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.