Question

(Round all intermediate calculations to at least 4 decimal places.)

According to a Health of Boston report, female residents in Boston have a higher average life expectancy as compared to male residents (The Boston Globe, August 16, 2010). You collect the following sample data to verify the results of the report. You also use the historical (population) standard deviation of 8.2 years for females and 8.6 years for males. (You may find it useful to reference the appropriate table: z table or t table)

Female			Male
x−1x−1	=	81.1	x−2x−2	=	74.8
n1	=	32	n2	=	32

Assume that μ₁ is the population mean of life expectancy for females and μ₂ is the population mean of life expectancy for males.

a. Set up the hypotheses to test whether the average life expectancy of female Bostonians is higher than that of male Bostonians.

• H₀: μ₁ − μ₂ = 0; H_A: μ₁ − μ₂ ≠ 0

• H₀: μ₁ − μ₂ ≥ 0; H_A: μ₁ − μ₂ < 0

• H₀: μ₁ − μ₂ ≤ 0; H_A: μ₁ − μ₂ > 0

b. Calculate the value of the test statistic and the p-value. (Round "Test statistic" value to 2 decimal places and "p-value" to 4 decimal places.)

c. At the 10% significance level, what is the conclusion?

• Reject H₀; females live longer than males.

• Reject H₀; females do not live longer than males.

• Do not reject H₀; females live longer than males

• Do not reject H₀; females do not live longer than males

Answer 1

a)  H0: μ1 − μ2 ≤ 0; HA: μ1 − μ2 > 0

b)

sample #1   ------->              
mean of sample 1,    x̅1=   81.1000          
population std dev of sample 1,   σ1 =    8.2          
size of sample 1,    n1=   32          
                  
sample #2   --------->               1.023519452
mean of sample 2,    x̅2=   74.8000          
population std dev of sample 2,   σ2 =    8.6          
size of sample 2,    n2=   32          
                  
difference in sample means = x̅1 - x̅2 =    81.1   -   74.8   =   6.3
                  
std error , SE =    √(σ1²/n1+σ2²/n2) =    2.1006          
                  
Z-statistic = ((x̅1 - x̅2)-µd)/SE =    6.3   /   2.1006   = 3.00
                  
  
                  
p-value =        0.0014   [excel function =NORMSDIST(z)]      

c) Reject H0; females live longer than males.