A sample of 77 measurments, randomly selected from a normally distributed population, resulted in a sample mean, x¯=5.2 and sample standard deviation ?=1.05. Using ?=0.01, test the null hypothesis that the mean of the population is 5.1 against the alternative hypothesis that the mean of the population, ?<5.1 by giving the following: (a)    the degree of freedom :    (b)    the critical ? value :    (c)    the test statistic :

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A sample of 77 measurments, randomly selected from a normally distributed population, resulted in a sample mean, x¯=5.2 and sample standard deviation ?=1.05. Using ?=0.01, test the null hypothesis that the mean of the population is 5.1 against the alternative hypothesis that the mean of the population, ?<5.1 by giving the following:
(a)    the degree of freedom :   
(b)    the critical ? value :   
(c)    the test statistic :  

 

The final conclustion is


A. We can reject the null hypothesis that ?=5.1 and accept that ?<5.1.
B. There is not sufficient evidence to reject the null hypothesis that ?=5.1.

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