How do states stack up against each other in SAT scores? To compare State 1 and State 2 scores, random samples of 100 students from each state were selected and their SAT scores recorded with the following results. (Use u, for State 1 and u, for State 2.) State Mean Sample Standard Size Deviation State 1 1,121 100 196 State 2 1,049 100 163 (a) Use the critical value approach to test for a significant difference in the average SAT scores for these two states at the 5% level of significance. State the null and alternative hypotheses. O Ho: (H, - 12) = 0 versus Ha: (41 - 12) = 0 O Ho: (M - 12) = 0 versus He: (41 - (2) = 0 O Ho: (H - 12) = 0 versus Ha: (41 - 12) = 0 O Ho: (My - 12) = 0 versus Ha: (41 - (2) = 0 OH: (H, - 12) = 0 versus He: (u1 - 12) = 0 Find the test statistic. (Round your answer to two decimal places.) Find the rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.) State your conclusion. O Ho is rejected. There is sufficient evidence to indicate that there is a difference in the average SAT scores for the two states. O Ho is not rejected. There is insufficient evidence to indicate that there is a difference in the average SAT scores for the two states. O Ho is not rejected. There is sufficient evidence to indicate that there is a difference in the average SAT scores for the two states. O Ho is rejected. There is insufficient evidence to indicate that there is a difference in the average SAT scores for the two states. (b) Use the p-value approach to test for a significant difference in the average SAT scores for these two states. (Use a = 0.05.) Find the p-value. (Round your answer to four decimal places.) 42) ? v 0 p-value = ? = If you were writing a research report, how would you report your results? A TI- is or is not sufficient or insufficent? The null hypothesis [--Select-- v rejected. There is --Select--- v | evidence to conclude that (#1 - (2) ? v 0.Analyses of drinking water samples for 100 homes in each of two different sections of a city gave the following information on lead levels (in parts per million). Section 1 Section 2 Sample Size 100 100 Mean 34.2 36.0 Standard Deviation 5.9 6.0 (a) Calculate the test statistic and its p-value to test for a difference in the two population means. (Use Section 1 - Section 2. Round your test statistic to two decimal places and your p-value to four decimal places.) 2 = p-value = Use the p-value to evaluate the statistical significance of the results at the 5% level. O Ho is not rejected. There is sufficient evidence to indicate a difference in the mean lead levels for the two sections of the city. O Ho is rejected. There is sufficient evidence to indicate a difference in the mean lead levels for the two sections of the city. O Ho is rejected. There is insufficient evidence to indicate a difference in the mean lead levels for the two sections of the city. O Ho is not rejected. There is insufficient evidence to indicate a difference in the mean lead levels for the two sections of the city. (b ) Calculate a 95% confidence interval to estimate the difference in the mean lead levels in parts per million for the two sections of the city. (Use Section 1 - Section 2. Round your answers to two decimal places.) parts per million to parts per million (c) Suppose that the city environmental engineers will be concerned only if they detect a difference of more than 5 parts per million in the two sections of the city. Based on your confidence interval in part (b), is the statistical significance in part (a) of practical significance to the city engineers? Explain. O Since all of the probable values of uj - 2 given by the interval are between -5 and 5, it is not likely that the difference will be more than 5 ppm, and hence the statistical significance of the difference is not of practical importance to the the engineers. O Since all of the probable values of uj - u2 given by the interval are all greater than 5, it is likely that the difference will be more than 5 ppm, and hence the statistical significance of the difference is of practical importance to the the engineers. O Since all of the probable values of uj - u2 given by the interval are all less than -5, it is likely that the difference will be more than 5 ppm, and hence the statistical significance of the difference is of practical importance to the the engineers.An experiment was planned to compare the mean time (in days) required to recover from a common cold for persons given a daily dose of 4 milligrams (mg) of vitamin C, u2, versus those who were not, u, . Suppose that 30 adults were randomly selected for each treatment category and that the mean recovery times and standard deviations for the two groups were as follows. No Vitamin 4 mg Supplement Vitamin C Sample Size 30 30 Sample Mean 6.5 5.3 Sample Standard Deviation 2.7 1.4 (a) If you want to show that the use of vitamin C reduces the mean time to recover from a common cold, give the null and alternative hypotheses for the test. O Ho: ( H, - 12) = 0 versus H: (u, - 42 ) =0 O Ho: (1 - 12) = 0 versus Ha : (1 1 - 12) = 0 O Ho: (Hy - 42) = 0 versus Ha : (41 - 142) = 0 O Ho: (Hy - 12) = 0 versus Ha: (1, - 12) = 0 O HO : ( 1 - 12) = 0 versus Ha : (41 - 12) = 0 Is this a one- or a two-tailed test? O one-tailed test O two-tailed test (b) Conduct the statistical test of the null hypothesis in part (a) and state your conclusion. Test using a = 0.05. (Round your answer to two decimal places.) Find the test statistic. 2 = Find the rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.) Z Conclusion: O Ho is rejected. There is insufficient evidence to indicate that Vitamin C reduces the mean recovery time. O Ho is not rejected. There is sufficient evidence to indicate that Vitamin C reduces the mean recovery time. O Ho is not rejected. There is insufficient evidence to indicate that Vitamin C reduces the mean recovery time. O Ho is rejected. There is sufficient evidence to indicate that Vitamin C reduces the mean recovery time.Independent landcrn sampies were selected from two quantitative populations, with sample data given below Using the p-value approach for the data given below, is there sufcient evidence to show that \"1 is larger than 11.2 at the 1% levei pl significance? x2 =123.5, USE SALT Use the value of the test statistics 1.03 to calculate the p-value for the test. {Round your answerto four decimal places.) p-value = State your ccnciusion. 0 H0 is not rejected There is sufficient evidence to indicate that the mean for population 1 is larger than the mean For population 2 O H0 is rejected. There is insuident evidence to indicate that the mean for population 1 is larger than the mean for popuiation 2. O HCl is rejected. There is sufcient evidence to indicate that the mean for population 1 is larger than the mean for population 2. 0 H0 is riot rejected There is insureient evidence l1] indicate that the mean for population 1 is larger than Ihe mean for population 2. Is this result consistent with the one obtained using the critical value approach, with II = 0.01? 0 Yes ONO Independent Iandom samples were selected from two quantitative populations, with sample sizes, means, and variances given below. Populaljon 1 2 Sample Size 64 E4 Sample Mean 3.8 5.0 Sample Variance 9.88 12.52 The value of he test statislic is 2.03. l USE SALT Calculate the pvalue for a test of signicant difference in the population means for the given data. (Round your answer to four decimal places.) Use d1e pvalue to test for a signicant difference in he population means at the 5% signicance level. CI Ho is not rejected. There is sufficient evidence to indicate a difference in means. 0 H0 is rejected. There is insufcient evidence to indicate a difference in means. CI H0 is not rejected. There is insufcient evidence to indicate a difference in means. CI Ho is rejected. There is sufficient evidence to indicate a difference in means. Is this result consistent with he one obtained using d1e critical value approach, with as = 0.05? CI Yes ONo Consider the following situation. a twotailed test at the o; = 0.1 Find the appropriate rejection regions. {Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.) IE use SALT 2.: 2.: State your conclusion if the observed test statistic was 2 = 2.13. If appropriate, provide a measure of reliability for your conclusion. CI The null hypothesis is rejected at the 10% level. 0 The null hypothesis is rejected at the [1.1% level. 0 The null hypothesis is not rejected. Consider the following situation. a twotailed test at the as = 0.1 Find the appropriate rejection regions. {Round your answers to two decimal places. If the test is one-tailedf enter NONE for the unused region.) IQ use SALT 2...: 2.: State your conclusion if the observed test statistic was 2 = 2.18. If appropriate, provide a measure of reliability for your conclusion. CI 'he null hypothesis is rejected at the 10% level. 0 "he null hypothesis is rejected at the 0.1% level. 0 "he null hypothesis is not rejected