Question

Suppose that you are testing the hypotheses H0 : muμequals=1313 vs. HA : muμless than<1313. A sample of size 2525 results in a sample mean of 13.513.5 and a sample standard deviation of 1.51.5.
a) What is the standard error of the mean?
b) What is the critical value of t* for a 9595 % confidence interval?
c) Construct a 9595 % confidence interval for muμ.
d) Based on the confidence interval, at alphaαequals=0.0250.025 can you reject H0 ? Explain.

Answer 1

a)

Standard error of the mean = / sqrt(n)

= 1.5 / sqrt(25)

= 0.3

b)

df = n -1 = 25 - 1 = 24

t critical value at 0.05 level with 24 df = 2.064

c)

95% confidence interval for is

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

13.5 - 2.064 * 0.3 < < 13.5 + 2.064 * 0.3

12.8808 < < 14.1192

95% confidence interval for is (12.8808 , 14.1192)

d)

Since claimed mean 13 is lies in confidence interval, we do not have sufficient evidence to reject H0.