Question

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Question
Message posted by Joy Ndem on November 2, 2000 at 12:00 AM (ET)

A large famly-held department store selling furniture and flooring, including carpeting, had undergone a major expansion in the past several years. In particular, the flooring department had expanded from two installation crews to an installation supervisor, a measurer, and 15 installation crews. A sample of 50 complaints in a recent year concerning carpeting installation was selected. The following data (attached) represent the number of days between the receipt of the complaint and the resolution of the complaint.

(a) At the .05 level of significance, is there evidence that the average number of days between the receipt of the complaint and the resolution of the complaint is greater than 20?
(b) What assumption must hold in order to perform the test in (a)?

54 5 35 137 31 27 152 2 123 81 74 27 11 19
29 61 35 94 31 26 5 12 4 165 32 29 28 29
14 13 13 10 5 27 4 52 30 22 36 26 20 23
Can you help.
Thanks.

READERS RESPOND:
(In chronological order. Most recent at the bottom.)

Re: Question
Message posted by Nancy Diehl on November 3, 2000 at 12:00 AM (ET)

First of all, the wording to your question falls into the subject area of Hypothesis Testing.
The question refers testing if the sample average supports a hypothesis that it follows
a distribution with a mean greater than 20. In order to test this hypothesis the assumption that
is made is that the data follows a normal distribution. You really should do a stem and leaf
to see what the distribution looks like. It's clearly not normal, it's in fact more exponential
in shape or severly skewed to the right. Hence, to perform a hypothesis based on a
normal distribution would be inaccurate. Another tell-tale sign is that the sample average
is 39.4 (by the way, there were only 42 samples, not 50) and the standard deviation is 40.3.
A clue to an exponential distribution is when you see the average and standard deviation
are of the same value, which is suggested here with your data.

Re: Question
Message posted by JG on November 3, 2000 at 12:00 AM (ET)

How was the data collected and is your sample 'random' ? Is the data sequential in time ?

Re: Question
Message posted by SOF on November 3, 2000 at 12:00 AM (ET)

Do you have an M/M/1 queing problem ? Do some complaints take a long time to resolve because they are 'waiting in line' for their turn ? Try constructing a box-and-whiskers plot for your data.

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