1. The quality-control manager at a lightbulb factor needs to determine whether
ID: 3179958 • Letter: 1
Question
1. The quality-control manager at a lightbulb factor needs to determine whether the mean life of a large shipment of lightbulbs is equal to 375 hours. The population standard deviation is 100 hours. A random sample of 64 lightbulbs indicates a sample mean life of 350 hours. a. At the 0.05 level of significance is there evidence that the mean life is different from 375 hours? b. Compute the p-value and interpret its meaning. c. Construct a 95% confidence interval estimate of the population mean life of the lightbulbs.
Explanation / Answer
H0 : = 375
H1 : 375 (claim)
= 0.05 (significance level)
/2= 0.025(two-tailed)
A. Since the key word "different" is the question, then this is a two-tailed test. Therefore, divide 0.05 by 2 = .025(per tail). We find the critical values by going to the z-score tables for normal distribution.
Notice that the area= .025 corresponds to z-scores(critical values)= ±1.96.
To calculate test-statistic manually: (350-375)/(120/64) =-25/15= -1.66 .
Since the test-statistic does not land within the critical values region, then we can conclude at a 0.05 significance level that there is not sufficient evidence to support the claim that the mean life is different from 375 hours.
B. Using Graphing calculator TI-83: go to STATS, TESTS, Z-Test, Stats, 0:375, :120, x:350, n:64, : 0, CALCULATE. p-value=.096 which is greater than =0.05.
Therefore we support the null hypothesis(H0)and reject the claim of the alternative hypothesis(H1).
C .Using graphing calculator TI-83: STATS, TESTS,7ZInterval...,Stats, :120, x:350, n:64, C-Level:.95, Calculate= (320.6, 379.4)
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