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 null hypothesis would be rejected
D.It is the probability of committing type II error and it is the largest significant level at which a null hypothesis would be rejected
The p-value or probability value is defined for a given statistical model, as the probability that, when the null hypothesis is true, the statistical summary will be equal to, or more extreme than, the actual observed result in the hypothesis testing.
When we use a hypothesis test in statistics, a p-value helps us to determine the significance of our results.
Hypothesis tests are used to test the validity of a claim that is said about a population. This claim is called null hypothesis.
The alternative hypothesis is one which we believe if the null hypothesis is concluded to be false.
So it is the probability of acceptance the null hypothesis. Higher the value of p value more significant the model.
Type I error is defined as the rejection of a true null hypothesis.
Type II error is defined as the acceptance of a false null hypothesis.
It means a true statement about the P value is It is the probability of committing type I error and it is the smallest significant level at which a null hypothesis would be rejected.
Hence option A is the correct answer
Which of the following statements is true about the P-value? A. It is the probability of...
Which of the following is true of the p-value? Select one: a. It is the probability of rejecting the null hypothesis when the alternative hypothesis is true. b. It is the extreme value of the test statistic obtained when the alternative hypothesis is true. c. It is the smallest significance level at which a null hypothesis can be rejected. d. It is the probability of rejecting the null hypothesis when the null hypothesis is 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.
When Ho: p = 0.25 is true and n = 10 only, the probability of cornmitting Type I error is about 0.08 which is substantially greater than the fixed α = 0.05. This is an issue for practical use of the hypothesis testing. By changing the null value 0.01 p 0.5 and the sample size 10Sn 1000, investigate the probability of committing Type I error. a. Complete the following table by the probability of committing Type I error. (First, write...
In order to test whether a certain coin is fair, it is tossed ten times and the number of heads (X) is counted. Let p be the "head probability". We wish to test the null hypothesis: p = 0.5 against the alternative hypothesis: p > 0.5 at a significance level of 5%. (a) Suppose we will reject the null hypothesis when X is smaller than h. Find the value of h. (b) What is the probability of committing a type...
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,
α is the probability of a Type I error, which occurs when we accept the alternative H1 when the null hypothesis Ho is true. True False A Type II error occurs when when a false null hypothesis is rejected. True False If a null hypothesis is rejected at the 5% significance level but not at the 1% significance level, then the p-value of the test is less than 1%. True False The power of a test is the probability of...
Which of the following is a TRUE statement about hypothesis testing? The probability of a Type I error plus the probability of a Type II error always equals one. The power of a test concerns its ability to detect a null hypothesis. If there is sufficient evidence to reject a null hypothesis at the 5% level, then there is sufficient evidence to reject it at the 10% level. Whether to use a one-sided or a two-sided test is typically decided...
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...
Which of the following statements is true? I. If the p-value is 0.01, we reject H0 for any alpha level less than 0.01. II. If we use an alpha level of 0.05, then a p-value of 0.005 is not statistically significant. III. If we use an alpha level of 0.05, then we fail to reject the null hypothesis if the p-value is 0.1. Group of answer choices I only II only III only I and III II and III
Which of the following statements is true? I. If the p-value is 0.01, we reject H0 for any alpha level less than 0.01. II. If we use an alpha level of 0.05, then a p-value of 0.005 is not statistically significant. III. If we use an alpha level of 0.05, then we fail to reject the null hypothesis if the p-value is 0.1.