Question

A physician wants to develop criteria for determining whether a patient's pulse rate is atypical, and she wants to determine whether there are significant differences between males and females. Use the sample pulse rates below. Male 96 64 88 64 84 84 68 64 68 64 Female 68 84 104 60 76 88 96 76 72 124 a. Construct a 95% confidence interval estimate of the mean pulse rate for males. ___<μ<___ (Round to one decimal place as needed.) b. Construct a 95% confidence interval estimate of the mean pulse rate for females. ___<μ<___ (Round to one decimal place as needed.) c. Compare the preceding results. Can we conclude that the population means for males and females are different? A. Yes, because the two confidence intervals do not overlap, we can conclude that the two population means are different. B. Yes, the population mean for males appears to be greater than the population mean for females. C. Yes, the population mean for females appears to be greater than the population mean for males. D. No, because the two confidence intervals overlap, we cannot conclude that the two population means are different. A physician wants to develop criteria for determining whether a patient's pulse rate is atypical, and she wants to determine whether there are significant differences between males and females. Use the sample pulse rates below. Male 96 64 88 64 84 84 68 64 68 64 Female 68 84 104 60 76 88 96 76 72 124 a. Construct a 95% confidence interval estimate of the mean pulse rate for males. ___<μ<___ (Round to one decimal place as needed.) b. Construct a 95% confidence interval estimate of the mean pulse rate for females. ___<μ<___ (Round to one decimal place as needed.) c. Compare the preceding results. Can we conclude that the population means for males and females are different? A. Yes, because the two confidence intervals do not overlap, we can conclude that the two population means are different. B. Yes, the population mean for males appears to be greater than the population mean for females. C. Yes, the population mean for females appears to be greater than the population mean for males. D. No, because the two confidence intervals overlap, we cannot conclude that the two population means are different.

Answer 1

a) 66.1 < μ < 82.7

b) 71.9 < μ < 97.7

c) D. No, because the two confidence intervals overlap, we cannot conclude that the two population means are different.

Explanation:

Confidence interval is given by the formula

M±t×(
`(s)/(√(N) )`) where

• M is the sample mean
• t is the corresponding t value for 95 confidence level
• s is the sample standard deviation
• N is the sample size

a. Construct a 95% confidence interval estimate of the mean pulse rate for males.

For men:

M=74.4 t=2.262 s=11.6207 N=10 then confidence interval is:

74.4±2.262×(
`(11.6207)/(√(10 ) )`) ≈ 74.4±8.3

b. Construct a 95% confidence interval estimate of the mean pulse rate for females.

For women:

M=84.8 t=2.262 s=18.0488 N=10 then confidence interval is:

84.8±2.262×(
`(18.0488 )/(√(10 ) )`) ≈ 84.8±12.9

c. Compare the preceding results. Can we conclude that the population means for males and females are different?

Difference of Population means for males and females are not statistically significant, since confidence intervals overlap.