Question

A paint manufacturer uses a large amount of titanium dioxide. A new vendor claims that its titanium dioxide has a mean of 25 and a variance of 0.4. The manufacturer doubts this and plans a sample study of n=10 shipments to find out if the variance is more than 0.4 with a =0.05. The sample variance came out to be s2 = 0.9. Assume the population distribution is normal. What is the value of the test statistics and degrees of freedom (df) respectively: O 22.5, df=10 O 20.25, df=9 O 0.0324, df=9 O 0.036, df=10

Answer 1

From provided information,

n = 10

= 0.9

2 S

$\sigma ^{2}$ = 0.4

We want to test the following hypothesis

Ho : $\sigma ^{2} = 0.4$

Ha : $\sigma ^{2} > 0.4$   

Test statistic = $\frac{(n-1)*s^{2}}{\sigma ^{2} }$

Test statistic = (9 * 0.9)/0.4

Test statistic = 20.25

DF = (n- 1) = 9

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