Question 8In a survey, 28 people were asked how much they spent on their child's last birthday gift. The resultswere roughly bell-shaped with a mean of $49 and standard deviation of $8. Construct a confidenceinterval at a 80% confidence level.Give your answers to one decimal place.士Interpret your confidence interval in the context of this problem.

Name: Question 8In a survey, 28 people were asked how much they spent on th
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Description: Question 8In a survey, 28 people were asked how much they spent on their child's last birthday gift. The resultswere roughly bell-shaped with a mean of $49 and standard deviation of $8. Construct a confidenceinterval at a 80% confidence level.Give y

Given Information: Sample size (n) = 28 Mean x¯= 49 Standard deviation s= 8 Confidence level = 80% =…

Answered: In a survey, 28 people were asked how…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Given Information:

Sample size (n) = 28

Mean $\bar{x}$ = 49

Standard deviation $s$ = 8

Confidence level = 80% = 0.80

Since, sample size is less than 30 and the distribution is roughly bell shaped, t-distribution would be appropriate:

Significance level $α = 1 - 0.80 = 0.20$

Confidence interval is obtained using the formula:

$C . I = \bar{x} \pm t * (\frac{s}{\sqrt{n}})$

Using t-table, critical value at degrees of freedom $d f = n - 1 = 28 - 1 = 27$ 80% confidence level or 0.20 significance level is 1.314

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