A manager of the credit department for an oil company would

A manager of the credit department for an oil company would like to determine whether the mean monthly balance of credit card holders is different than $80. an auditor selects a random sample of 100 accounts and finds that the mean owed is $88.40 with a sanple standard deviation of $23.65.(*3) state correct hypothesis and test to determine whether the auditor should conclude that there is evidence that the mean balance is different from 75 dollar. Use alpha = 0.05. Calculate confidence level using the same alpha. What is your conclusion for the above stated hypothesis.

Solution

a) H0 : population mean = 80 ag. H1 : population mean not equals 80..

Test statistic = ( 88.40 - 80) / ( 23.65 / sqrt ( 100) ) = 3.551797...

d.f = 100-1 = 99..
p-value = 0.0002938341....which is less than 0.05 = alpha..

critical value at alpha 0.05 = + or - 1.984217..

so, we should reject null hypothesis and state that there is enough evidence to conclude that the mean is different from 80...

b) confidence interval for alpha = 0.05..

= [ 88.40 - ( 1.984217 * 23.65 / sqrt ( 100) ) , 88.40 + ( 1.984217 * 23.65 / sqrt ( 100) ) ]
= [ 83.70733 , 93.09267]
the interval doesn\'t even include the point 80 , so reject H0 in favour of H1 i.e, the mean is different from 80......