Question

The manager of a department store is thinking about establishing a new billing system for the store's credit customers. She determines that the new system will be cost effective only if the mean monthly account is more than $170. A random sample of 400 monthly accounts is drawn for which the sample mean is $178. The manager knows that the accounts are approximately normally distributed with a standard deviation of $65.

Can the manager conclude from this that the new system will be cost-effective? Explain using both region approach (at 5% significance level) and a P-Value approach.

Answer 1

Solution :

= 170

= 178

s = 65

n = 400

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 170

H_a : > 170

Test statistic = t

= ( - ) / s / n

= (178-170) /35 / 400

= 2.462

Test statistic is t value = 2.462

P-value = 0.0071

= 0.05  

P-value <

0.0071 < 0.05

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is greater than 170, at the 0.05 significance level