in a survey, 16 people were asked how much they spent on their child's last birthday gift. the results were roughly bell-shaped with a mean of $32 and standard deviation of $7. find the margin of error at a 95% confidence level.

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20-12-2022
Mathematics

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in a survey, 16 people were asked how much they spent on their child's last birthday gift. the results were roughly bell-shaped with a mean of $32 and standard deviation of $7. find the margin of error at a 95% confidence level.

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debjitbhowal4568 debjitbhowal4568 · Answer 1 · 2022-12-25T00:23:23-05:00

The margin of error is (31.15, 32.85).

The margin of Error is a statistical expression that is used to determine the percentage point by which the result arrived will differ from the value of the entire population, and it is calculated by dividing the standard deviation of the population by the sample size and lastly multiplying the resultant with the critical factor. A higher error indicates a high chance that the result of the sample reported may not be the true reflection of the whole population. The formula for the margin of error is calculated by multiplying a critical factor (for a certain confidence level) with the population standard deviation. Then the result is divided by the square root of the number of observations in the sample.

Mathematically, it is represented as,

Margin of Error = Z * ơ / √n

Given:

Number of people = n = 16

Mean = μ = $32

Standard deviation = σ = $7

Confidence level = 95%

Thus, the z value would be 1.96.

The confidence interval can be calculated as follows:

Confidence interval = μ ± z(σ/√n)

= 32 ± 1.96 × (7/16)

= 32 ± 0.85

= (31.15, 32.85)

Thus, the margin of error is (31.15, 32.85).

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