A sample of 50 items is selected to determine whether or not

A sample of 50 items is selected to determine whether or not to accept the hypothesis that a population means differs from a value of 20. The sample mean and standard deviation are 18 and 7, respectively. The null hypothesis is not rejected, which of the following is a possible value for the level of significance associated with this test?

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   20  
Ha:    u   =/   20  
              
As we can see, this is a    two   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    18          
uo = hypothesized mean =    20          
n = sample size =    50          
s = standard deviation =    7          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.020305089          
              
Also, the p value is              
              
p =    0.043351751          
              
Thus, if Ho is not rejected, then alpha < 0.0433.

Thus, alpha could be anything under 0.0433. For example, 0.005, 0.01, 0.025, etc. [ANSWER]