Question

A group of students take a math test. To test if sleep has an effect on their performance, they get 8 hours of sleep for 2 weeks each night, and then take the same math test again. Their scores are listed below. Did sleep have a significant different on their math test performance? (alpha=0.05)

Math Test 1	Math Test 2
84	86
95	95
53	70
96	98
82	86
79	75
68	78
93	95

Find the sum of the difference scores and the mean of the difference scores.

		Σ= 33 Mean D = 4.125
		Σ= -33 Mean D = -4.125
		Σ= 433 Mean D = -4.125
		Σ= 33 Mean D = -5.30

Find the variance of the difference scoress

		S2D=42.41
		S2D=433
		S2D=50.00
		S2D=296

Find the standard error of the mean difference

		SD = 5.30
		SD = 6.00
		SD = 2.30
		SD= 42.41

Calculate the t-statistic

		t = 1.79
		t = -1.79
		t = .77
		t= -.77

Find the t-critical value

		+/- 2.365
		+/- 2.447
		+/-2.306

1. What decision should you make concerning the null hypothesis?

   		Fail to reject the null hypothesis, because the t-statistic is greater than the t-critical value
   		Fail to reject null hypothesis, because the t-statistic is less than the t-critical value
   		Reject the null hypothesis, because the t-statistic is less than the t-critical value
   		Reject the null hypothesis, because the t-statistic is greater than the t-critical value

Answer 1