Question

You are a HR manager for a fortune 500 firm in the metro area. You have been charged with determining why the firm faces a challenging time hiring new engineers. Based on your research, you think it has to do with starting salary. In order to test your hypothesis, you survey 10 engineers at the firm. The following are the results…

69,000   70,000   65,000 63,000 74,000 80,000 66,000 74,500 71,300 69,350

In addition to the salary data at the firm, you determine that the average salary for engineers in the industry is 76,000. Your job is to determine, based on your survey, whether your firm’s salary is statistically competitive. In order to address your question, what are the null and alternative hypotheses, which statistical analysis will you perform and what are your findings?

Answer 1

Sample size = n = 10

Sample mean = = 70215

Standard deviation = s = 5043.1499

Claim: The average salary for engineers in the industry is 76,000.

The null and alternative hypothesis is

Level of significance = 0.05

Here population standard deviation is unknown so we have to use t-test statistic.
Test statistic is

Degrees of freedom = n - 1 = 10 - 1 = 9

Critical value = 2.262 ( Using t table)

Test statistic | t | > critical vaue we reject null hypothesis.

Conclusion:

The average salary for engineers in the industry is NOT 76,000.