Question

A sample of 55 account balances of a credit card company showed a sample mean balance of $1,050. Assume that the population standard deviation is $175. At a 5% level of significance, test to determine if the population mean account balance is significantly different from $1,000. What is your conclusion?

Answer 1

Solution :

= 1000

= 1050

= 175

n = 55

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 1000

H_a :     1000

Test statistic = z

= ( - ) / / n

= (1050 - 1000) /175 / 55

= 2.119

P(z >2.119 ) = 1 - P(z <2.119 ) = 0.0341

P-value = 0.0341

= 0.05  

p = 0.0341 < 0.05, it is concluded that the null hypothesis is rejected.

There is enough evidence to claim that the population mean μ is different than 1000, at the 0.05 significance level.