1. Which of the following statements are not generally true? a. A type I error is...
1. Which of the following statements are not generally true?
a. A type I error is usually more serious than a type II error.
b. A type II error is usually more serious than a type I error.
c. A test with significance level is one for which the type I error probability is controlled at the specified level.
d. When an experiment and a sample size are fixed, then decreasing the size of the rejection region to obtain a smaller value of (probability of type I error) results in a larger value of (probability of type II error) for any particular parameter value consistent with the alternative hypothesis Ha .
e. None of the above statements are true.
and why?
Homework Answers
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1. Which of the following statements are not generally true?
a. A type I error is...
State whether the following statements true or false, and Why? 1. The type I error and...
State whether the following statements true or false, and Why? 1. The type I error and type II error are related. A decrease in the probability of one generally results in an increase in the probability of the other. 2. The size of the critical region, and therefore the probability of committing a type I error, can always be reduced by adjusting the critical value(s). 3. An increase in the sample size n will reduce α and β simultaneously. 4....
Consider the following four statements concerning hypothesis tests. I. We can decrease the probability of a...
Consider the following four statements concerning hypothesis tests. I. We can decrease the probability of a Type II error by increasing the sample size. II. We can decrease the probability of a Type II error by decreasing the sample size. III. We can decrease the probability of a Type I error by increasing the level of significance . IV. We can decrease the probability of a Type I error by decreasing the level of significance . Which statements above are...
6. Which of the following statements about hypothesis testing are true? • A type I error...
6. Which of the following statements about hypothesis testing are true? • A type I error occurs if H, is rejected when it is true. • A type II error occurs if He is rejected when it is true. • The power of a test is the probability of failing to reject H, when it is false.
6. Which of the following statements about hypothesis testing are true? • A type I error...
6. Which of the following statements about hypothesis testing are true? • A type I error occurs if His rejected when it is true. • A type II error occurs if H, is reject ed when it is true, • The power of a test is the probability of failing to reject H, when it is false,
The notion of Type I and Type II Errors is very important in hypothesis testing. The...
The notion of Type I and Type II Errors is very important in hypothesis testing. The Ho/Ha should be set up such that a Type I Error is more serious than a Type II Error. A common example used to discuss Type I and Type II errors is the example of a trial in the US. Under US law, a defendant is considered "innocent until proven guilty." You could set up this hypothesis test as follows: Ho: defendent is...
Which of the following statements is true about the P-value? A. It is the probability of...
Which of the following statements is true about the P-value? A. It is the probability of committing type I error and it is the smallest significant level at which a null hypothesis would be rejected B. It is the probability of committing type I error and it is the largest significant level at which a null hypothesis would be rejected C. It is the probability of committing type II error and it is the smallest significant level at which a...
Let μ denote the true average radioactivity level (picocuries per liter). The value 5 pCi/L is...
Let μ denote the true average radioactivity level (picocuries per liter). The value 5 pCi/L is considered the dividing line between safe and unsafe water. Would you recommend testing H0: μ = 5 versus Ha: μ > 5 or H0: μ = 5 versus Ha: μ < 5? Explain your reasoning. [Hint: Think about the consequences of a type I and type II error for each possibility.] ---One should test H0: μ = 5 versus Ha: μ < 5.A type...
a. Explain a Type II error and power in context of choosing a smaller level of significance. b. Explain a Type II error...
a. Explain a Type II error and power in context of choosing a smaller level of significance. b. Explain a Type II error and power in context of a greater difference between the null hypothesis claim and the true value of the population parameter.
Which of the following statements is FALSE? a.) The power of a hypothesis test is the...
Which of the following statements is FALSE? a.) The power of a hypothesis test is the probability of not making a Type II error. b.) Alpha (α) is equal to the probability of making a Type I error. c.) The probability of rejecting the null hypothesis when the null hypothesis is true is called a Type I Error. d.) A smaller sample size would increase the effectiveness of a hypothesis test.
1. In hypothesis testing, which of the following statements is/are true? The test statistic can be...
1. In hypothesis testing, which of the following statements is/are true? The test statistic can be smaller than 1.0. II. The p-value can never be larger than 1.0. II. The “p" in p-value stands for “practical.” O I, II and III are all true O ll only O I only Ill only O I and II are both true
6. Which of the following statements about hypothesis testing are true? • A type I error occurs if H, is rejected when it is true. • A type II error occurs if He is rejected when it is true. • The power of a test is the probability of failing to reject H, when it is false.
6. Which of the following statements about hypothesis testing are true? • A type I error occurs if His rejected when it is true. • A type II error occurs if H, is reject ed when it is true, • The power of a test is the probability of failing to reject H, when it is false,
1. In hypothesis testing, which of the following statements is/are true? The test statistic can be smaller than 1.0. II. The p-value can never be larger than 1.0. II. The “p" in p-value stands for “practical.” O I, II and III are all true O ll only O I only Ill only O I and II are both true
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