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 :-

χ^{2} = ( ( 19-1 ) * 4.41 ) / 2.56

**χ ^{2} = 31.0078**

Part b)

**P value = P ( χ ^{2} > 31.0078 ) =
0.0287**

Looking for the value χ^{2} = 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.**

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