A random sample of 12 secondyear university students enrolle

A random sample of 12 second-year university students enrolled in a business statistics course was drawn. At the course\'s completion, each student was asked how many hours he or she spent doing homework in statistics. The data are listed below.

20, 29, 28, 22, 26, 22, 22, 18, 23, 21, 20, 27
It is known that the population standard deviation is 7. The instructor has recommended that students devote 2 hours per week for the duration of the 12-week semester, for a total of 24 hours. Test to determine whether there is evidence at the 0.07 significance level that the average student spent less than the recommended amount of time. Fill in the requested information below.

A. The value of the standardized test statistic:
-0.4107

Note: For the next part, your answer should use interval notation. An answer of the form (,a) is expressed (-infty, a), an answer of the form (b,) is expressed (b, infty), and an answer of the form (,a)(b,) is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:
(-infty,-2.0067)U(2.0067, infty)

C. The p-value is
0.6892

D. Your decision for the hypothesis test:

A. Reject H0.
B. Do Not Reject H1.
C. Do Not Reject H0.
D. Reject H1.

I have included my values but they are marked wrong, please help.

Solution

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   24  
Ha:    u   <   24  
              
As we can see, this is a    left   tailed test.      
Getting the test statistic, as              
              
X = sample mean =    23.16666667          
uo = hypothesized mean =    24          
n = sample size =    12          
s = standard deviation =    3.511884584          
              
Thus, t = (X - uo) * sqrt(n) / s =    -0.821994937   [ANSWER, TEST STATISTIC]

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b)

As we can see, this is a    left   tailed test.  
              
Thus, getting the critical t,              
df = n - 1 =    11          
tcrit =    -   1.590630579      
              
Thus, the rejection region is (-infty, -1.5906). [ANSWER]

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c)      
              
Also, the p value is, as df = 11              
              
p =    0.214268751   [ANSWER]

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d)

As P > 0.07, we DO NOT REJECT HO. [ANSWER, C]

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