Question

An industrial company claims that the mean pH level of the water in a nearby river if 6.8, but you suspect that this in incorrect. You randomly select 19 water samples and find that the Ph level of these 19 samples has a mean of 6.7 with a standard deviation of .24.

a) Find the value of the test statistic = [Round to 3 decimals]

b) Find the p-value [round to 3 decimals]

c) If the level of significance was 5%, what would your decision be?

Answer 1

Solution :

This is the two tailed test,  

The null and alternative hypothesis is ,

H0 :   = 6.8

Ha :    6.8

a) Test statistic = t =

= ( - ) / s / n

= (6.7 - 6.8) / 0.24 / 19

Test statistic = t = -1.816

b) degrees of freedom = n - 1 = 1 9 - 1 = 18

P(Z < -1.816 ) = 0.043

P-value = 2 * P(Z < -1.816 )

P-value = 2 * 0.043

P-value = 0.086

c) = 0.05  

P-value >

Fail to reject the null hypothesis