PSYC 220

Homework 4 

1. We reject the null hypothesis when:

a) our test statistic exceeds our critical value

b) our critical value exceeds our test statistic

c) our critical value equals our test statistic

d) when z = 1.96

e) when z = 2.33

2. When we reject the null hypothesis, we are saying that…

a) we have proven the alternative hypothesis to be true

b) we have proven the null hypothesis to be true

c) our sample is too unlikely to have been produced by the null distribution

d) our sample had a mean approximately the same as the population

e) our sample had a standard deviation smaller than the population 

3. As the probability of committing a Type I error goes up:

a) We are more likely to reject the null hypothesis

b) We are less likely to reject the null hypothesis

c) Probability of Type II error goes up

d) Probability of falsely retaining the null goes up

e) Probability of correctly retaining the null goes up

4. If our α = .05, we should make Type I Errors ___% of the time?

a) 2.5

b) 5

c) 95

d) .01

e) .025

5. What’s an example of a situation where someone might prefer to make to make a Type I error rather than a Type II error? 

IMPORTANT: For the following three questions, whenever you test a hypothesis, be sure to specify both hypotheses, report the critical Z, the standard error, the test statistic and then make a decision. Report your decision in a sentence.

6. The population of workers in a company take an average of 75 steps (µ = 75 and σ=12) a day. The company wants to see whether providing pedometer (a device that tells people how many steps they’ve taken that day) to their employees would alter the amount of exercise they got. The company selected a sample of 9 employees and provided them with pedometers. This sample of workers took an average of 84 steps a day. Assuming the population is normally distributed, use an alpha of .05 to test the hypothesis that the pedometer altered the number of steps taken.

7. The population of adults with tablets and/or smartphones get an average of 6 hours 

(µ = 6 and σ = 2) of sleep a night. To see whether electronic use was interfering with sleep, researchers had a sample of 25 adults turn off their smartphones and tablets 1 hour before going to bed. This sample got an average of 6.7 hours of sleep a night. Assuming the population is normally distributed, use an alpha of .05 to test the hypothesis that turning off their electronics early affected the number of hours of sleep they got.

8. A company uses a productivity measure to assess how efficiently employees use their time at work. The population of employees had an average productivity rating of 55 (µ=55 and σ = 21). To see how working from home (sometimes called telecommuting) would affect productivity the company selected a sample of 49 employees to work from home.  Their average productivity rating was 48. Test the hypothesis that working from home affected productivity using an alpha of .01.