Question

A sample of 81 account balances of a credit company showed an average balance of $1,200. The population standard deviation is $126. You want to determine if the mean of all account balances is significantly different from $1,150. Use a .05 level of significance.

a) State the null and alternative hypotheses.

b) Calculate test statistic.

c) What is the p-value for this test?

d) What is the critical value for this test?

e) What is your conclusion? Why?

Answer 1

a)

H0: = 1150

Ha: 1150

b)

Test statistics

z = - / / sqrt(n)

= 1200 - 1150 / 126 / sqrt(81)

= 3.57

This is test statistics value.

c)

p-value = 2 * P( Z > z)

= 2 * P (Z > 3.57)

= 2 * 0.0002

= 0.0004

d)

Critical values at 0.05 level = -1.96 , 1.96

e)

Since p-value < 0.05 level, we have sufficient evidence to reject H0.

We conclude at 0.10 level that we have enough evidence to support the claim.