(b) Interpret this interval in context. 95% of students will have a difference between reading and writing scores that falls within our confidence interval O We can be 95% confident that the average difference between reading and writing scores of all students is contained within our confidence interval O We can be 95% confident that our confidence interval contains the mean difference between reading and writing scores of these 200 students (c) Does the confidence interval provide convincing evidence that there is a real difference in the average scores? Explain. Ono, because or confidence interval contains both positive and negative values Ono, since 0 is contained in our confidence interval Oyes, since 0 is contained in our confidence interval Oyes, because negative scores are impossible and our confidence interval contains them. Question 6 > 0/1 pt 5 3 0 Details 5.22 High School and beyond, Part II: We considered the differences between the reading and writing scores of a random sample of 200 students who took the High School and Beyond Survey in Exercise 5.21. The mean and standard deviation of the differences are Xread-write = -0.545 and 8.887 points respectively. (a) Calculate a 95% confidence interval for the average difference between the reading and writing scores of all students. lower bound: points (please round to two decimal places) upper bound: points (please round to two decimal places)This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null 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 greater than 0. O There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0. O The sample data support the claim that the mean difference of post-test from pre- test is greater than 0. O There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is greater than 0.0 Question 5 v IZ 0/1 pt '0 3 G) Details You wish to test the following claim (Ha) at a signicance level of o: : 0002. For the context of this problem, p.03 : p2 #1 where the first data set represents a pre- test and the second data set represents a post-test. Hg:yd:0 Haipd > 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 : 32.3 with a standard deviation of the differences of 3d : 37.9. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = i i What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value =' i The p-value is... 0 less than (or equal to) o: O greater than a: This p-value leads to a decision to... O reject the null O accept the null O fail to reject the null As such, the final conclusion is that... O There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 78.6. O There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 78.6. O The sample data support the claim that the population mean is not equal to 78.6. O There is not sufficient sample evidence to support the claim that the population mean is not equal to 78.6.0 Question 4 v 1 0/1 pt '0 3 G) Details You wish to test the following claim (H3) at a signicance level of (I : 0.10. Hap. : 78.6 Hp 7 78.6 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n : 26 with mean M : 77.4 and a standard deviation of SD : 9.8. What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value =| | The p-value is... 0 less than (or equal to) o: O greater than or This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null As such, the final conclusion is that... O There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 62.9. O There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 62.9. O The sample data support the claim that the population mean is not equal to 62.9. O There is not sufficient sample evidence to support the claim that the population mean is not equal to 62.9.. Question 2 > 0/1 pt 9 3 0 Details You wish to test the following claim (Ha) at a significance level of a = 0.01. Ho:M = 62.9 Ha: M + 62.9 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 7 with mean M = 70.1 and a standard deviation of SD = 13.6. 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... O less than (or equal to) a O greater than a. Question 1 0/1 pt 1 3 0 Details The national average SAT score is roughly 1500. We would like to see if the high school seniors who apply to Duke have higher than average SAT scores. We randomly sample 100 applicants' files and record their SAT scores. Which of the following is the correct set of hypotheses for this research question? Hint: think about how many samples we have data from. OHo: p = 1500; HA: p > 1500 OHo: X = 1500; HA: X > 1500 OHo: H = 1500; HA: H = 1500 O Ho: H Duke= H National; HA: I Duke> H National O Ho: H = 1500; HA: [ > 1500