Please help and explain how you got to the answer you did Th

Please help and explain how you got to the answer you did. Thank you!!!

Solution

A)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   1545  
Ha:    u   <   1545 [ANSWER, OPTION 7]

************************  
B)

X = sample mean =    1567.833333   [ANSWER]

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

C)

s = standard deviation =    17.96014105   [ANSWER]

********************  
D)                      
              
Getting the test statistic, as              
              
X = sample mean =    1567.833333          
uo = hypothesized mean =    1545          
n = sample size =    6          
s = standard deviation =    17.96014105          
              
Thus, t = (X - uo) * sqrt(n) / s =    3.114118961 [answer, TEST STATISTIC]

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

E)

          
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    5          
tcrit =    -   2.570581836      
              
Also, the p value is              
              
p =    0.01321368          
              
Comparing t and tcrit (P<0.025), we   REJECT THE NULL HYPOTHESIS.          
              
Thus, it is OPTION 3. [ANSWER, REJECT HO, less than 1545]