Question

We have created a 95% confidence interval for the mean with the result (10 to 15). What decision will we make if we test

H0: Mean = 16 and H1: Mean not equal to 16 at alpha = 0.05?

		A.Reject H0 and accept H1.
		B.Accept H0 and reject H1.
		C.Can't tell from the information given.

Answer 1

SOLUTION:

From given data,

We have created a 95% confidence interval for the mean with the result (10 to 15). What decision will we make if we test H₀: Mean = 16 and H₁: Mean not equal to 16 at alpha = 0.05?

mean =(15+10)/2 =22.5

95% confidence interval

Confidence interval is 95%

95% = 95/100 = 0.95

= 1 - Confidence interval = 1-0.95 = 0.05

/2 = 0.05 / 2

= 0.025

Z_/2 = Z_0.025 = 1.96

95% margin of error =(15-10)/2 =2.5 =1.96*se

se =2.5/1.96 =1.27551

at 0.05 level, margin of error =1.6449*se =1.6449*1.27551 =2.09808

at 0.05 level,, CI = (22.5-2.09808, 22.5-2.09808)

at 0.05 level,, CI = (20.401 , 24.598)

This interval does not contain 16.

therefore

Reject H₀ and accept H₁.

Answer: Option (A) is correct.