Problem: If significance level = 1% on a left-sided sided test, Z distribution, n = 30. What is the critical value? (If there is more than one then type in either to 4 decimal places).
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We are given a left-sided test with a significance level of 1% (α = 0.01). Show more…
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The p-value is the maximum probability allowed for the sample statistic to be considered unusual. The p-value is represented by the area in the tail(s) to the extreme of the test statistic(s). The significance level, α, is the maximum probability allowed for the sample statistic to be considered unusual. The significance level is represented by the area in the tail(s) to the extreme of the critical value(s). To find the p-value, you start with finding the test statistic from the sample. To find the critical value(s), you start with the significance level and locate the cut-offs in the z (or t) distribution that cut-off that area in the specified tail(s). A type I error is the probability that you reject the null hypothesis but the null hypothesis is actually true. Which of the answers gives the probability of a type I error? Group of answer choices α A type II error is when you fail to reject the null hypothesis, but the null hypothesis is actually not true. The probability of making a type II error is called β. The power of a test is 1 - β. The power of a test tells you the probability that you did not make a type II error. You want β to be as close to 0 as possible and the power to be as close to 1 as possible. Both β and the power of a test depend on what the true population parameter is. β can be found by finding the probability that the test statistic is NOT in the rejection region if the true population parameter is equal to a specified value. Step 1: Find the rejection region. This is based on the critical value(s) and the null and alternate hypotheses of the test. The rejection region will be centered around the assumed (but inaccurate) value for the population parameter in the hypothesis. Step 2: Find the probability of getting a test statistic NOT in the rejection region found in step 1 IF a new value is the true population parameter. Write exact answers unless otherwise specified. Example: Null hypothesis: μ = 5.1. Alternate Hypothesis: μ > 5.1. Assume σ = 2, n = 25. Find the probability of a type II error (β) and the power of the test if the true population parameter is 5.6. Significance level = .05. Critical Value = invNorm(0.95) = ________ . Remember this is a z-score in the sampling distribution. Round to 2 decimal places. Data value in sampling distribution based on assumed population parameter: N(5.1, 2/√25) = ________ (Do not round) Rejection region in N(5.1, 2/√25) = [____ , ∞). (Do not round) Find the z-score of the data value you found IF the true population parameter is 5.6 (so in N(5.6, 2/√25). β = probability NOT in rejection region = P( Z < ____ ) = ____(round probability to 4 decimal places). power = probability IN rejection region = P(Z > ____ ) = ____ (round probability to 4 decimal places).
Lucas F.
You wish to test the following claim (Ha) at a significance level of α = 0.01. For the context of this problem, let H0 represent the null hypothesis and H1 represent the alternative hypothesis, where the first data set represents the pre-test and the second data set represents the post-test: H0: μd = 0 H1: μd ≠ 0 You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-test samples for n = 22 subjects. The average difference (post - pre) is d = 16.7 with a standard deviation of the differences of s = 43.6. What is the test statistic for this sample? (Report answer accurate to three decimal places) Test statistic: What is the P-value for this sample? (Report answer accurate to four decimal places) P-value: The p-value is less than (or equal to) α, greater than α, or equal to α. This test statistic leads to a decision to reject the null hypothesis, accept the null hypothesis, or fail to reject the null hypothesis. As such, the final conclusion is that: - There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0. - There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0. - The sample data support the claim that the mean difference of post-test from pre-test is not equal to 0. - There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is not equal to 0.
Madhur L.
It is desired to compare the average test scores at the two schools. Suppose that random samples of college freshmen are selected from two universities: 15 students from school A and 17 students from school B. The summary statistics of a standardized test are given in the following table. Test if there is a difference in mean test scores at the two schools, assuming that test scores came from normal distributions. Use a 0.05 level of significance. Sample Size | Average Score | Standard Deviation ------------|---------------|------------------ School A (1) | 15 | 100 | 15 School B (2) | 17 | 90 | 18 Part A: What hypothesis test should be used? a. Independent samples t-test b. Matched pairs t-test c. Independent samples z-test d. Test for two proportions Part B: What are the null and alternative hypotheses? a. H0: mu1-mu2=0, Ha: mu1-mu2 <0 b. H0: mu1-mu2 not=0, Ha: mu1-mu2=0 c. H0: mu1-mu2=0, Ha: mu1-mu2 not=0 d. H0: mu1-mu2=0, Ha: mu1-mu2 >0 Part C: Compute the value of the pooled variance. a. 277.8 b. 15.6 c. 16.6 d. 260.4 Part D: Find the value of the test statistic. a. -1.694 b. -0.287 c. 1.694 d. 0.287 Part E: Find the rejection region. a. z<-1.960 and z>1.960 b. t<-1.697 and t>1.697 c. t>1.697 d. t<-2.042 and t>2.042 Part F: What is your decision? a. Do not reject H0, because the value of the test statistic falls in the rejection region. b. Do not reject H0, because the value of the test statistic does not fall in the rejection region. c. Reject H0, because the value of the test statistic does not fall in the rejection region. d. Reject H0, because the value of the test statistic falls in the rejection region. Part G: Interpret the conclusion in the context of the problem. At the 0.05 level of significance, a. There is not sufficient evidence of a difference in mean test scores between the two schools. b. There is not sufficient evidence that the mean test scores are equal. c. There is sufficient evidence that the mean test scores are equal. d. There is sufficient evidence of a difference in mean test scores between the two schools.
Sri K.
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