Question

To test H0 : σ=2.9 versus H1 : σ≠2.9​, a random sample of size n=21 is obtained from a population that is known to be normally distributed.

​(a) If the sample standard deviation is determined to be s=2.6​, 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=0.05 level of​ significance, determine the critical values.The critical values are

χ^2_0.025=____ and χ^2_0.975=____.

​(Round to three decimal places as​ needed.)

​(c) Draw a​ chi-squared distribution and depict the critical region. Choose the correct graph below.

​(d) Will the researcher reject the null​ hypothesis? Why? Choose the correct answer below.

A. Yes​, because the test statistic is not in the critical region.

B. Yes​, because the test statistic is in the critical region.

C. No​, because the test statistic is not in the critical region.

D. No​, because the test statistic is in the critical region.

Answer 1

a)

Sample standard deviation=2.6
          
Population standard deviation=2.9
          
Sample size=21  
Degree of freedom =n-1=   20
Chi square test statistic formula is       

  
          
= 16.076

(b) and

bu using Excel command =CHIINV(1-(0.05/2),20) and =CHIINV((0.05/2),20)

(c)

(d) C. No​, because the test statistic is not in the critical region.