Question

The table below shows pulse rates taken from random samples of adults. The data have been sorted by age. Use one-way analysis of variance (ANOVA) to test the claim that the three different age groups have the same mean pulse rate. Use α = .05 .

              Adult Pulse Rates by Age Group
20-29   64 64 76 64 60 88 72 56 88 72 68 80 72  72 68  64
30-39   88 72 85 60 84 84 64 56 72 68 80 76 60  76 80  60
40-49   72 60 84 72 56 64 70 76 68 96 72 64 80 104 88 124

Express the claim in symbolic form.

Group of answer choices

μ_20-29 = μ_30-39 = μ_40-49

μ_20-29 ≥ μ_30-39 ≥ μ_40-49

Fewer than one mean is different.

At most one mean is different.

μ_20-29 > μ_30-39 > μ_40-49

μ_20-29 ≠ μ_30-39 ≠ μ_40-49

μ_20-29 ≤ μ_30-39 ≤ μ_40-49

More than one mean is different.

μ_20-29 < μ_30-39 < μ_40-49

At least one mean is different.

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Question 20.83 pts

The table below shows pulse rates taken from random samples of adults. The data have been sorted by age. Use one-way analysis of variance (ANOVA) to test the claim that the three different age groups have the same mean pulse rate. Use α = .05 .

              Adult Pulse Rates by Age Group
20-29   64 64 76 64 60 88 72 56 88 72 68 80 72  72 68  64
30-39   88 72 85 60 84 84 64 56 72 68 80 76 60  76 80  60
40-49   72 60 84 72 56 64 70 76 68 96 72 64 80 104 88 124

What is the alternative hypothesis, H₁?

Group of answer choices

Fewer than one mean is different.

μ_20-29 > μ_30-39 > μ_40-49

μ_20-29 < μ_30-39 < μ_40-49

μ_20-29 ≠ μ_30-39 ≠ μ_40-49

μ_20-29 = μ_30-39 = μ_40-49

More than one mean is different.

At most one mean is different.

At least one mean is different.

μ_20-29 ≥ μ_30-39 ≥ μ_40-49

μ_20-29 ≤ μ_30-39 ≤ μ_40-49

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Question 30.84 pts

The table below shows pulse rates taken from random samples of adults. The data have been sorted by age. Use one-way analysis of variance (ANOVA) to test the claim that the three different age groups have the same mean pulse rate. Use α = .05 .

              Adult Pulse Rates by Age Group
20-29   64 64 76 64 60 88 72 56 88 72 68 80 72  72 68  64
30-39   88 72 85 60 84 84 64 56 72 68 80 76 60  76 80  60
40-49   72 60 84 72 56 64 70 76 68 96 72 64 80 104 88 124

Find the critical value(s). (Round to the nearest ten-thousandth. If more than one value is found, enter the smallest critical value.)

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Question 40.84 pts

The table below shows pulse rates taken from random samples of adults. The data have been sorted by age. Use one-way analysis of variance (ANOVA) to test the claim that the three different age groups have the same mean pulse rate. Use α = .05 .

              Adult Pulse Rates by Age Group
20-29   64 64 76 64 60 88 72 56 88 72 68 80 72  72 68  64
30-39   88 72 85 60 84 84 64 56 72 68 80 76 60  76 80  60
40-49   72 60 84 72 56 64 70 76 68 96 72 64 80 104 88 124

Find the value of the test statistic. (Round to the nearest ten-thousandth.)

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Question 50.83 pts

The table below shows pulse rates taken from random samples of adults. The data have been sorted by age. Use one-way analysis of variance (ANOVA) to test the claim that the three different age groups have the same mean pulse rate. Use α = .05 .

              Adult Pulse Rates by Age Group
20-29   64 64 76 64 60 88 72 56 88 72 68 80 72  72 68  64
30-39   88 72 85 60 84 84 64 56 72 68 80 76 60  76 80  60
40-49   72 60 84 72 56 64 70 76 68 96 72 64 80 104 88 124

What is the statistical conclusion?

Group of answer choices

Fail to reject H₀

Reject H₀

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Question 60.83 pts

The table below shows pulse rates taken from random samples of adults. The data have been sorted by age. Use one-way analysis of variance (ANOVA) to test the claim that the three different age groups have the same mean pulse rate. Use α = .05 .

              Adult Pulse Rates by Age Group
20-29   64 64 76 64 60 88 72 56 88 72 68 80 72  72 68  64
30-39   88 72 85 60 84 84 64 56 72 68 80 76 60  76 80  60
40-49   72 60 84 72 56 64 70 76 68 96 72 64 80 104 88 124

State the conclusion in words.

Group of answer choices

The sample data support the claim that the three different age groups have the same mean pulse rate.

There is sufficient evidence to warrant rejection of the claim that the three different age groups have the same mean pulse rate.

There is not sufficient evidence to warrant rejection of the claim that the three different age groups have the same mean pulse rate.

There is not sufficient sample evidence to support the claim that the three different age groups have the same mean pulse rate.

Answer 1

1)

2)

3)

count, ni =	16	16	16
mean , x̅ i =	70.500	72.81	78.13
std. dev., si =	9.107	10.426	17.761
sample variances, si^2 =	82.933	108.696	315.450
total sum	1128	1165	1250		3543
grand mean , x̅̅ =	Σni*x̅i/Σni =				73.81

square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	10.973	1.000	18.598
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	175.563	16.000	297.563		489.125
SS(within ) = SSW = Σ(n-1)s² =	1244.000	1630.438	4731.750		7606.1875

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   48
df within = N-k =   45
  
mean square between groups , MSB = SSB/k-1 =    244.5625
  
mean square within groups , MSW = SSW/N-k =    169.0264
  
F-stat = MSB/MSW =    1.4469
P value =   0.2460

	SS	df	MS	F	p-value	F-critical
Between:	489.13	2	244.56	1.45	0.2460	3.20
Within:	7606.19	45	169.03
Total:	8095.31	47

CRITICAL =3.20

4)

T STATS = F VALUE =1.45

5)

F-stat < critical value, Do not reject Ho

Fail to reject H₀

₆₎

There is not sufficient evidence to warrant rejection of the claim that the three different age groups have the same mean pulse rate.

THANKS

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