The annual incomes of a random sample of 10 individuals in a certain city are given...

The annual incomes of a random sample of 10 individuals in a certain city are given below. Construct at 95% confidence interval for the average yearly income of individuals in this city.

65100, 52400, 32000, 33300, 72200, 39700, 39400, 42800, 54300, 68200,

Solutions

Expert Solution

the necessary calculation table :-

income (x)	x²
65100	4238010000
52400	2745760000
32000	1024000000
33300	1108890000
72200	5212840000
39700	1576090000
39400	1552360000
42800	1831840000
54300	2948490000
68200	4651240000
sum=499400	sum=26889520000

sample size (n) = 10

[ for these values you can directly use any software or excel or your calculator ..i am just showing all calculations for your clarification]

degrees of freedom = (n-1) = (10-1) = 9

t critical value for alpha=0.05,df = 9, both tailed test be:-

[ using t distribution table ]

the 95% confidence interval for the average yearly income of individuals in this city is :-

* as nothing is mentioned i have rounded off the final answer to nearest whole number .

interpretation:-

we are 95% confident that the average yearly income of individuals in this city will be between 39412 and 60468.

*** if you have any doubt regarding the problem please write it in the comment box.if you are satisfied please give me a LIKE if possible...

orchestra answered 1 year ago

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