Consider a class survey of 259 students at Queens Academy in

Consider a class survey of 259 students at Queen’s Academy in which students reported studying an average of 350 minutes on a typical weeknight. The sample standard deviation is found to be 67 minutes. Regard these students as an SRS from the population of all first-year students at this school.

Does the study give good evidence that students report studying less than six hours per weeknight on average?

A) Perform a hypothesis test, report the P-value, and state the conclusion (based on the = .01 significance level).

B) Find a 99% confidence interval for the mean amount of time that first-year Queen’s Academy students would report studying on a typical weeknight.

Solution

A.

Formulating the null and alternative hypotheses,          
          
Ho:   u   =   360
Ha:    u   <   360
          
As we can see, this is a    1   tailed test.  
          
Thus, getting the critical z,          
          
zcrit =    -2.326347874      
          
Getting the test statistic, as          
          
X = sample mean =    350      
uo = hypothesized mean =    360      
n = sample size =    259      
s = standard deviation =    67      
          
Thus, z = (X - uo) * sqrt(n) / s =    -2.402011483      
          
Also, the p value is          
          
p =    0.008152598      
          
Comparing z and zcrit (or, p and significance level), we   REJECT THE NULL HYPOTHESIS.      

There is a significant evidence that the students sleep less than six hours per weeknight on average.

**************************

B.

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
              
X = sample mean =    350          
z(alpha/2) = critical z for the confidence interval =    2.575829304          
s = sample standard deviation =    67          
n = sample size =    259          
              
Thus,              
              
Lower bound =    339.2763656          
Upper bound =    360.7236344          
              
Thus, the confidence interval is              
              
(339.2763656   ,   360.7236344) [ANSWER]