In a survey, 12 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $45 and standard deviation of $5. Find the margin of error at a 98% confidence level.

Question

24-12-2023
Mathematics

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In a survey, 12 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $45 and standard deviation of $5. Find the margin of error at a 98% confidence level.

Answer :

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alphagorrilla alphagorrilla · Answer 1 · 2023-12-24T13:55:27-05:00

Answer:

To find the margin of error at a 98% confidence level, we can use the formula:

Margin of Error = Critical Value * Standard Deviation

1. Find the critical value: Since the confidence level is 98%, we need to find the z-score corresponding to that confidence level. The z-score can be found using a z-table or a statistical calculator. For a 98% confidence level, the critical value (z-score) is approximately 2.33.

2. Calculate the margin of error: Multiply the critical value by the standard deviation. In this case, the standard deviation is $5. Therefore, the margin of error is:

Margin of Error = 2.33 * $5 = $11.65

So, at a 98% confidence level, the margin of error is approximately $11.65.

This means that if we were to repeat the survey multiple times, about 98% of the time, the true average amount spent on a child's last birthday gift would fall within $11.65 of the mean ($45).