Question

2. A sample of 32 students took a class designed to improve their SAT math scores. Their scores before and after the class are recorded in the sheet ‘SAT Scores’ in the ‘Lab12 Chp 10n11 S20’ spreadsheet.

(a) Are the samples independent or paired?

(b) Consider constructing a 90% confidence interval for the average increase in scores after taking the class.

               i. Find the point of estimate using proper notation. Show your work including all relevant quantities needed. Round your answer to 2 decimal places.

               ii. Find the margin of error. Show your work including all relevant quantities needed using proper notation. Round your answer to 4 decimal places.

               iii. Construct the confidence interval by filling in the blanks below. Round you answer to 2 decimal places. 


________________ < ________________ < ________________

               iv. The class instructor claims that the average increase in scores is 10 points. Does the confidence interval contradict this claim? Justify your answer. 


(c) Consider the question: on average, do students who take this SAT math course score 10 points more than those that don’t at a 5% significance level?

               i. State the null and alternate hypothesis using proper notation. 


               ii. Circle the type of critical value(s)/test statistic and corresponding region needed to answer the problem. 


    • z-score or t-score 


    • Identify the degrees of freedom, if not applicable write NA: 


    • right-tailed, left-tailed, or two-tailed 


               iii. Find the critical value(s) using proper notation. Round your answer to 3 decimal places. 


               iv. Find the test statistic using proper notation. Show your work including all relevant quantities needed. Round your answer to 4 decimal places. 


               v. Compute the P-value of the test statistic. Round your answer to 4 decimal places.

               vi. Can you reject the null hypothesis? Justify your answer.

               vii. Answer the question.

Before	After
383	420
334	368
378	396
467	488
470	489
473	473
443	448
459	473
426	428
493	525
382	382
473	474
408	407
433	434
478	490
502	508
394	430
513	525
483	482
447	482
440	479
439	451
435	431
451	454
453	463
491	511
526	529
473	493
440	466
481	482
459	455
399	404

Please Help and Thank You!

Answer 1

Que.2

a. This is paired sample.

Observation table:

Before	After	d	(d-d_bar)^2
383	420	37	578.8836
334	368	34	443.5236
378	396	18	25.6036
467	488	21	64.9636
470	489	19	36.7236
473	473	0	167.4436
443	448	5	63.0436
459	473	14	1.1236
426	428	2	119.6836
493	525	32	363.2836
382	382	0	167.4436
473	474	1	142.5636
408	407	-1	194.3236
433	434	1	142.5636
478	490	12	0.8836
502	508	6	48.1636
394	430	36	531.7636
513	525	12	0.8836
483	482	-1	194.3236
447	482	35	486.6436
440	479	39	679.1236
439	451	12	0.8836
435	431	-4	286.9636
451	454	3	98.8036
453	463	10	8.6436
491	511	20	49.8436
526	529	3	98.8036
473	493	20	49.8436
440	466	26	170.5636
481	482	1	142.5636
459	455	-4	286.9636
399	404	5	63.0436
		414	5709.8752

b.

i.

Point estimate:

Where d = After - before

ii.

Margin of error:

where,

Degrees od freedom = n-1 = 32-1 = 31

Critical value = 1.695

ME = 1.695 * (13.57 / sqrt(32)) = 14.0661

iii.

Confidence interval:

iv.

Since confidence interval contain value 10, hence confidence interval contradict this claim.