Software can generate samples from almost exactly Normal dis

Software can generate samples from (almost) exactly Normal distributions. Here is a random sample of size 5 from the Normal distribution with mean 10 and standard deviation 2.

6.49      7.52      10.20      13.61      9.93     

These data match the conditions for a z test better than real data will: the population is very close to Normal and has known standard deviation = 2, and the population mean is = 10. Although we know the true value of , suppose we pretend that we do not and we test the following hypotheses.

H₀: = 8

H_a: 8

(a) What is the z statistic? (Round your answer to two decimal places.)
z =

(b) What is the P-value? (Round your answer to four decimal places.)
P-value =

Solution

A)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   8  
Ha:    u   =/   8  
              
As we can see, this is a    two   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    10          
uo = hypothesized mean =    8          
n = sample size =    5          
s = standard deviation =    2          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.236067977 [ANSWER]          

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B)
              
Also, the p value is,as it is two tailed,              
              
p =    0.025347319   [ANSWER]