60 and older 935 O Calculate a confidence interval x 1.8786 1.3214 Interpret the interval. 63.4 0.11 t confidence level approximately 95% for the difference between population mean height for the younger women and that for the older women. (Use #20-39-60 and older) x )
60 and older 935 O Calculate a confidence interval x 1.8786 1.3214 Interpret the interval. 63.4 0.11 t confidence level approximately 95% for the difference between population mean height for the younger women and that for the older women. (Use #20-39-60 and older) x )
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
just answer A and the test statistic. Thank u
![A report included the following information on the heights (in.) for non-Hispanic white females.
Sample Sample Std. Error
Size
Mean
Mean
64.9
0.09
63.4
0.11
Age
20-39
60 and older
866
935
(a) Calculate a confidence interval at confidence level approximately 95% for the difference between population mean height for the younger women and that for the older women. (Use 20-39 - μ60 and older')
1.3214
X
1.8786
]x )
X
Interpret the interval.
O We are 95% confident that the true average height of younger women is greater than that of older women by an amount outside the confidence interval.
O We cannot draw a conclusion from the given information.
O We are 95% confident that the true average height of younger women is less than that of older women by an amount within the confidence interval.
We are 95% confident that the true average height of younger women is greater than that of older women by an amount within the confidence interval.
(b) Let μ₁ denote the population mean height for those aged 20-39 and μ₂ denote the population mean height for those aged 60 and older. Interpret the hypotheses Ho: M₁ M₂ = 1 and ₂: M₁ - H₂ > 1.
O The null hypothesis states that the true mean height for younger women is more than 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is 1 inch higher than for older
women.
O The null hypothesis states that the true mean height for older women is more than 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women is 1 inch higher than for younger
women.
O The null hypothesis states that the true mean height for older women is 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women is more than 1 inch higher than for younger
women.
The null hypothesis states that the true mean height for younger women is 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is more than 1 inch higher than for older
women.
Carry out a test of these hypotheses at significance level 0.001. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
z = 11.26
x
P-value = 0.0001
(c) Based on the P-value calculated in (b) would you reject the null hypothesis at any reasonable significance level? Explain your reasoning.
O Fail to reject Ho. The data suggests that the difference in the true average heights exceeds 1.
O Reject Ho. The data does not suggest that the difference in the true average heights exceeds 1.
O Fail to reject Ho. The data does not suggest that the difference in the true average heights exceeds 1.
Ⓒ Reject Ho. The data suggests that the difference in the true average heights exceeds 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d420b9a-482d-47e6-8321-72477fc946ab%2Fdfe13100-ac7f-447f-9027-309549f11928%2Fkhwb3x7_processed.png&w=3840&q=75)
Transcribed Image Text:A report included the following information on the heights (in.) for non-Hispanic white females.
Sample Sample Std. Error
Size
Mean
Mean
64.9
0.09
63.4
0.11
Age
20-39
60 and older
866
935
(a) Calculate a confidence interval at confidence level approximately 95% for the difference between population mean height for the younger women and that for the older women. (Use 20-39 - μ60 and older')
1.3214
X
1.8786
]x )
X
Interpret the interval.
O We are 95% confident that the true average height of younger women is greater than that of older women by an amount outside the confidence interval.
O We cannot draw a conclusion from the given information.
O We are 95% confident that the true average height of younger women is less than that of older women by an amount within the confidence interval.
We are 95% confident that the true average height of younger women is greater than that of older women by an amount within the confidence interval.
(b) Let μ₁ denote the population mean height for those aged 20-39 and μ₂ denote the population mean height for those aged 60 and older. Interpret the hypotheses Ho: M₁ M₂ = 1 and ₂: M₁ - H₂ > 1.
O The null hypothesis states that the true mean height for younger women is more than 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is 1 inch higher than for older
women.
O The null hypothesis states that the true mean height for older women is more than 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women is 1 inch higher than for younger
women.
O The null hypothesis states that the true mean height for older women is 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women is more than 1 inch higher than for younger
women.
The null hypothesis states that the true mean height for younger women is 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is more than 1 inch higher than for older
women.
Carry out a test of these hypotheses at significance level 0.001. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
z = 11.26
x
P-value = 0.0001
(c) Based on the P-value calculated in (b) would you reject the null hypothesis at any reasonable significance level? Explain your reasoning.
O Fail to reject Ho. The data suggests that the difference in the true average heights exceeds 1.
O Reject Ho. The data does not suggest that the difference in the true average heights exceeds 1.
O Fail to reject Ho. The data does not suggest that the difference in the true average heights exceeds 1.
Ⓒ Reject Ho. The data suggests that the difference in the true average heights exceeds 1.
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