b) A school district wants to evaluate the effectiveness of a new teaching method for improving students' math scores. They believe the improvement in math scores is normally distributed with o 4 points. A sample of 25 students is randomly selected and their math scores are measured before and after the new teaching method is implemented. The sample standard deviation of the differences in math scores is 5.2 points. Does the school district have evidence to support their assumed standard deviation of 4 points? Use critical values of X6.975 and X3.025 (a 95% window). i) ii) Find the value of the test statistic for this sample and the two critical values. X0.975 = YES x² = Does the school district have evidence to support their assumed standard deviation of 4 points? Circle YES or NO and briefly explain your answer. NO X0.025 =

The mean number of english courses taken in two-year time period by male and female college students is believed to be about the same. An experiment is conducted and data are collected from 29 males and 16 females. The males took an average of 3 english courses with a standard deviation of 0.8. The females took an average of four english courses with a standard deviation of 1.0. Are the means statistically the same?

In 2019, College Board reported that the mean score for the math section of the SAT was 528 with a standard deviation of 110. A math department at local university would like to give a scholarship to any student that scored in the top 2.5% of students in the math section. What is the minimum score needed to get this scholarship? Assume the scores are normally distributed. A/

Do men take a different amount of time than women to get out of bed in the morning? The 54 men observed averaged 4.3 minutes to get out of bed after the alarm rang. Their standard deviation was 1.4. The 59 women observed averaged 5 minutes and their standard deviation was 2.8 minutes. What can be concluded at the a = 0.01 level of significance? a. For this study, we should use t-test for the difference between two independent population means b. The null and alternative hypotheses would be: Ho: μ1 = + μ2 (please enter a decimal) H₁: μ1 # ♦ μ2 (Please enter a decimal) (please show your answer to 3 decimal places.) c. The test statistic t = d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is α f. Based on this, we should fail to reject + the null hypothesis.