Question

I have no idea how to solve these types of problems. Can anyone help me out?

If n=20,

μ=15,

=20 and S=10, to do a one-sided hypothesis test

with significance level,

α=1%,

you will read a t-value table of:

Answer 1

n = 20          Sample Size       
x̅ = 20           Sample Mean       
s = 10           Sample Standard Deviation       
μ = 15           Population Mean       
α = 0.01        1% level of significance       
        
We have to do a one-sided hypothesis test        
Since sample mean is greater than population mean, we do the one-sided right tailed test        
        
One sided right tailed test        
The null and alternative hypotheses are         
Ho : μ = 15        
Ha : μ > 15             (Right sided test)       
        
Test statistic t is given by         
        
            
        
test statistic t = 2.2361        
        
df = Degrees of freedom = n - 1 = 20 -1 = 19        
We find the p-value using Excel function T.DIST (t, df, TRUE)     
p-value = 1 - T.DIST(2.2361, 19, TRUE)        
p-value = 0.0188        
        
Since 0.0188 > 0.01        
that is p-value > α        
Hence we do not reject Ho        
Decision :        
Fail to reject Ho        
        
Conclusion        
There is not enough statistical evidence to conclude that         
the population mean is greater than 15