A software company allows their programmers to work from hom

A software company allows their programmers to work from home an average of 20 hours per week. A department of from home with a standard deviation of 5.6 hours At alpha = 0.05 is their sufficient evidence to conclude a difference consider the number of hours working from home t = 1.38; The null hypothesis is rejected There is enough evidence to support the claim that programmers work 20 hours per week from home 18.9

Solution

6.

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   20  
Ha:    u   =/   20  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    14          
tcrit =    +/-   2.144786688      
              
Getting the test statistic, as              
              
X = sample mean =    22          
uo = hypothesized mean =    20          
n = sample size =    15          
s = standard deviation =    5.6          

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Thus, t = (X - uo) * sqrt(n) / s =    1.383208338                  
As t < 2.144, re do not rejct the null hypothesis.

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Note that              
Margin of Error E = t(alpha/2) * s / sqrt(n)              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    22          
t(alpha/2) = critical t for the confidence interval =    2.144786688          
s = sample standard deviation =    5.6          
n = sample size =    15          
df = n - 1 =    14          
Thus,              
Margin of Error E =    3.101176633          
Lower bound =    18.89882337          
Upper bound =    25.10117663          
              
Thus, the confidence interval is              
              
(   18.9   ,   25.1   )

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Combining these, the answer is OPTION D. [ANSWER D]