Question

Suppose that you are testing the hypotheses H0​: μ=70 vs. HA​: μ≠70. A sample of size 41 results in a sample mean of 65 and a sample standard deviation of 1.7.

a) What is the standard error of the​ mean? ​

b) What is the critical value of​ t* for a 99​% confidence​ interval? ​

c) Construct a 99​% confidence interval for μ. ​

d) Based on the confidence​ interval, at α=0.010 can you reject H0​? Explain.

Answer 1

a)

Standard error (SE) = Standard deviation / Sqrt (n)

= 1.7 / sqrt(41)

= 0.2655

b)

df = n -1 = 41 - 1 = 40

t critical value at 0.01 significance level = 2.704

c)

99% confidence interval for is

- t * SE < < + t * SE

65 - 2.704 * 0.2655 < < 65 + 2.704 * 0.2655

64.282 < < 65.718

99% CI is ( 64.282 , 65.718 )

d)

Since claimed mean 70 is not contained in confidence interval, we have sufficient evidence to reject H0.