A sample of 16 overweight people take a new reducing pill for 6 weeks and have a mean weight loss of 20 lbs . The standard deviation is 8 lbs . You may assume that the distribution is normal .a) Find a 95 % confidence interval for the mean weight loss .b) If the same information was found using a sample of 50 , how would that cffect the length of the confidence interval the standard standard deviation of S.16.) Find a 99% confidence interval for the mean price of regular gasoline.b) If we had used a 95% confidence level, how would that have effected thelength of the confidence interval?c) Based on your answer in part a) of this problem do you accept or rejectthe Retailers claim that the mean price is $2.18 Please explain youranswer.4) A sample of 16 overweight people take a new reducing pill for 6 weeksand have a mean weight loss of 20 lbs. The standard deviation is 8 Ibs.You may assume that the distribution is normal.a) Find a 95% confidence interval for the mean weight loss.b) If the same information was found using a sample of 50, how would thatcffect the length of the confidence interval5) The mean score for the Verbal SAT in the USA is M =480, the standarddeviation is6- 90 A sample of 100 students in a school district had a samplemeanX 512.At the 1 % significance level is the data suflicient to show that the SATscores are higher in this district

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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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A sample of 16 overweight people take a new reducing pill for 6 weeks and have a mean weight loss of 20 lbs . The standard deviation is 8 lbs . You may assume that the distribution is normal .

a) Find a 95 % confidence interval for the mean weight loss .

b) If the same information was found using a sample of 50 , how would that cffect the length of the confidence interval the standard

standard deviation of S.16.
) Find a 99% confidence interval for the mean price of regular gasoline.
b) If we had used a 95% confidence level, how would that have effected the
length of the confidence interval?
c) Based on your answer in part a) of this problem do you accept or reject
the Retailers claim that the mean price is $2.18 Please explain your
answer.
4) A sample of 16 overweight people take a new reducing pill for 6 weeks
and have a mean weight loss of 20 lbs. The standard deviation is 8 Ibs.
You may assume that the distribution is normal.
a) Find a 95% confidence interval for the mean weight loss.
b) If the same information was found using a sample of 50, how would that
cffect the length of the confidence interval
5) The mean score for the Verbal SAT in the USA is M =480, the standard
deviation is6- 90 A sample of 100 students in a school district had a sample
meanX 512.
At the 1 % significance level is the data suflicient to show that the SAT
scores are higher in this district

Expert Solution

Step 1

The sample mean = 20.

Sample standard deviation, s is 8.

The sample size, n is 16.

From the EXCEL, using the formula, =T.INV.2T(0.05,15), the critical value is 2.1314.

The 95% confidence interval mean is calculated as follows:

$\begin{array}{l} C I = \bar{x} \pm t (\frac{s}{\sqrt{n}}) \\ = 20 \pm 2.1314 \times \frac{8}{\sqrt{16}} \\ = 20 \pm 4.2628 \\ = (15.7372, 24.2628) \end{array}$

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