Confidence intervals review. It is known that monthly spending by individuals in a community is normally distributed. To estimate the average monthly spending, a statistician asked 4 people randomly about their monthly spending. The following are the number of dollars these for spent in April: 480, 510, 501, 505. With 98% confidence, over what interval doesthe mean of people's monthly spending lie?

sdentatoiz

sdentatoiz

Answered question

2022-09-09

Confidence intervals review
It is known that monthly spending by individuals in a community is normally distributed. To estimate the average monthly spending, a statistician asked 4 people randomly about their monthly spending. The following are the number of dollars these for spent in April: 480, 510, 501, 505. With 98% confidence, over what interval doesthe mean of people's monthly spending lie?

Answer & Explanation

incibracy5x

incibracy5x

Beginner2022-09-10Added 21 answers

Step 1
Use a t-test. Compute a solution c of the equation
F ( c ) = 1 2 ( 1 + 0.98 )
where F(c) is the distribution function of the Student's t-distribution (use a table to solve this equation), and compute the sample std. deviation s and the sample mean x.
Step 2
The required confidence interval is simply
( x s c n , x + s c n )
where n is the number of samples; here n = 4

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