Question

The records show that the lifetimes of electric bulbs manufactured in the past by BIG Corporation have a mean of 8840 hours and a variance of 15783. The corporation claims that the current variance, c?, is less than 15783 following some adjustments in its production unit. A random sample of 31 bulbs from the current production lot has a mean lifetime of 8842 hours, with a variance of 11977. Assume that the lifetimes of recently manufactured bulbs are approximately normally distributed. Is there enough evidence to conclude, at the 0.1 level of significance, that the corporation's claim is valid? Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. р 0 р The null hypothesis: x S ca The alternative hypothesis: old O-O OSDOO The type of test statistic: (Choose one) The value of the test statistic: (Round to at least three decimal places.) 0 x 5 2 The p-value Save For Later Submit Assignment Check

Answer 1

Answer:

Given,

Ho : $\sigma ^{2}$ = 15783

H1 : $\sigma ^{2}$ < 15783

Here it is a one tailed chi square test

sample n = 31

degree of freedom = n - 1 = 31 - 1 = 30

test statistic $\chi ^{2}$ = (n-1)*s^2/$\sigma ^{2}$

substitute values

= (31-1)*11977/15783

= 22.766

P value = 0.824756

= 0.8248

Here we observe that, p value > alpha, so we fail to reject Ho.

So there is no sufficient evidence to support the claim.