1. The P-value of a test of the null hypothesis is (a) the probability the null hypothesis is true. (b) the probability the null hypothesis is false. (c) the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed. (d) the probability, assuming the null hypothesis is false, that the test statistic will take a value at least as extreme as that actually observed.

1. The P-value of a test of the null hypothesis is (a) the probability the null hypothesis is true. (b) the probability the null hypothesis is false. (c) the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed. (d) the probability, assuming the null hypothesis is false, that the test statistic will take a value at least as extreme as that actually observed.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A researcher sets his decision criteria at p = .10. That is, she decides that she will reject the null hypothesis if the z – value she obtains has a probability of .10 or less. What is this researcher’s probability of making Type I error?
A researcher sets his decision criteria at p = .01. That is, she decides that she will reject the null hypothesis if the z – value she obtains has a probability of .01 or less. What is this researcher’s probability of making Type I error?
(a) Suppose the null and alternative hypothesis of a test are: Ho: μ = 59.9 Η: μ > 59.9 Then the test is: left-tailed F3 two-tailed (b) If you conduct a hypothesis test at the 0.09 significance level and calculate a P-value of 0.13, then what should your decision be? $ 4 Submit Question O Fail to reject Ho O Reject Ho O Not enough information is given to make a decision 8 % this question below right-tailed 5 < 6 F6 & 7 F7 PrtScn FB Home ( 9 F9 E
Test the claim that the mean GPA of night students is larger than 2.4 at the 0.025 significance level. The null and alternative hypothesis would be: Ho: µ = — 2.4 Но:р 2.4 Н: + 2.4 H:p> 0.6 H:д> 2.4 Hi:p #0.6 Hi:p < 0.6 Н:р < 2.4 The test is: left-tailed two-tailed right-tailed Based on a sample of 65 people, the sample mean GPA was 2.41 with a standard deviation of 0.03 The test statistic is: (to 2 decimals) The p-value is: (to 2 decimals) Based on this we: O Reject the null hypothesis O Fail to reject the null hypothesis
For a hypothesis test with a probability of a Type II error of 60% and a probability of a Type I error of 5%, which of the following statements is most accurate? A. The power of the test is 40%, and there is a 5% probability that the test statistic will exceed the critical value(s). B. There is a 95% probability that the test statistic will be between the critical values if this is a two tailed test. C. There is a 5% probability that the null hypothesis will be rejected when actually true, and the probability of rejecting the null when it is false is 40%.
State whether each of the following is true or false.a. The significance level of a test is the probability that the null hypothesis is false.b. A Type I error occurs when a true null hypothesis is rejected.c. A null hypothesis is rejected at the 0.025 level but is not rejected at the 0.01 level. This means that the p-value of the test is between 0.01 and 0.025.d. The power of a test is the probability of accepting a null hypothesis that is true.e. If a null hypothesis is rejected against an alternative at the 5% level, then using the same data, it must be rejected against that alternative at the 1% level.f. If a null hypothesis is rejected against an alternative at the 1% level, then using the same data, it must be rejected against the alternative at the 5% level.g. The p-value of a test is the probability that the null hypothesis is true.
A. The P-value of a test statistic in a right-tailed test is best described as B. the probability of obtaining a sample statistic at random no greater than the test statistic, given we assume the null hypothesis is true C. the probability of obtaining a sample statistic at random no greater than the test statistic, given we assume the null hypothesis is false D. the probability of obtaining a sample statistic at random at least as great as the test statistic, given we assume the null hypothesis is true the probability of obtaining a sample statistic at random at least as great as the test statistic, given we assume the null hypothesis is false
Which one of the following statements is incorrect: A. A type I error consists of rejecting the null hypothesis when it is true B. A type II error consists of accepting the null hypothesis when it is false C. You can control simultaneously both the Type I and Type II error probabilities when the sample size is fixed D. Hypothesis testing and confidence intervals are related concepts
In hypothesis testing, O if the P-value is 0.01, we should conclude there is a 1% chance the null hypothesis is false. O neither the test statistic nor the P-value can ever be negative. O we always begin the hypothesis test by assuming the null hypothesis is true. O if the P-value is 0.99, we should conclude that the null hypothesis is true. O results that are statistically significant will always be practically important (or practically significant).
A researcher sets his decision criteria at p = .05. That is, she decides that she will reject the null hypothesis if the z – value she computes for a z-test would be obtained by chance alone at a probability of .05 or lower. What is this researcher’s probability of making Type I error?
2. A random variable|x has the following probability distribution. Find the value of p and then evaluate the following probabilities: P(X 5) and P(0 < X < 6). Find the mean of the probability distribution. 1 3 4 6 17 P(X) 2p 2p 3p p2 2p2 7p? + p Value of p = P(X < 5) =. P(X 2 5) = P(0 < X < 5) = Mean (u) =