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.Ha: 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. Type I Type II
Question
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.Ha: 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. Type I Type II
Solution 1
This is an example of a Type II error. In hypothesis testing, a Type II error occurs when the null hypothesis (H0) is not rejected when it is false. In this case, the null hypothesis that the product does not change the height of the plant is not rejected, but in reality, the product does make the plant grow taller. This is a false negative result.
Solution 2
This is an example of a Type II error. In hypothesis testing, a Type II error occurs when the null hypothesis (H0) is not rejected when it is false. In this case, the null hypothesis that the product does not change the height of the plant is not rejected, but in reality, the product does make the plant grow taller. This is a false negative result.
Similar Questions
Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test with the following hypotheses.H0: The food is safe.Ha: The food is not safe.Is the following an example of a type I or type II error?The sample suggests that the food is safe, but it actually is not safe.Group of answer choicesType IType II
Which one of the following statements about the Type I error of hypothesis testing is wrong? a. It is closely related to the significance level of the test. b. It means that we may fail to reject the null hypothesis H0 when H1 is true. c. It means that we may reject the null hypothesis H0 when H0 is actually true. d. Researchers can control the probability of Type I error.
In hypothesis testing, a Type 2 error occurs whenQuestion 12Answera.The null hypothesis is rejected when the null hypothesis is true.b.The null hypothesis is not rejected when the null hypothesis is true.c.The null hypothesis is rejected when the alternative hypothesis is true.d.The null hypothesis is not rejected when the alternative hypothesis is true.
Suppose you are testing your friend to see whether she can tell the difference between the name brandand generic peanut butter. You give her 40 samples selected randomly, half from the name brand andhalf from the generic brand. The null hypothesis is that she is just guessing and should get about halfright. Explain what type I error would be in this case.A) Type I error would be saying that your friend cannot tell the difference between the two kinds ofpeanut butter, when she really can.B) Type I error would be saying that your friend can tell the difference between the two kinds of peanutbutter, when she really can.C) Type I error would be saying that your friend can tell the difference between the two kinds of peanutbutter, when she really cannot.D) Type I error would be saying that your friend cannot tell the difference between the two kinds ofpeanut butter, when she really cannot
Hypothesis testing is based ona) minimizing the type I error b) minimizing the type II errorc) minimizing the sum of type I and type II errorsd) none of these
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