A sample of 50 observations results in a sample mean of 221

A sample of 50 observations results in a sample mean of 221. the population standard deviation is known to be 47.b.  Does the above sample evidence enable to conclude that the population mean is greater than 200 with a 5% significance level? conduct the test based on the critical value appoach. c. Does the above sample evidence enable to conclude that the population mean is greater than 200 with a 5% significance level? Conduct the test based on the p-value approach. d. Does the above sample evidence enable to conclude that the population mean is greater than 200 with a 10% significance level? Conduct the test based on the p-value approach. e. Does the above sample evidence enable to conclude that the population mean is different from 200 with a 5% significance level? Conduct the test based on the p-value approach.

Solution

b)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   200  
Ha:    u   >   200  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    +   1.644853627      
              
Getting the test statistic, as              
              
X = sample mean =    221          
uo = hypothesized mean =    200          
n = sample size =    50          
s = standard deviation =    47          
              
Thus, z = (X - uo) * sqrt(n) / s =    3.159413278          
As |z| > 1.6449, then we REJECT THE NULL HYPOTHESIS.

Thus, there is sufficient evidence to enable us to conclude that the population mean is greater than 200 with a 5% significance level. [CONCLUSION]

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c)

              
Also, the p value is              
              
p =    0.000790436          

As P < 0.05, WE REJECT HO.

Thus, there is sufficient evidence to enable us to conclude that the population mean is greater than 200 with a 5% significance level. [CONCLUSION]

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D)

As P < 0.10, WE REJECT HO.

Thus, there is sufficient evidence to enable us to conclude that the population mean is greater than 200 with a 10% significance level. [CONCLUSION]

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e)

As

p = 0.000790436*2 = 0.001580872 < 0.05, we reject Ho.

Thus, there is sufficient evidence to enable us to conclude that the population mean is different from 200 with a 5% significance level. [CONCLUSION]