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A hypothesis test is completed and we have sufficient evidence that a certain population mean is more than 215. Suppose that in reality the population mean is more than 215. Determine if a correct decision has been made. If an error has been made, indicate which type of error it is.

Question

A hypothesis test is completed and we have sufficient evidence that a certain population mean is more than 215. Suppose that in reality the population mean is more than 215. Determine if a correct decision has been made. If an error has been made, indicate which type of error it is.

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Solution

In this scenario, a correct decision has been made. The hypothesis test concluded that the population mean is more than 215, and in reality, the population mean is indeed more than 215. Therefore, there is no error in this case.

In hypothesis testing, there are two types of errors that can occur:

  1. Type I error: This occurs when we reject the null hypothesis when it is actually true. In other words, we conclude that there is an effect when there isn't one.

  2. Type II error: This occurs when we fail to reject the null hypothesis when it is actually false. In other words, we conclude that there is no effect when there actually is one.

In this case, neither of these errors has occurred, so a correct decision has been made.

This problem has been solved

Similar Questions

We would like to test whether the population mean is less than 30. Suppose that a hypothesis test is conducted to determine if the mean of the population has decreased. Describe what a Type II error would mean for this example.

What types of error can occur when making decisions based on test of hypothesis? Be specific.

Hypothesis Testing

We wish to conduct a test of hypothesis on two independent population means. The alternative hypothesis of the test states that the means differ. Both populations are assumed normal with equal variance. We draw 10 observations for the first sample and 20 observations for the second sample. State the decision rule for the test if the level of significance is 0.01.Question 2Select one:a.we reject Ho if t > 2.4671b.we reject Ho if t <-2.4671 or t > 2.4671c.we reject Ho if t > 2.3263d.we reject Ho if t <-2.7633 or t > 2.7633

A student believes that the average grade on the quiz in Math is greater than 85. She plans on taking a sample to test her belief. The correct null hypothesis is Group of answer choicesPopulation mean is greater than or equal to 85Population mean is less than 85Population mean is greater than 85Population mean is less than or equal to 85

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