The records show that the lifetimes of electric bulbs manufactured in the past b

Question

The records show that the lifetimes of electric bulbs manufactured in the past by BIG Corporation have a mean of hours and a variance of . The corporation claims that the current variance, , is less than following some adjustments in its production unit. A random sample of bulbs from the current production lot has a mean lifetime of hours, with a variance of . Assume that the lifetimes of recently manufactured bulbs are approximately normally distributed. Is there enough evidence to conclude, at the level of significance, that the corporation's claim is valid?

The records show that the lifetimes of electric bulbs manufactured in the past by BIG Corporation have a mean of 9690 hours and a variance of 14992 . The corporation claims that the current variance, . is less than 14992 following some adjustments in its production unit. A random sample of 24 bulbs from the current production lot has a mean lifetime of 9684 hours, with a variance of 9182. Assume that the lifetimes of recently manufactured bulbs are approximately normally distributed. Is there enough evidence to conclude, at the 0.05 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. (If necessary consult a list of formulas.) 1 The null hypothesis: . Do The type of test statistic: Choose one) The value of the test statistic: Round to at least three decimal places. The critical value at the 0.05 level of significance: Round to at least three decimal places. Can we support the claim that the current variance of lifetimes o electric bulbs manufactured by them is less than 14992? Clear Undo Undo Help Next >> Explain

Explanation / Answer

The null hypothesis: s2 14992

The alternative hypothesis: s2 < 14992

The type of test statistics: chi-square test

The value of the test statistics: 14.087

(n-1)*(s2/s2) = (24-1)*(9182/14992) = 14.087

The critical value: 35.172

For 23 degrees of freedom at 5% level of significance we get the critical chi-square value from critical chi-square table as 35.172

Can we support the claim: Yes

Here the test statistics is less than the critical value (14.087 < 35.172); we reject the null hypothesis.

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