Question

An economist is studying salaries for high technology companies and wants to test the claim that the average salary for high
tech employees is less than $70,000.
The economist selects a sample of 35 random employees from various high tech companies and records their salaries.
Based on past studies, the economist determines that the population standard deviation is $8,500.
The economist conducts a one-mean hypothesis test at the 5% significance level to test the claim that the average salary for
high tech employees is less than $70,000.
The setup for the null and alternative hypothesis is given as:
Hoμ = 70,000; Ha < 70,000, which is a left-tailed test.
The sample data for 35 salaries is shown in the dataset below.
Use Excel to test the claim that the average salary for high tech employees is less than $70,000, where a = 0.05. Calculate
the test statistic, z, and the p-value, rounding to three decimal places.

Answer 1

The decision would be to fail to reject the null hypothesis and conclude that there is insufficient evidence.

How to solve for the mean of the data set

The formula is fx/n

To get fx we have to sum all of the values of x = 2430161

The total number in the data set = 35

Mean = 2430161/35

= 69433.17

This test is a left tail test.

sd = 8500

We have to make the hypothesis

H0: u = 70000

H1 : U < 70000

z0.05 = 1.645

The decision would be to reject if z < critical value

Z= (69433.17 - 70000)/(8500/√35)

= -0.395

P-value can be gotten from the z score = 0.348

Given that the p value is > 0.05, we would have to fail to reject the null. The conclusion would be that there is insufficient evidence to support claim.

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