The noise level in a hospital may be a critical factor influencing a patient’s speed of recovery.

Suppose for the sake of discussion that a research commission has recommended a maximum mean noise level of 30 decibels

(db) with a standard deviation of 10 db. The staff of a hospital intend to sample one of its wards to determine whether the noise level is significantly higher than the recommended level. The following hypothesis test will be completed:

Ho:   30 (

) vs. Ha:   30,   0.05

a. Identify the correct interpretation for each hypothesis with regard to the recommendation and justify your choice.

Ho: (1) Noise level is not significantly higher than the recommended level, or (2) Noise level is significantly higher than the recommended level.

Ha: (1) Noise level is not significantly higher than the recommended level, or (2) Noise level is significantly higher than the recommended level.

b. Which statement best describes the type I error?

(i) Decision reached was that noise level is within the recommended level when in fact it actually was within.

(ii) Decision reached was that noise level is within the recommended level when in fact it actually exceeded it.

(iii) Decision reached was that noise level exceeds the recommended level when in fact it actually was within.

(iv) Decision reached was that noise level is within the recommended level when in fact it actually exceeded it.

c. Which statement in part b best describes the type II error?

d. If  were changed from 0.05 to 0.01, identify and justify the effect (increases, decreases, or remains the same) on P(type I error) and on P(type II error).