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   Female
96   68
64   96
76   68
88   64
72   60
60   84
60   96
72   96
68   64
64   124

a. Construct a

9595​%

confidence interval estimate of the mean pulse rate for males.

nothingless than<muμless than<nothing

​(Round to one decimal place as​ needed.)

b. Construct a

9595​%

confidence interval estimate of the mean pulse rate for females.

nothingless than<muμless than<nothing

​(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 females appears to be greater than the population mean for males.

C.

​Yes, the population mean for males appears to be greater than the population mean for females.

D.

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

Answer 1

a)

Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   9          
't value='   tα/2=   2.2622   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   11.9257   / √   10   =   3.7712
margin of error , E=t*SE =   2.2622   *   3.7712   =   8.5311
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    72.00   -   8.531129   =   63.4689
Interval Upper Limit = x̅ + E =    72.00   -   8.531129   =   80.5311
95%   confidence interval is (   63.5 < µ <   80.5 )

b)

sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   20.7632
Sample Size ,   n =    10
Sample Mean,    x̅ = ΣX/n =    82.0000

Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   9          
't value='   tα/2=   2.2622   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   20.7632   / √   10   =   6.5659
margin of error , E=t*SE =   2.2622   *   6.5659   =   14.8531
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    82.00   -   14.853109   =   67.1469
Interval Upper Limit = x̅ + E =    82.00   -   14.853109   =   96.8531
95%   confidence interval is (   67.1 < µ <   96.9 )

c)

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