2 3 4 5 6 7 8 9 10 15.3 16.0 16.3 16.8 17.1 15.8 15.7 16.6 17.0 15.5 T- values 15.8 16.2 16.5 16.3 17.7
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Consider the following dependent random samples:
| Observations | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 15.3 | 16.0 | 16.3 | 16.8 | 17.1 | 15.8 | 15.7 | 16.6 | 17.0 | 15.5 | |
| T- values | 15.8 | 16.2 | 16.5 | 16.3 | 17.7 | 16.1 | 16.3 | 17.0 | 17.3 | 15.2 |
a) Do hypothesis testing to see if µd < 0 at the α = .025.
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- Consider two random samples that are assumed to be dependent and not normally distributed. Sample 1 7 15 20 30 32 18 26 17 10 Sample 2 27 8 25 18 20 16 21 17 16 Time left 23:35:19 The analyst wants to test, using the sign test, whether the two populations differ at 1% level of significance. Which one of the following statements is incorrect? Select one: O 1. The sample size is 9. O 2. The rejection region is Z≥2.58 or Z<-2.58. O 3. The test statistic is 0.7071. O 4. The null hypothesis is not rejected at 1% level of significance. O 5. The alternative hypothesis is H₁: The two populations differ.Assume that both populations are normally distributed. a) Test whether . Population 1 Population 2 10 11.1 Pt2 at the a= 0.05 level of significance for the given sample data 10 9.8 2.3 (b) Construct a 95% confidence interval about u, - H3. 2.7 H1 H1 > H2 O C. Ho H1-H2 H1 H1> H2 D. Ho H1=H2 %3D Detemine the P-value for this hypothesis test. P = (Round to three decimal places as needed.) %24The following data are from a completely randomized design. In the following calculations, use ? = 0.05. Treatment1 Treatment2 Treatment3 62 82 68 46 71 54 53 88 61 39 63 45 xj 50 76 57 sj2 96.67 124.67 96.67 a) Use analysis of variance to test for a significant difference among the means of the three treatments. State the null and alternative hypotheses: A) H0: ?1 = ?2 = ?3Ha: ?1 ≠ ?2 ≠ ?3 B) H0: Not all the population means are equal.Ha: ?1 = ?2 = ?3 C) H0: ?1 = ?2 = ?3Ha: Not all the population means are equal. D)H0: ?1 ≠ ?2 ≠ ?3Ha: ?1 = ?2 = ?3 E) H0: At least two of the population means are equal.Ha: At least two of the population means are different. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. A) Do not reject H0. There is not sufficient evidence to conclude that the means of the three treatments are…
- Provided below are summary statistics for independent simple random samples from two populations. Use the pooled t-test and the pooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval. x₁ = 11, S₁ = 2.5, n₁ = 15, x₂ = 14, s₂ = 2.2, n₂ = 15 a. Two-tailed test, α = 0.10 b. 90% confidence interval Ha: H1 H2 Next, compute the test statistic. t= (Round to three decimal places as needed.) Now determine the critical values. ±ta/2= ± What is the conclusion of the hypothesis test? Since the test statistic b. The 90% confidence interval is from to (Round to three decimal places as needed.) (Round to three decimal places as needed.) in the rejection region, Ha: H1 = H₂ Ho. Time Remaining: 01:35:24 NextThe following three independent random samples are obtained from three normally distributed populations with equal variance. The dependent variable is starting hourly wage, and the groups are the types of position (internship, co-op, work study). Group 1: Internship Group 2: Co-op Group 3: Work Study 10.75 12.5 8.5 9.75 10.25 12.5 11.5 13 15.25 10.75 14.25 14.5 11.25 10.5 14 10.5 11 15 13.75 12.75 11.75 11.5 12.5 15.75 11.75 12.75 12 13.25 13.75 14 12.75 14.25 12.25 Conduct a one-factor ANOVA to determine if the group means are equal using α=0.01α=0.01. Group means:Group 1 mean: Group 2 mean: Group 3 mean: ANOVA summary statistics:F-test statistic = p=p= Conclusion: The sample data suggests there is a correlation in the starting hourly wages. There is not sufficient data to conclude that at least one group's average starting hourly wage is different. The sample data suggests the starting hourly wages are dependent There is not…This test statistic leads to a decision to... A.) reject the null B.) accept the null C.) fail to reject the null You wish to test the following claim (Ha) at a significance level of α=0.002α=0.002. Ho:μ=55.6 Ha:μ>55.6You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=601n=601 with mean ¯x=57.1x¯=57.1 and a standard deviation of s=19.9s=19.9.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... A.) less than (or equal to) αα B.) greater than α As such, the final conclusion is that... A.) There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 55.6. B.) There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than…
- Under what circumstances is a t statistic used instead of a z-score for a hypothesis test? Justin wants to know whether a commonly prescribed drug does improve the attention span of students with attention deficit disorder (ADD). He knows that the mean attention span for students with ADD who are not taking the drug is 2.3 minutes long. His sample of 12 students taking the drug yielded a mean of 4.6 minutes. Justin can find no information regarding σx , so he calculated s2x =1.96. Determine the critical region using a one-tailed test with alpha = .05. Conduct the hypothesis test (Do the math and compare the t-critical and t-obtained values). State your conclusions in terms of H0 (Should you reject the H0 or fail to reject/accept the H0). Based on your analysis, is there a relationship between the drug and attention span?Nine students took the SAT. Their scores are listed below. Later on, they read a book on test preparation and retook the SAT. Their new scores are listed below. Assume that the distribution is normally distributed. 1. Can it be concluded at α = .05 that the scores have changed? Do the hypothesis test. 2. Construct a 95% confidence interval for μd. Student 1 2 3 4 5 6 7 8 9 Before Reading 720 860 850 880 860 710 850 1200 950 After Reading 740 860 840 920 890 720 840 1240 970You may need to use the appropriate technology to answer this question. Consider the following hypothesis test. H0: ?d ≤ 0 Ha: ?d > 0 (a) The following data are from matched samples taken from two populations. Compute the difference value for each element. (Use Population 1 − Population 2.) Element Population Difference 1 2 1 21 19 2 28 28 3 18 17 4 20 18 5 26 26 (b) Compute d. (c) Compute the standard deviation sd. (d) Conduct a hypothesis test using ? = 0.05. Calculate the test statistic. (Round your answer to three decimal places.) Calculate the p-value. (Round your answer to four decimal places.) p-value = What is your conclusion? Reject H0. There is insufficient evidence to conclude that ?d > 0. Reject H0. There is sufficient evidence to conclude that ?d > 0. Do not Reject H0. There is sufficient evidence to conclude that ?d > 0. Do not reject H0. There is insufficient evidence to conclude that ?d >…
- Heeeelpppp1. The tables below show the results of an independent samples t-test in SPSS conducted using the SPSS data we have been using this semester. Two groups ("Yes" and "No") are compared on their "final". Yes and no refer to whether they attended the review sessions or not. Review the results carefully and answer the questions below. (12 points) final final Attended review sessions? No Yes Equal variances assumed Equal variances not assumed Levene's Test for Equality of Variances F Group Statistics 219 Sig. N .641 35 70 t -2.693 d. What are the df for the t-test we use? 103 Mean Independent Samples Test -2.719 59.83 64.14 Std. Deviation 7.591 7.810 df Sig. (2-tailed) 103 .008 69.872 .008 e. Are the groups significantly different from each other? f. Which group scored higher? Yes Group No Group The two groups are not significantly different_ t-test for Equality of Means Mean Difference -4.314 Std. Error Mean -4.314 1.283 .933 Std. Error Difference 1.602 1.587 95% Confidence Interval of the…Consider the experimental results for the following randomized block design. Make the calculations necessary to set up the analysis of variance table. Treatments A BC 10 9 2 12 6 5 Blocks 3 18 15 14 4 20 18 18 8 6 Use a = 0.05 to test for any significant differences. State the null and alternative hypotheses. O Ho: At least two of the population means are equal. H: At least two of the population means are different. Ho: Not all the population means are equal. Ho: HA = HB = "c H: Not all the population means are equal. %3D O Ho: HA = HB = Hc Ho: MA * MB * Mc H: HA = MB = Hc %3D Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value State your conclusion. Reject Hg. There is not sufficient evidence to conclude that the means of the three treatments are not equal. O Do not reject H,: There is not sufficient evidence to conclude that the means of the three treatments are not equal. Reject H..…
