It says I got the wrong answers but doesnt specify which one

It says I got the wrong answers but doesn\'t specify which ones. Can someone please help me out.

Consider the following hypothesis test: Ho: 45 Ha: 45 A sample of 36 is used. Identify the p-value and state your conclusion for each of the following sample results. Use a a. With C-44 and s-5.2, the p-value is between.005 and.01 Can it be concluded that the population mean is less than 45? t be condluded that the No b. with 43 and s = 4.6, the p-value is between .005 and.01 Can it be concluded that the population mean is less than 45? c. With T-46 and s-5.0, the p-value is greater than .20 Can it be concluded that the popluation mean is less than 45? t be condluded that the No

Solution

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   45  
Ha:    u   <   45  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha =    0.01          
zcrit =    -   2.326347874      
              
Getting the test statistic, as              
              
X = sample mean =    44          
uo = hypothesized mean =    45          
n = sample size =    36          
s = standard deviation =    5.2          
              
Thus, z = (X - uo) * sqrt(n) / s =    -1.153846154          
              
Also, the p value is, using a table/technology,

p =    0.124281624

Thus,              
              
P IS GREATER THAN 0.10. [ANSWER]

Thus, NO, it cannot be concluded that the population mean is less than 45. [ANSWER]

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b)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   45  
Ha:    u   <   45  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha =    0.01          
zcrit =    -   2.326347874      
              
Getting the test statistic, as              
              
X = sample mean =    43          
uo = hypothesized mean =    45          
n = sample size =    36          
s = standard deviation =    4.6          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.608695652          
              
Also, the p value is              
              
p =    0.004544402          

Thus,              
              
P IS LESS THAN 0.005. [ANSWER]

Thus, YES, it can be concluded that the population mean is less than 45. [ANSWER]

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c)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   45  
Ha:    u   <   45  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha =    0.01          
zcrit =    -   2.326347874      
              
Getting the test statistic, as              
              
X = sample mean =    46          
uo = hypothesized mean =    45          
n = sample size =    36          
s = standard deviation =    5          
              
Thus, z = (X - uo) * sqrt(n) / s =    1.2          
              
Also, the p value is              
              
p =    0.88493033

Thus, the P value is VERY BIG (please choose the option with the largest P value). [ANSWER]

Thus, NO, it cannot be concluded that the population mean is less than 45. [ANSWER]

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