The owner of a small business thinks that his long-distance phone bill is approx

Question

The owner of a small business thinks that his long-distance phone bill is approximately the same each month of the year. He keeps his phone bills for the year and discovers that he spent $159 in January, $133 in February, $162 in March, $155 in April, $155 in May, $144 in June, $161 in July, $119 in August, $132 in September, $140 in October, $151 in November, and $122 in December. He wonders if this evidence contradicts his belief in a uniform distribution of phone bills across the months of the year.

Explanation / Answer

from above data we can assume that bill amounts are independent as well for chi square test expected value in cell >5

hence from above applying chi square test on above:

for above chi stat =17.428

degree of freedom =n-1=11

p value=0.0958

as p vlaue is less then 0.05 , we can not reject null hypothesis that bill amount is approx. uniform throughout the year.

observed Expected Chi square category Probability O E=total*p =(O-E)^2/E Jan 1/12 159.00 144.42 1.47 Feb 1/12 133.00 144.42 0.90 Mar 1/12 162.00 144.42 2.14 Apr 1/12 155.00 144.42 0.78 May 1/12 155.00 144.42 0.78 Jun 1/12 144.00 144.42 0.00 Jul 1/12 161.00 144.42 1.90 Aug 1/12 119.00 144.42 4.47 Sep 1/12 132.00 144.42 1.07 Oct 1/12 140.00 144.42 0.14 Nov 1/12 151.00 144.42 0.30 Dec 1/12 122.00 144.42 3.48 1733 1733 17.428

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