Kurtis is a statistician who claims that the average salary of an employee in the city of Yarmouth is no more than $55,000per 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.

Question
Asked Oct 19, 2019

Kurtis is a statistician who claims that the average salary of an employee in the city of Yarmouth is no more than $55,000per 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.

check_circleExpert Solution
Step 1

From the given information, the null and alternative hypotheses are:

 

Null hypothesis:

 

H0: μ ≤ $55,000.

 

Alternative hypothesis:

 

Ha: μ > $55,000 (Right tail test).

 

The sample mean salary income is x-bar = $56,500, the sample size is = 61 and the sample standard deviation is = $3,750.

Step 2

The test statistic value is obtained as 3.12 ...

t=
vn
56,500 55,000
3,750
V61
3.12
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t= vn 56,500 55,000 3,750 V61 3.12

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Hypothesis Testing

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