Question

To test Upper H 0 : sigma equals 1.6 versus Upper H 1 : sigma greater than 1.6​, a random sample of size n equals 19 is obtained from a population that is known to be normally distributed.

​(a) If the sample standard deviation is determined to be s equals 2.1​, compute the test statistic.

​(b) If the researcher decides to test this hypothesis at the alpha equals 0.01 level of​ significance, use technology to determine the​ P-value. ​

(c) Will the researcher reject the null​ hypothesis?

Answer 1

Part a)

Test Statistic :-

χ² = ( ( 19-1 ) * 4.41 ) / 2.56
χ² = 31.0078

Part b)

P value = P ( χ² > 31.0078 ) = 0.0287

Looking for the value  χ² = 31.0078 in chi square table across n - 1 = 19 - 1 = 18 degree of freedom.

Part c)

Reject null hypothesis if P value < α = 0.01
Since P value = 0.0287 > 0.01, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

P value is greater than α = 0.01, researcher Fail to Reject null hypothesis.