Alyson Silvastein a scientist reports that the average numbe

Alyson Silvastein, a scientist, reports that the average number of hours a person can go without sleep and still function normally is 29. Bob Jones claims that the average number is actually higher than 29 hours. He takes a random sample of 49 people and finds that the average is 31 hours that they could go without sleep and still function normally. Suppose it is known the standard deviation of the number of hours of sleep is 5 hours. What is the test value for the test of Bob claim?

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   29  
Ha:    u   >   29  
              
As we can see, this is a    right   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    31          
uo = hypothesized mean =    29          
n = sample size =    49          
s = standard deviation =    5          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.8   [ANSWER]