Question

Question 7 A production line produces three layer masks witha mean weight of 20 grams and a standard devlation of 040 grams. Anew process supposedly will produce the same type of masks with the same mean and asmaller standard deviation. Asample of 41 masks produced by the new method has a sample standard deviation of 0.30 grams. At a signinicance level of 5%, what can we conclude?

O The variance has not declined because the observed varlance is not less than0211(Criticalvalue

O The variance has declined because the observed varlance is less than 0.224 (Critical value

O The variance has declined because the observed variance isless than 0.211 (Critical value

O The variance has declined because the observed var leshan 0417(Criticar valuel

O The variance has not declined because the observed variances not less than 5%Citical value

O The variance has declined becsuse the obsen wriance is less than 0.106 (Criticavalue!

O The variance has not declined because the observed variance more than0 116Cical valuel

a The comrect answer is not listed

Answer 1

σ = 0.4, s = 0.3, n = 41

Level of significance = 0.05, Degrees of freedom: df = n-1 = 40

H₀: σ = 0.4, H₁: σ < 0.4

Test statistic (Observed variance) = (n−1)(s/σ)² = 40*(0.3/0.4)^2 = 22.5

Critical value (Using Excel function CHISQ.INV(probability,df)) = CHISQ.INV(0.05,40) = 26.51

Since test statistic is less than critical value, we do not reject the null hypothesis.

The variance has not declined because the observed variances is less than 5% Critical value.

The correct answer is not listed.