Consider the following hypothesis test A sample of 50 provid

Consider the following hypothesis test: A sample of 50 provided a sample mean of 14.15. The population standard deviation is 3. Compute the value of the test statistic (to 2 decimals). What is the p-value (to 4 decimals)? Using alpha =.05, can it be concluded that the population mean is not equal to 15? Using alpha =.05, what are the critical values for the test statistic? (to 2 decimals) (+ or -) State the rejection rule: Reject H_0 if z is - Select your answer - the lower critical value and the upper critical value. Can it be concluded that the population mean is not equal to 15?

Solution

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   15  
Ha:    u   =/   15  
              
As we can see, this is a    two   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    14.15          
uo = hypothesized mean =    15          
n = sample size =    50          
s = standard deviation =    3          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.003469213 [ANSWER]

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B)

Also, the p value is              
              
p =    0.045126949   [answer]

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C)      
              
As P < 0.05, YES, we can conclude that the populaiton mean is not equal to 15. [ANSWER, YES]

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d)

At 0.05 level, the critical values are

z = +/- 1.96 [ANSWER]

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e)

Reject Ho if z is LESS THAN the lower critical value and GREATER THAN the upper critical value.

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f)

YES, becasue zstat < -1.96. [ANSWER]