Question

please help me finding the value of the sample test statistic?

A) The manufacturer of a sports car claims that the fuel injection system lasts 48 months before it needs to be replaced. A consumer group tests this claim by surveying a random sample of 10 owners who had the fuel injection system replaced. The ages of the cars at the time of replacement were (in months):

25

44

45

48

53

46

30

51

42

52

Use the sample data to calculate the mean age of a car when the fuel injection system fails and the standard deviation. (Round your answers to two decimal places.)

x =	------months
s =	---------months

What is the value of the sample test statistic? (Round your answer to three decimal places.)

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B) Six sets of identical twins were randomly selected from a population of identical twins. One child was taken at random from each pair to form an experimental group. These children participated in a program designed to promote creative thinking. The other child from each pair was part of the control group that did not participate in the program to promote creative thinking. At the end of the program, a creative problem-solving test was given, with the results shown in the table below.

Twin Pair	A	B	C	D	E	F
Experimental group	55	33	12	25	33	47
Control Group	37	23	3	18	21	42

Higher scores indicate better performance in creative problem solving. Do the data support the claim that the program of the experimental group did promote creative problem solving? Use α = 0.01. (Let d = experimental − control.)

What is the value of the sample test statistic? (Round your answer to three decimal places.)
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C) A hospital reported that the normal death rate for patients with extensive burns (more than 40% of skin area) has been significantly reduced by the use of new fluid plasma compresses. Before the new treatment, the mortality rate for extensive burn patients was about 60%. Using the new compresses, the hospital found that only 40 of 88 patients with extensive burns died. Use a 1% level of significance to test the claim that the mortality rate has dropped since using the new treatment.

What is the value of the sample test statistic? (Round your answer to two decimal places.)
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Answer 1

A).

∑x = 436

∑x² = 19784

n = 10

Mean , x̅ = Ʃx/n = 436/10 = 43.60

Standard deviation, s = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(19784-(436)²/10)/(10-1)] = 9.2760 = 9.28

Test statistic:

t = (x̅ - µ)/(s/√n) = (43.6 - 48)/(9.276/√10) = -1.500

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B).

Experimental	Control	Difference
55	37	18
33	23	10
12	3	9
25	18	7
33	21	12
47	42	5

∑d = 61

∑d² = 723

n = 6

Mean , x̅d = Ʃd/n = 61/6 = 10.1667

Standard deviation, sd = √[(Ʃd² - (Ʃd)²/n)/(n-1)] = √[(723-(61)²/6)/(6-1)] = 4.5350

Test statistic:

t = (x̅d)/(sd/√n) = (10.1667)/(4.535/√6) = 5.491

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c)

n = 88, x = 40

p̄ = x/n = 0.4545

Null and Alternative hypothesis:

Ho : p = 0.6 ;H1 : p < 0.6

Test statistic:

z = (p̄ -p)/√(p*(1-p)/n) = (0.4545 - 0.6)/√(0.6 * 0.4/88) = -2.79