Question

In: Statistics and Probability

1.    M 644 2.    F 345 3.    F 710 4.    F 655 5.    F 539 6.   ...


1.    M 644

2.    F 345

3.    F 710

4.    F 655

5.    F 539

6.    M 492

7.    M 598

8.    F 481

9.    F 622

10. F 545

11. M 707

12. F 332

13. M 538

14. F 470

15. M 469

16. F 483

17. M 572

18. F 487

19. M 358

20. F 440

21. F 637

22. M 447

23. F 482

24. M 485

25. F 417

26. M 569

27. M 541

28. F 596

29. F 395

30. M 526

31. M 643

32. M 435

33. F 511

34. F 766

35. F 467

36. F 562

37. M 460

38. M 483

39. F 644

40. F 606

The first task you have is to select a sample of 40 students. Carefully explain your procedure and reasoning for selecting these 40 students.   Use your sample to describe the high school’s performance as a whole. Produce the proper statistical summaries and graphs.

Next, use your sample to create a 95% confidence interval for the mean SAT math score at this high school. Interpret the interval. Based on your confidence interval, compare the performance of these students with the statewide mean math score of 503.

Your last portion of the project is to address this following question. Nationally males tend to have higher Math scores than Females. Use the sample to determine if that is true at this high school.   Be sure to check all assumptions and conditions when determining the answer to this question.

Solutions

Expert Solution

95% CONFIDENCE INTERVAL IS


sample mean = 528.98
t critical = 2.02
sM = √(101.561^2/40) = 16.06
μ = M ± t(sM)
μ = 528.98 ± 2.02*16.06
μ = 528.98 ± 32.4808

95% CI [496.4992, 561.4608].

You can be 95% confident that the population mean (μ) falls between 496.4992 and 561.4608.

Since statewide wide mean math score is in the 95% confidence interval therefore the performance of randomly selected 40 students math score is NOT different from 503 score.

NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

To conduct this test we will check the following assumption:

1) Random sample is normally distributed.

2) Population variances are equal.

From above table we can see that Equal variance assumption is satisfied. Since P value from Levene's test is 0.248>0.05 THEREFORE WE FAIL TO REJECT NULL HYPOTHESIS H0 THEREFORE VARIANCES ARE EQUAL.

t value = -0.08

Degrees of freedom=38

The P-Value is .468329. The result is not significant because p > .05.

Decision: Fail to reject null hypothesis H0.

Conclusion: We dont have sufficient evidence to show that males tend to have higher Math scores than Females.

orchestra answered 2 years ago
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