(2)A lightbulb producing firm wants to determine if it can claim that the lightb

Question

(2)A lightbulb producing firm wants to determine if it can claim that the lightbulbs it produces last 1000 burning hours. Officials of the Quality Control Department of the firm take a sample of 100 lightbulbs from the firm's production line and find that the sample mean and standard deviation are 980 hours and 80 hours respectively. Show how the officials should go about the process of conducting this test at the 5% level of significance (3)A purchaser of electronic components wants to test the hypothesis that they last less than 100 hours. To do this she takes a random sample of 36 such components and finds that, on average, they last 96 hours with a standard deviation of 8 hours. If the purchaser knows that the life time of the components is normally distributed, should she accept the hypothesis that they last less than 100 hours at the 1% level of significance? (4)A producer of steel cables wants to test if the steel cables it produces have a breaking strength of 5000 lb. A breaking strength of less than 5000 lb. would not be adequate and cables with strength of more than 5000 lb. would unnecessarily increase production costs. The producer takes a sample of 64 cables and finds the average breaking strength is 5100 lb. with a standard deviation of 480 lb. Should the producer accept the hypothesis that its steel cable has a breaking strength of 5000 lb at the 1% level of significance? NOTE: We did # (4) in class but we did the test at the 5% level of significance! So try it at the 1% level.

Explanation / Answer

(2) Since here we are planning to determine the claim of the firm that the bulbs last 1000 hrs

now since if the bulb lasts more than 1000 hrs then also it would be alright for the firm so., it becomes a one tail test since below 1000hrs only makes the firm worried while above 1000hrs the firm would be happy

So., Ho: mean =1000hr

and so., H1: mean <1000hrs

now the sample of n= 100 bulbs with sample mean of 980hrs is found and tested for 95% confidence or 5% significance so

Using the equation

Zcal= (X'-mu)/(sd/sqrt(n))

we get Zcal= (980-1000)/(80/sqrt(100)) = -20/8 = -2.5

While from the Z table for 95% confidence level the value of Zck is -1.645 (From z table) and so if the Zcal<Zck we have to reject the Null hypothesis and here -2.5<-1.645 and so we have to reject Ho

So here we can say that the firm cannot claim that the bulb will last for 1000hrs.

As per Chegg policy & time time crunch I won't be able to answer more than 1 Question. So here I have answered all the sub parts of the 1st question. If you want the answers for the rest pls post them seperately. Hope You understand.

Hope the above answer has helped you in understanding the proble. Please upvote the ans if it has really helped you. Good Luck!!

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