Question

A)

As the population ages, there is increasing concern about accident-related injuries to the elderly. An article reported on an experiment in which the maximum lean angle—the farthest a subject is able to lean and still recover in one step—was determined for both a sample of younger females (21–29 years) and a sample of older females (67–81 years). The following observations are consistent with summary data given in the article:

YF:	28,	35,	33,	27,	28,	32,	31,	36,	32,	29
OF:	17,	15,	22,	13,	12

Does the data suggest that true average maximum lean angle for older females (OF) is more than 10 degrees smaller than it is for younger females (YF)? State and test the relevant hypotheses at significance level 0.10. (Use μ₁ for younger females and μ₂ for older females.)

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

t	=
P-value	=

B)

An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola.

Beverage	Sample Size	Sample Mean	Sample SD
Strawberry Drink	15	537	25
Cola	15	553	16

Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value. (Use

α = 0.05.)

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

t	=
P-value	=

I just need p-value and test statistics *******

Answer 1

Result:

A)

As the population ages, there is increasing concern about accident-related injuries to the elderly. An article reported on an experiment in which the maximum lean angle—the farthest a subject is able to lean and still recover in one step—was determined for both a sample of younger females (21–29 years) and a sample of older females (67–81 years). The following observations are consistent with summary data given in the article:

YF:	28,	35,	33,	27,	28,	32,	31,	36,	32,	29
OF:	17,	15,	22,	13,	12

Does the data suggest that true average maximum lean angle for older females (OF) is more than 10 degrees smaller than it is for younger females (YF)? State and test the relevant hypotheses at significance level 0.10. (Use μ₁ for younger females and μ₂ for older females.)

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

t	2.87
P-value	0.0066

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	10
Level of Significance	0.1
Population 1 Sample
Sample Size	10
Sample Mean	31.1
Sample Standard Deviation	3.0713732
Population 2 Sample
Sample Size	5
Sample Mean	15.8
Sample Standard Deviation	3.962322551
Intermediate Calculations
Population 1 Sample Degrees of Freedom	9
Population 2 Sample Degrees of Freedom	4
Total Degrees of Freedom	13
Pooled Variance	11.3615
Standard Error	1.8462
Difference in Sample Means	15.3000
t Test Statistic	2.8708
Upper-Tail Test
Upper Critical Value	1.3502
p-Value	0.0066
Reject the null hypothesis

B)

An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola.

Beverage	Sample Size	Sample Mean	Sample SD
Strawberry Drink	15	537	25
Cola	15	553	16

Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value. (Use

α = 0.05.)

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

t	-2.09
P-value	0.023

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	15
Sample Mean	537
Sample Standard Deviation	25
Population 2 Sample
Sample Size	15
Sample Mean	553
Sample Standard Deviation	16
Intermediate Calculations
Population 1 Sample Degrees of Freedom	14
Population 2 Sample Degrees of Freedom	14
Total Degrees of Freedom	28
Pooled Variance	440.5000
Standard Error	7.6638
Difference in Sample Means	-16.0000
t Test Statistic	-2.0877
Lower-Tail Test
Lower Critical Value	-1.7011
p-Value	0.0230