Question

The manufacturer of a certain brand of auto batteries claims that the mean life of these batteries is 45 months. A consumer protection agency that wants to check this claim took a random sample of 24 such batteries and found that the mean life for this sample is 43.05 months. The lives of all such batteries have a population standard deviation of 4.5 months. Perform a hypothesis test at 10% significance level and state your decision using critical value approach.

Answer key: Can’t be tested using z table as population distribution is not known, so we can’t assume sampling distribution is normal as n<30. Hence z-table can’t be used.

So, the math can't be solved by critical value approach? can it be solved by P-value approach? if so, please show with figure and decision process.

Answer 1

Slu Given M=45 months ł = = 43.05 month mean à Ho: M=45 Sample Size n=25 o= 4.5 (Sample against HAM#45 Since na 30 so ux small test semple t-test for single mean test statistic is ă-m st re ta n-) u 43.05 -45 vt =-2.1667 25-1 4.5/525 It l = 2.1667 with (254) Critical value at loy. t so 0.10, 24 0,21 Ho t is 1-3178 df =24 we reject Since It I 7 ie HAM #45 accept Ha. .: M 745 = 0.040383 Ž 0.0404 result is Sunce significant ie we reject to accept ha - mean life q batteries is not 45 p value the P coolo

P-value=0.0404 =4 = 2 3 + data-แ3 tel.3178 t-1.3178