Question

10. According to the National Health and Nutrition Examination Survey and the Epidemiologic Follow-up Study the mean systolic blood pressure for individuals aged 25 to 59 is 127.3 with a standard deviation of 20.2. A sample measurement of systolic blood pressure from 15 EDUR 8131 Statistics students is taken to learn whether EDUR 8131 students have blood pressure that differs from the national average.

(a) Perform a one sample Z test on these data to learn whether a difference in blood pressure exists:

• present calculated Z test value, and

• write a brief conclusion about your finding. Use α = .05 for hypothesis testing.

(b) Construct a 95% confidence interval about the sample mean for these data. Sample Systolic Blood Pressure: 143 176 131 95 139 145 169 139 181 161 151 195 132 175 143

Answer 1

a)

Ho :   µ =   127.3                  
Ha :   µ ╪   127.3       (Two tail test)          
                          
Level of Significance ,    α =    0.05                  
population std dev ,    σ =    20.2000                  
Sample Size ,   n =    15                  
Sample Mean,    x̅ = ΣX/n =    151.6667                  
                          
'   '   '                  
                          
Standard Error , SE = σ/√n =   20.2000   / √    15   =   5.2156      
Z-test statistic= (x̅ - µ )/SE = (   151.667   -   127.3   ) /    5.216   =   4.67
                          
  
p-Value   =   0.0000   [ Excel formula =NORMSDIST(z) ]              
Decision:   p-value<α, Reject null hypothesis                       
Conclusion: There is enough evidence to conclude that a difference in blood pressure exists

b)

Level of Significance ,    α =    0.05          
'   '   '          
z value=   z α/2=   1.9600   [Excel formula =NORMSINV(α/2) ]      
                  
Standard Error , SE = σ/√n =   20.200   / √   15   =   5.2156
margin of error, E=Z*SE =   1.9600   *   5.216   =   10.222
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    151.67   -   10.222   =   141.444
Interval Upper Limit = x̅ + E =    151.67   -   10.222   =   161.889
95%   confidence interval is (   141.44   < µ <   161.89   )