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1. Looking at all employee records, the standard deviation of salary is known to be approximately $4,000. We wish to construct a 95% confidence interval for the mean salary of male employees. Forty-eight male employees are surveyed. The sample mean is $62,500. The sample standard deviation is $3,500. (See video link below if needed.)

a) x=

b) =

c) n=

2. Calculate the error bound.

z = (x-)/

z=

3. Using the same mean, standard deviation, and sample size, how would the error bound change if the confidence level were reduced to 90%? Why?

4. The mean entry-level salary of an employee at your hospital is $38,000. You believe it is higher for males in the company. State the null and alternative hypotheses.

H₀ = _____

H₁ = _____

5. A coworker claims the mean satisfaction rating of employees is 3.2 (on a scale from 1 to 5, where 5 is extremely satisfied). You conduct a test to see if the claim is true. State the Type I and Type II errors in complete sentences.

Type I Error:

Type II Error:

6. A hospital human resource manager claims the mean commute time (one way) is 23.2 minutes for nurses. You feel the commute time is less and want to investigate. The mean for 25 randomly selected nurses is 22 minutes with a standard deviation of 4.8 minutes. At the = 0.01 level, is the commute significantly less than the human resource manager's mean commute time? State your conclusion and provide evidence to back up your claim.

7. A random survey of 50 employees revealed that the mean age of an employee is 39.8 years with a standard deviation of 7.9 years. Conduct a hypothesis test with = 0.05 to determine if the population mean age of an employee could likely be 36 years. State your conclusion and provide evidence to back up your claim.