Question

If a 90% confidence interval for mean pH is (13.2, 14.1), which of the following is certainly true? Select one: a. Testing H0: µ = 13 vs. H0: µ > 13 will lead to rejecting H0 at α = 0.05. cross out b. The 80% confidence interval will contain 13. cross out c. Testing H0: µ = 13 vs. H0: µ > 13 will lead to not rejecting H0 at α = 0.05 cross out d. Testing H0: µ = 14 vs. H0: µ < 14 will lead to rejecting H0 at α = 0.05. cross out e. The 95% confidence interval will not contain 14.

Answer 1

90% Confidence interval for mean is ( 13.2 , 14.1)

[ Before answering the question please note the following points:

• α= 0.05 means 95% confidence level
• 95% confidence interval will be wider than 90% of the confidence interval
• 80% confidence interval will be narrower than 90% of the confidence interval

]

a. Testing H0: µ = 13 vs. H0: µ > 13 will lead to rejecting H0 at α = 0.05

FALSE, As α= 0.05 means 95% confidence interval, which is wider than the 90% interval, So it will contailn 13,

So, we cannot reject H0.

b. The 80% confidence interval will contain 13.

FALSE, As 80% will be narrower than 90% interval, so we are not sure that 13 will be there in the interval or not

c. Testing H0: µ = 13 vs. H0: µ > 13 will lead to not rejecting H0 at α = 0.05

TRUE   As it will contain 13 ( already explained in part (a) )

d. Testing H0: µ = 14 vs. H0: µ < 14 will lead to rejecting H0 at α = 0.05

FALSE,  As α= 0.05 means 95% confidence interval, which is wider than the 90% interval, So it will contailn 14

So, we cannot reject H0.

e. The 95% confidence interval will not contain 14.

FALSE, As 95% will be widwr than 90% of the confidence interval, so it will contain 14