Distinguishing type I and type II errors In each of the following scenarios, ide
ID: 3175240 • Letter: D
Question
Distinguishing type I and type II errors In each of the following scenarios, identify if a type I error, a type II error, or neither has occurred. An engineer designs an improved light bulb. The previous design had an average lifetime of 1200 hours. The mean lifetime of a random sample of 2000 new bulbs is found to have a mean lifetime of 1201 hours. Although the difference from the old mean lifetime of 1200 hours is quite small, the P-value is 0.03 and the effect is statistically significant at the 0.05 level. In fact, there is no difference between the mean lifetimes of the new and old designs. A medical researcher is working on a new treatment for a certain type of cancer. The average survival time after diagnosis on the standard treatment is two years. In an early trial, she tries the new treatment on three participants, who have an average survival time after diagnosis of four years. Although the survival time has doubled, the results are not statistically significant even at the 0.10 significance level. In fact, the new treatment does increase the mean survival time in the population of all patients with this particular type c. A women thinks she is pregnant, buys a pregnancy stick, and takes the test. The result shows that she is not pregnant The women therefore keeps her current life style and continues to drink and smoke, when in fact she is pregnant.Explanation / Answer
Result:
a).
Type I error
Type I error is the incorrect rejection of a true null hypothesis.
b).
Type II error
Type II error is the failure to reject a false null hypothesis.
c).
Neither has occurred.
( this a case report and there is no hypothesis test).