Reading interventions ~ Jasmine is a reading curriculum specialist for a large urban school district. She regularly conducts pilot studies of promising educational programs to determine if they should be implemented throughout the district. During fall term last year, she randomly selected a group of 24 eighth graders at a large middle school to participate in a supplemental tutoring program. Call this group the "Fall Cohort."At the end of the term the Fall Cohort students were evaluated using a standardized test. The sample mean score for the 24 students was 67.27 points with a standard deviation of 14.55 points.Historically, scores for students in the district on this assessment have been normally distributed with a mean of 62.4 points. Jasmine wants to use statistical inference to determine if mean scores on this exam for students in the Fall Cohort are higher than the historical mean.Round all calculated values to 4 decimal places.1. Which set of hypotheses statements below should Jasmine use to answer her research question?A. H0H0: = 62.4 vs. HAHA: > 62.4 B. H0H0: xx = 62.4 vs. HAHA: xx > 67.27 C. H0H0: = 62.4 vs. HAHA: 62.4 D. H0H0: = 62.4 vs. HAHA: xx > 67.27

2. Which of the following conditions must be met to perform this hypothesis test? Select all the correct answers. A. The scores for all students in the district must be normally distributed. B. The scores for students in the Fall Cohort must be normally distributed. C. We must be able to expect that at least 5 students will have scores above the historical mean. D. The observations must be independent. E. The sample must be large enough so that at least 10 students fail and 10 succeed.

3. Calculate the test statistic for Jasmine's hypothesis test.t=t=

4. Jasmine calculated a p-value of 0.0573. Which of the following is a correct interpretation of the p-value?A. The p-value is the probability of obtaining a sample result equal to or greater than 67.27 under the null model where 0=62.40=62.4. B. There is a 5.7335% chance that the true mean is =62.4=62.4. C. In repeated sampling, we expect the sample mean to be within 0.0573 of the true mean, on average. D. The p-value is the proportion of times in repeated sampling under the null model that the true mean will be more than 67.27.

5. Calculate the effect size for Jasmine's hypothesis test.d^=d^=

6. Using the summary values for the data collected in the Fall Cohort, calculate a 95% confidence interval for the mean score for all students who might participate in the reading intervention program.( , )

7. Jasmine decides she wants to have a 95% confidence interval with a margin of error of no more than 3 points. What is the required sample size she needs to achieve this?Use a t* value rounded to THREE decimal places and the summary values for the data collected in the Fall Cohort to determine the answer. Your answer should be an integer value.n=n=