Answered: Karen wants to advertise how many…

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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Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 47 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 8.2 and a standard deviation of 3.1. What is the 99% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Enter your answers accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

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Step 1

$\mathbf{Solution}$

$\mathbf{given:}$

$\mathrm{Sample\;size\;(n)=47}$

$\mathrm{Sample\;mean\;(\bar x)=8.2}$

$\mathrm{Sample\;standard\;deviation\;(s)=3.1}$

Since population standard deviation is unknown, Use t-distribution to find t-critical value.

Find t-critical value:

$\mathbf{degrees\;of\;freedom\;(df)}=n-1=47-1=\mathbf{46}$

$\mathrm{\small Confidence\;level\;(C)=99\%=\frac{99}{100}=0.99}$

$\mathrm{\small \alpha =1-C=1-0.99=0.01}$

Refer t-distribution table OR use excel function "=T.INV.2T(0.01,46)" to find the critical value of t.

$\mathbf{\therefore t_{\frac{\alpha }{2}}=2.687 }$

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