Question

Plastic sheets produced by a machine are periodically monitored for possible fluctuations in thickness. If the true variance in thicknesses exceeds 24 square millimeters, there is cause for concern about product quality. Thickness measurements for a random sample of 10 sheets produced in a particular shift were taken, giving the following results (in millimeters):
96 35 180 54 50 228 225 228 229 230
Quality department claims that there is no concern about product quality. Based on this information;
a) State your hypothesis H0 and H1.
b) State the decision rule (exactly as in the book), sample statistics, table value and test statistic (with the exact formula) in the same order as in the extra-solved examples on hypothesis testing.
c) Test, at the 10% significance level, the null hypothesis that there is no concern about product quality

Answer 1

Solution-A:

Ho: sigma^2=24

Ha:sigma^2>24

Right tail test

For the given sample

standard deviation=

test statistic

chi sq=(n-1)*s^2/sigma^2

=(10-1)* 7376.5/24

= 2766.188

crititcal chisq for alpha=0.10 and df=9

=CHISQ.INV.RT(0.1,9)

14.68365657

decision rule

if chi sq test statistic>critical chi sq(14.68365657) reject Ho

and if chi sq test statistic<critical chi sq(14.68365657),fail to reject Ho

test statistic >critical chi sq value

reject Ho

Accept Ha