Please show your work stepbystep 39 Consider the following h

Please show your work step-by-step.

39. Consider the following hypothesis test. H0: mu = 17 Ha: mu neq 17 A sample of 25 gives a sample mean of 14.2 and sample variance of 25. a) At a = 0.05, what is the rejection rule? b) Compute the value of the test statistic c) What is the p-value? d) What is your conclusion?

Solution

Formulating the null and alternative hypotheses,          
          
Ho:   u   =   17
Ha:    u   =/=   17
          
As we can see, this is a    2   tailed test.  
          
Thus, getting the critical t,          
df = n - 1 =    24      
tcrit =    2.063898562      

Thus, the rejection rule is when t < -2.064 or t > 2.064. [ANSWER]

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Getting the test statistic, as          
          
X = sample mean =    14.2      
uo = hypothesized mean =    17      
n = sample size =    25      
s = standard deviation =    5      
          
Thus, t = (X - uo) * sqrt(n) / s =    -2.8   [ANSWER, PART B]

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Also, the p value is, by technology,      
          
p =    0.009929181   [part c]

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Comparing t and tcrit (or, p and significance level), we   REJECT THE NULL HYPOTHESIS.

There is significant evidence that u=/= 17. [PART D]