A sample of 15 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The meanweight was 2 ounces with a standard deviation of 0.12 ounces. The population standard deviation is known to be 0.1 ounce.NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Construct a 90% confidence interval for the population average weight of the candies.(i) State the confidence interval. (Round your answers to three decimal places.)(ii) Sketch the graph.aaC.L. =(iii) Calculate the error bound. (Round your answer to three decimal places.)O Part (f)Construct a 98% confidence interval for the population average weight of the candies.(i) State the confidence interval. (Round your answers to three decimal places.)(ii) Sketch the graph.C.L. =0(i) Calculate the error bound. (Round your answer to three decimal places.)

Given, n = 15 Mean, -x = 2 Standard deviation, s = 0.12 CI = -x ±Zα* SE Part (1) Z critical value for 90% CI is 1.645 SE = s/n = 0.12/15 = 0.031 90% CI = 2 ±1.645* 0.031 = 2 ± 0.051 = (1.949, 2.051) Error bound = Z*s/n = 1.645* 0.031 = 0.051Part (2) Z critical value for 98% CI is 2.326 SE = s/n = 0.12/15 = 0.031 90% CI = 2 ±2.326* 0.031 = 2 ± 0.072 = (1.928, 2.072) Error bound = Z*s/n = 2.326* 0.031 = 0.072

Answered: A sample of 15 small bags of the same…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Transcribed Image Text:A sample of 15 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was 2 ounces with a standard deviation of 0.12 ounces. The population standard deviation is known to be 0.1 ounce. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Construct a 90% confidence interval for the population average weight of the candies.
(i) State the confidence interval. (Round your answers to three decimal places.)
(ii) Sketch the graph.
a
a
C.L. =
(iii) Calculate the error bound. (Round your answer to three decimal places.)
O Part (f)
Construct a 98% confidence interval for the population average weight of the candies.
(i) State the confidence interval. (Round your answers to three decimal places.)
(ii) Sketch the graph.
C.L. =0
(i) Calculate the error bound. (Round your answer to three decimal places.)

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