Question

Kurtis is a statistician who claims that the average salary of an employee in the city of Yarmouth is no more than $55,000 per year. Gina, his colleague, believes this to be incorrect, so she randomly selects 61 employees who work in Yarmouth and record their annual salary. Gina calculates the sample mean income to be $56,500 per year with a sample standard deviation of 3,750. Using the alternative hypothesis Ha:μ>55,000, find the test statistic t and the p-value for the appropriate hypothesis test. Round the test statistic to two decimal places and the p-value to three decimal places.

Answer 1

Answer with explanation:

Let
`\mu` be the population mean.

As per given , we have

Alternative hypothesis :
`\mu>55000` , since it is right -tailed so the test is a right tailed test.

`\overline{x}=56500`

s= 3750 , since population standard deviation is unknown so we use t-test.

n=61

Degree of freedom : df= n-1=60

Test statistic :
`t=(x-\mu)/((s)/(√(n)))`

`\\\\=(56500-55000)/((3750)/(√(61)))\\\\=3.12409987036\approx3.12`

P-value (For right tailed test) =0.0014 [using right-tailed p-value table for t-test]