Question

The average final exam score for the statistics course is 77%. A professor wants to see if the average final exam score for students who are given colored pens on the first day of class is lower. The final exam scores for the 12 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 79.65, 57. 72. 84. 54,60,69.69.85,58,79 What can be concluded at the the a = 0.05 level of significance level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: ? ? H: ? c. The test statistic ? V (please show your answer to 3 decimal places.) d. The p-value- (Please show your answer to 4 decimal places.) e. The p-value is ? f. Based on this, we should Select an answer the null hypothesis. g. Thus, the final conclusion is that ... The data suggest the population mean is not significantly lower than 77 at a = 0.05, so there is statistically insignificant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is equal to 77. The data suggest that the population mean final exam score for students who are given colored pens at the beginning of class is not significantly lower than 77 at a -0.05, so there is statistically insignificant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is lower than 77. The data suggest the populaton mean is significantly lower than 77 at a = 0.05, so there is statistically significant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is lower than 77. Hint: Helpful Videos: Calculations [+] Setup [+] Interpretations [+] Textbook Pages Help

Answer 1

	x	x2
	79	6241
	65	4225
	57	3249
	72	5184
	84	7056
	54	2916
	60	3600
	69	4761
	69	4761
	85	7225
	58	3364
	79	6241
Total	831	58823

n=12

Sample mean

831 * n 12

x = 69.25

The standard deviation of sample is given by

Σχ2 (Σα)? In s = η -1

58823 (831) 712 S = 12 - 1

58823 – 57546.75 S= 11

s= V116.0227

s = 10.7714

Answer(a):

For this study, we should use one sample t-test

Answer(b):

H₀:

_u = 77

H₁:

μ<77

Answer(c):

The test statistic to test the above hypotheses is

t = x-t SW Vn

69.25 – 77 t 10.7714,12

-7.75 t = 3.11

t = -2.492

The value of test statistic for above test is -2.492

Answer(d):

The p-value for above test is 0.015

Answer(e):

We have level of significance, α=0.05

The p-value is Less than α

Answer(f):

Based on this, we should Reject the null hypothesis.

Answer(g):

The correct option is C.