Question

Records show that the lifetimes of batteries manufactured by a certain company have a mean of 620 hours and a standard deviation of 136. The company advertises that, currently, the standard deviation is less than 136, following some adjustments in production practices. A random sample of 23 recently produced batteries from this company had a mean lifetime of 618 hours and a standard deviation of 96. Is there enough evidence to conclude, at the 0.05 level of significance, that the company's claim is correct? Assume that the lifetimes of this company's recently produced batteries are approximately normally distributed 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 o P The null hypothesis: s ce X The alternative hypothesis: (Choose one ✓ Chi sunce OSO The type of test statistic: DO egrees freedom: DO D<0 DO The value of the test statistic: (Round to at least three decimal places.) 0 X ? 0 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 standard deviation of lifetimes of batteries manufactured by them is less than 1367 Yes No

Answer 1

Given :

n = 23

$\sigma$ = 136

s = 96

Claim : The company advertises that, currently, the standard deviation is less than 136.

Hypothesis test :

The null and alternative hypothesis is

Ho : $\sigma$ = 136

Ha : $\sigma$ < 136

The type of test statistic is Chi-square. Degree f freedom = df = n-1 = 23-1 = 22 Test statistic X? = (n-1)s ( 23-1)(96)2 2 - 10.962 2 18496 a x = 10.962 *? critical value at 0.05 significance level; x critical = 12.338 Dicision Rule: 2212.338 Reject Ho, if a (12.338, we reject since x² Ho,

Yes, we support the claim that the current standard deviation of lifetimes of batteries manufactured by them is less than 136.