A machine that puts corn flakes into boxes is adjusted to pu

A machine that puts corn flakes into boxes is adjusted to put an average of 15.9 ounces into each box, with standard deviation of 0.23 ounce. If a random sample of 12 boxes gave a sample standard deviation of 0.39 ounce, do these data support the claim that the variance has increased and the machine needs to be brought back into adjustment? (Use a 0.01 level of significance.)

State the null and alternate hypotheses.

H₀: ² = 0.0529; H₁: ² 0.0529

H₀: ²= 0.0529; H₁: ²< 0.0529   

H₀: ² = 0.0529; H₁: ² > 0.0529

H₀: ² < 0.0529; H₁: ² = 0.0529

(ii) Find the sample test statistic. (Round your answer to two decimal places.)


(iii) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

Solution

Ho: o^2=0.0529
Ha: o^2 > 0.0529
The test statistic is
Chisquare =(n-1)*s^2/o^2
=12*0.1521/0.0529
^2 test statistic = 34.503
^2 p_value = EXCEL FORMULA = ROUND(CHIDIST(34.503,11),4) = 0.0003