Question

##1). An agriculture company is testing a new product that is designed to make plants grow taller. This can be thought of as a hypothesis test with the following hypotheses.

• H₀: The product does not change the height of the plant.
• H_a: The product makes the plant grow taller.

Is the following an example of a type I or type II error?

The sample suggests that the product does not change the height of the plant, but it actually does make the plant grow taller.

1. Type I
2. Type II

##2). In the 2010 General Social Survey, 17% of Americans said that they had no religious preference. In other words, they said they had “no religion” rather than being Protestant, Catholic, Jewish, or another religion. In 2014, the General Social Survey sampled 2,538 Americans and found that 21% of those surveyed said that they had no religious preference. The resulting p-value is 0.0003; thus, the null hypothesis is rejected. It is concluded that there has been an increase in the proportion of Americans who have no religious preference between 2010 and 2014.

What type of error is possible in this situation?

1. Type I
2. Type II
3. Neither
4. Both

##3). Suppose the results indicate that the null hypothesis should be rejected; thus, it is possible that a type I error has been committed.

Given the type of error made in this situation, what could researchers do to reduce the risk of this error?

1. Choose a 0.01 significance level instead of a 0.05 significance level.
2. Increase the sample size.

##4).  Suppose the results indicate that the null hypothesis should not be rejected; thus, it is possible that a type II error has been committed.

Given the type of error made in this situation, what could researchers do to reduce the risk of this error?

1. Choose a 0.01 significance level instead of a 0.05 significance level.
2. Increase the sample size.

Answer 1

Type I error is rejecting the true null hypothesis

Type II error is failing to reject the false null hypothesis

1) Here the sample suggests that the product does not change the height of the plant, but it actually does make the plant grow taller.

So here we have failed to reject the false null hypothesis

Hence it is Type II error

2) Here we reject the null hypothesis

So it is possible that null hypothesis might be true but we reject it

So we would be making Type II error