Question

The mean number of type 2 fibers of normal mice this age is 21.7. the n=90 mice yielded y-bar= 18.8, s=15.3 an alpha=0.05. is there significant evidence in the data to support the hypothesis that the mean number of type 2 fibers is different from 21.7 using an alpha-0.05 test? what is the p-value for the hypothesis test?

Answer 1

Given       
Population Mean = 21.7       
Sample Standard Deviation = s = 15.3       
From the data we find the sample mean       
Sample Mean = X̅ = 18.8       
n = 90       
The null and alternative hypothesis are       
Ho : μ = 21.7       
H1 : μ ≠ 21.7       
        
Since sample size is greater than 30, we use z-distribution       
Find Critical Value       
α = 0.05       
We find the z-critical value using Excel function NORM.S.INV for a two sided right tailed test       
z-crit = NORM.S.INV(0.01, true) = -2.3264       
For right sided test, z-crit = 2.3264       
Critical Region is given by :       
Reject Ho when z-calculated > 2.3264       
        
Find Calculated Value of test statistic z       
                 
z-calc = -1.7982       
        
We find p-value using Excel function NORM.S.DIST       
Since this is a 2-sided test, we multiply by 2 to get the p-value       
p-value = 2 * NORM.S.DIST(-1.7982, TRUE)       
                = 0.0721       
p-value = 0.0721       
        
0.0721 > 0.05       
Thus, p-value > α       
Hence we do not reject Ho       
Conclusion :       
There does not exist significant statistical evidence at alpha-0.05 to conclude that       
the mean number of type 2 fibers is different from 21.7