SOLUTION: In a survey, 10 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $36 and standard deviation of $4. Fin

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Question 1200322: In a survey, 10 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $36 and standard deviation of $4. Find the margin of error at a 95% confidence level.
Give your answer to three decimal places.
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: 2.479

Explanation:

At 95% confidence, the z critical value is roughly z = 1.960
Use a calculator with built in stats functions (eg: TI84) or a reference table to determine this value.

Here is one such table
https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf
Scroll to the bottom to locate 1.960, which is one cell above the "95% confidence level".

The margin of error formula for the mean is
E = z*sigma/sqrt(n)
where,
  • z = critical value mentioned earlier = 1.960
  • sigma = standard deviation = 4
  • n = sample size = 10
Take note that the mean isn't involved with the margin of error formula.

So,
E = z*sigma/sqrt(n)
E = 1.960*4/sqrt(10)
E = 2.479225685572
E = 2.479