Question

Ahmad was conducting some tests to determine if there was a relationship between taking sleeping pills and the amount of sleep a person gets. His null hypothesis was that taking sleeping pills did not have any effect on the amount of sleep a person receives. Ahmad's alternate hypothesis was that taking sleeping pills increases the amount of sleep a person will get. If Ahmad completed his study, which of the following statements would indicate a Type II error?

Ahmad's results showed that sleeping pills caused people to get more sleep, and in fact sleeping pills and the amount of sleep people were getting did have a positive cause and effect relationship.

Ahmad's results showed that sleeping pills did not affect the amount of sleep participants were getting when in fact sleeping pills were increasing the sleep people were getting.

Ahmad's results showed that taking sleeping pills did increase the amount of sleep people were getting when in fact sleeping pills were not affecting sleep.

Ahmad's results showed that sleeping pills did not affect the amount of sleep participants were getting when in fact there was not a cause and effect relationship between the two variables.

Answer 1

In hypothesis testing problem, we can commit two types of error, Type-I error and type-II error.

1. Type –I error: when we reject a true null hypothesis, we commit a type-I error

2. Type –II error: when we accept a false null hypothesis, we commit a type-II error

In the given problem, we have

H0: taking sleeping pills did not have any effect on the amount of sleep a person receives

H1: taking sleeping pills increases the amount of sleep a person will get

So if Ahmed accepts the null hypothesis (i.e. sleeping pills did not have any effect on the amount of sleep) when actually alternative hypothesis (i.e. sleeping pills increases the amount of sleep) was true, Ahmed will commit Type-II error.

Hence the correct option is B. Ahmad's results showed that sleeping pills did not affect the amount of sleep participants were getting when in fact sleeping pills were increasing the sleep people were getting.