Question

Instruction for Hypothesis Testing (Problems 17-25, Except 24) For One Population: Show your work for finding Test value, Critical value(s), or P-value. For Two Populations: Use your calculator to give the values of Test Value and P-value. O O O O Indicate your parameter Indicate the claim List the given information Then start your five steps. Pay attention to the method, such as Traditional or P- value Put the step numbers inside a box For step (1): Indicate Ho Indicate Hi Tell if Ho or Hy is the claim (put the word claim inside parentheses in front of the claim sentence) o Identify the type of test such as right-tail test, left-tail test, or two-tail test The name of the test is in the direction of H1 For step (2): Find Critical Value (CV) for Traditional method Find Test value for P-value method For step (3): Find Test value for Traditional method Find P-value for P-value method For step (4), decide to reject Ho or not reject Ho. Circle your result. For Traditional method, draw the bell curve. Separate critical region from non-critical region using CV and locate your test value on the graph For P-value method, compare your P-value with a. For step (5), write your summary according to the slide #5 of lesson 8.2. Other similar statements are not expectable! On this step: Underline is or is not, also underline reject or support. . O O . O O . o O o

Answer 1

1)Hypothesis:

H0: μ1 = μ2 = μ3

Ha: Not all means are equal

	Front	Middle	Back
	82	83	38
	83	78	59
	97	68	55
	93	61	66
	55	77	45
	67	54	52
	53	69	52
		51	61
		63		Total
SUM	530	604	428	1562
Average	75.714	67.111	53.5
∑X^2​	41994	41494	23460	106948
St. Dev.	17.632	10.948	8.96
SS	1865.428571	958.8889	562	3386.31746
n	7	9	8

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	1901.515873	2	950.7579365	5.896055789	0.009283764	3.466800112
Within Groups	3386.31746	21	161.2532124
Total	5287.833333	23
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	SST-SSW	k-1	SSB/dfB	MSB/MSW	FDIST(Fstat,dfB,dfW)	FINV(0.05,dfB,dfW)
Within Groups	∑SS	n-k	SSW/dfW
Total	∑X^2​-(1/n)(∑X)^2​	n-1

2)Test:

F stat = 5.8961

3)Critical value:

F critical = 3.4668

If F stat > F critical, Reject H0

If F stat < F critical, Accept H0

4)Decision:

F stat > F critical , Reject H0

P value < 0.05, Reject H0

There is enough evidence to conclude that not all mean scores of front, middle and back are same