Question

Given two independent random samples with the following results: n1=11 x1=141 s1=21 n2=17 x2=116 s2=24 Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed.

Step 1 of 3 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 2 of 3: Find the standard error of the sampling distribution to be used in construsting the confidence interval. round to the nearest whole number.

Step 3 of 3: construct the 99% confidence interval, round to the nearest whole number. (Lower endpoint, upper end point

Answer 1

Solution

Given ,

  = 141 = 116

s₁ = 21 s₂ = 24

n₁ = 11 n₂ = 17

For 99% confidence

= 1 - 0.99 = 0.01

/2 = 0.005

Formula for confidence interval for   ₁ - ₂

( - )     *

( - )     *   

Step 1 of 3 : Find the critical value

d.f. = n₁ + n₂ - 2 = 11 + 17 - 2 = 26

/2 = 0.005

   = _0.005,26 = 2.779 (using t table)

Step 2 of 3: Find the standard error

S.E. =   

= 8.858

Step 3 of 3: construct the 99% confidence interval

Point estimate = - = 141 - 116 = 25

Margin of error = * S.E. = 2.779 * 8.858   = 25

Confidence interval is  Point estimate Margin of error

(24 - 25 , 24 + 25 )

(-1 , 49)