Question

From past experience, Dr. R-P believes that the average score on a Research Methods Course is 75. A sample of 10 students exam scores is as follows:
80, 68, 72, 73, 76, 81, 71, 71, 65, 53.
Test the claim that the students average is still 75. Use α = 0.01. [You need to first compute the mean and the standard deviation, then the standard error from your sample. To do this, use the computational method for ungrouped data that we learned in chapter 5, page 128-129. (Show all your work; this gives you a complete view of where all these numbers we use in hypothesis testing or confidence interval come from)].

Answer 1

	X	X2
	80	6400
	68	4624
	72	5184
	73	5329
	76	5776
	81	6561
	71	5041
	71	5041
	65	4225
	53	2809
Sum =	710	50990

The sample mean is computed as follows:

Also, the sample variance is

Therefore, the sample standard deviation s is

Null hypothesis: The average score is 75

Alternate hypothesis: The average score is different than 75

At  α = 0.01 and df = n - 1 = 10 - 1 = 9 critical t value, t_c = 3.25

t = -1.58

Reject H0 if |t| < t_c

|t| = 1.58 < 3.25 = t_c

H0 is rejected

hence, The average score is different than 75