Question

Use this information to answer the following two questions. In 2000, the Mayo Clinic conducted a study of whether air dryers eliminate more germs than paper towels. Researchers recruited 100 people, contaminated their hands, and then instructed them to wash with soap and water for one minute. Afterward, they randomly assigned 50 participants to run their hands under a warm air dryer for a single 30-second cycle and 50 participants to use a paper towel for 15 seconds. The methods did not produce a significant difference in mean bacterial counts.

18. The hypotheses tested were: Let μ1 = the mean bacterial count after air drying. Let μ2 = the mean bacterial count after drying with paper towels. H0: μ1 = μ2 versus Ha: μ1 < μ2 Which of the following statements represents a Type II error?

Deciding that using air dryers yields a smaller mean bacterial count than using paper towels when it actually has the same mean.

Deciding that using air dryers yields about the same mean bacterial count as using paper towels when it actually has a smaller mean.

Deciding that using air dryers yields about the same mean bacterial count as using paper towels when it actually has the same mean.

Deciding that using air dryers yields a smaller mean bacterial count than using paper towels when it actually has a smaller mean.

19. What type of study is this? an observational study based on a convenience sample a randomized controlled experiment an observational study based on a stratified sample a matched pairs experiment

Answer 1

18. Type II error represents the situation of deciding that H0 is accepted when actually Ha is true.

So, here, in this case, Deciding that using air dryers yields about the same mean bacterial count as using paper towels when it actually has a smaller mean represents the type II error.

19. This study is an observational study based on a convenience sample a randomized controlled experiment since participants to run their hands under a warm air dryer & the participants to use a paper towel are selected randomly. So, there was no stratification. Also, the individuals are not taken in pairs during the analysis.