For the following scenarios, give the null and alternative hypotheses and state in words what µ represents in your hypotheses.Question 1: The National Assessment of Educational Progress (NAEP) is administered annually to 4th, 8th, and 12th graders in the United States. On the math assessment, a score above 275 is considered an indication that a student has the skills to balance a checkbook. In a random sample of 500 young men between the ages of 18 and 20, the mean NAEP math score is 272. Do we have evidence to support the claim that young men nationwide have a mean score b

The National Assessment of Educational Progress (NAEP) is administered annually to 4th, 8th, and 12th graders in the United States. On the math assessment, a score above 275 is considered an indication that a student has the skills to balance a checkbook. In a random sample of 500 young men between the ages of 18 and 20, the mean NAEP math score is 272. Do we have evidence to support the claim that young men nationwide have a mean score below 275?

A medical school admissions officer was interested in whether there is a difference in MCAT test scores (the standardized test used for medical school admission) between (1) biological sciences majors, (2) social science majors and (3) math majors. The admissions officer randomly sampled 50 students from each of these majors who applied to medical school in 2014 and recorded their MCAT score.Let µ1, µ2, and µ3 be the MCAT scores for students who majored in biological sciences, social sciences, and math, respectively.Which of the following are the appropriate null and alternative hypotheses?H0: μ1 = μ2 = μ3Ha: μ1, μ2, μ3, are not all equalH0: μ1, μ2, μ3, are not all equalHa: μ1 = μ2 = μ3H0: μ1 = μ2 = μ3Ha: μ1 ≠ μ2 ≠ μ3H0: μ1 ≠ μ2 ≠ μ3Ha: μ1 = μ2 = μ3

Are you smarter than a second grader? A random sample of 70 second graders in a certain school district are given a standardized mathematics skills test. The sample mean score is =x55. Assume the standard deviation of test scores is =σ21. The nationwide average score on this test is 50. The school superintendent wants to know whether the second graders in her school district have greater math skills than the nationwide average. Use the =α0.05 level of significance and the P-value method with the TI-84 Plus calculator.Part 1 of 5(a) State the appropriate null and alternate hypotheses.:H0  =μ50:H1  >μ50This hypothesis test is a ▼right-tailed test.Part 2 of 5(b) Compute the value of the test statistic. Round the answer to two decimal places.z=1.9Correct Answer:=z1.99Part: 2 / 52 of 5 Parts CompletePart 3 of 5(c) Compute the P-value of the test statistic. Round the answer to four decimal places.P-value=Skip PartCheckSave For LaterSubmit Assignment

On a nationwide test taken by high school students, the mean score was 49 and the standard deviation was 12. The scores were normally distributed. Complete the following statements.(a) Approximately 95% of the students scored between and .(b) Approximately of the students scored between 13 and 85.

The Director of the Department of Education in Queensland was analysing the last year average mathematics test scores in the schools under his control. He noticed that there were dramatic differences in scores among the schools. In an attempt to improve the scores of all the schools, he attempted to determine the factors that account for the differences. Accordingly, he took a random sample of 40 schools across the state and, for each, determined the mean mathematics test score, the percentage of teachers in each school who have at least one university degree in mathematics (math), the mean age, and the mean annual income ($ ‘000) of the mathematics teachers. These data are saved in the t10e5 Excel file.a) Perform a multiple regression analysis on these data with R. What is your sample regression equation?b) Is the model useful in explaining the variation among schools? Explain.c) Are the normality and homoskedasticity conditions satisfied? Explain.d) Is multicollinearity a problem? Explain.e) Interpret and the coefficients. Do you find their signs reasonable? Why or why not? Based on your expectations perform t-tests on the coefficients (use a = 0.05).f) Test the null hypothesis that neither the teachers’ mean age nor their mean annual income has a significant effect on the average mathematics test scores (use a = 0.05).