Calculat test statistics find the critical values of X2 and

Calculat test statistics find the critical values of X2 and use a X2 distribution table to find the limits containing the P-value. Determine whether there is sufficient evidence to support the given alternative hypothesis

test H0: o=14 versus H1:o< 14 given that a=0.025 n= 16 and s =10 compute the test statistic

X2=

find critical values=

is there sufficient evidence to support the alternative hypothesis

a.No because the test statistic is within the critical region and the P-value is less than or equal to the leval of signicance

b. Yes because the test statistic is within the critical region and the P-value is less than or equal to the level of significance

c. No because the test statistic is outside the critical region and the P-value is greater than the level of significance

d. Yes because the test statistic is outside the critical region and the P-value is greater than the level of significance

Solution

test statistic

X2= (n-1)*s^2/o^2

=(16-1)*10^2/14^2

=7.65

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It is a left-tailed test.

The degree of freedom =n-1=16-1=15

Given a=0.025, the critical value of X^2 with 0.025 and df=15 is 6.26 (from chisqure table)

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c. No because the test statistic is outside the critical region and the P-value is greater than the level of significance