Question

To test H0: σ=2.2 versus H1: σ>2.2, a random sample of size n=15 is obtained from a population that is known to be normally distributed. Complete parts (a) through (d).

(a) If the sample standard deviation is determined to be s=2.3, compute the test statistic.

χ^2_0=____

(Round to three decimal places as needed.)

(b) If the researcher decides to test this hypothesis at the α=0.01 level of significance, determine the critical value.

χ^2_0.01=____

(Round to three decimal places as needed.)

(c) Draw a chi-square distribution and depict the critical region.

(d) Will the researcher reject the null hypothesis?

(1)Reject H0 because χ^2_0 < χ^2_0.01.

(2) Do not reject H0 because χ^2_0 < χ^2_0.01.

(3) Reject H0 because χ^2_0 > χ^2_0.01.

(4) Do not reject H0 because χ^2_0 > χ^2_0.01.

Answer #1

The statistical software output for this problem is:

Hence,

a) =
**15.302**

b) Critical value = **29.141**

c) Critical region:

d) Do not reject H0 because χ^2_0 < χ^2_0.01

**Option 2** is correct.

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