standard deviation for the zinc group is 803 grams, while the population standard deviation for the placebo group is 897 grams. Determine the 95% confidence interval for the true difference between the mean birth weights for "zinc" babies versus "placebo" babies.

Step 1 of 2: Find the critical value that should be used in constructing the confidence interval.

Step 2 of 2:

Construct the 95%95% confidence interval. Round your answers to the nearest whole number.

Lower endpoint

Upper endpoint

Answer 1

SOLUTION:

From given data,

=135	=141
= 3075	= 3002
= 803	= 897

Step 1 of 2: Find the critical value that should be used in constructing the confidence interval.

95% confidence interval

Confidence interval = 95%

95% = 95/100 = 0.95

= 1 - Confidence interval = 1-0.95 = 0.05

/2 = 0.05 / 2

= 0.025

The critical value

Z_/2 = Z_0.025 = 1.96

Step 2 of 2: Construct the 95% confidence interval. Round your answers to the nearest whole number.

( - )   Z_/2 * sqrt (/ + / )

(3075 - 3002)   1.96 * sqrt (803²/135 + 897²/ 141)

73   1.96 * 102.38559357

73   200.6757634

( 73-200.6757634 ,   73+200.6757634 )

( -127.675 ,  273.675 )

(Round your answers to the nearest whole number.)

Lower end point : -128

Upper end point : 274