Question

Suppose that you are testing the hypotheses H0​: μ=12 vs. HA​: μless than<12. A sample of size 25 results in a sample mean of 12.5 and a sample standard deviation of 1.9. ​a) What is the standard error of the​ mean? ​b) What is the critical value of​ t* for a 90​% confidence​ interval? ​c) Construct a 90​% confidence interval for μ. ​d) Based on the confidence​ interval, at alphaαequals=0.05 can you reject H0​? Explain.

Answer 1

a)

Standard error of the mean = Standard deviation / sqrt(n)

= 1.9 / sqrt(25)

= 0.38

b)

df = n -1 = 25 - 1 = 24

t critical value at 90% confidence = 1.711

c)

90% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

12.5 - 1.711 * 0.38 < < 12.5 + 1.711 * 0.38

11.85 < < 13.15

90% CI is ( 11.85 , 13.15 )

d)

Since claimed mean 12 contained in confidence interval, we do not have sufficient evidence to reject H0.

We fail to reject the null hypothesis.