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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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Question

Part 1: One Sample t-Confidence Interval

Based on what you learned about confidence interval, select ALL the correct statements about the confidence interval.

____Longer interval is more precise

__X__A point estimate gives more information than an interval estimate.

_____The margin of error is the smallest possible difference between sample mean and population mean.

__X___When everything else is same, increasing sample size reduces (lowers) the length of interval.

___X__When everything else is same, increasing confidence level decreases (lowers) the length of interval.

______A point estimate is the single best guess for the parameter while an interval estimate is a range of plausible values for the parameter.

______None of these.

The following data represent the Sales (in $1000) data gathered from a marketing efficacy study in Week 1 of December 2019 at a fast-food chain.
Each row is an individual store that was randomly selected for this study.

Sales(In_Thousands)
71.63
62.37
63.2
74.48
36.83
70.35
43.48
43.57
47.5
49.63
49.78
51.59
58.22
60.14
61.58
67.23
70.06
75.92
77.4
85.46
87.55
89.23
60.95
71.58
64.92

a. Use Excel to create a descriptive statistics table of Sales(In_Thousand) variable along with the margin of error to compute a 98% confidence interval for average sales.
Using the result, fill in the blanks of the following statements rounded properly to 2 decimal places.

The average (in $1000) sales is______________.

The margin of error (in $1000) for 98% confidence interval is_____________.

The lower limit (in $1000) of 98% confidence interval for average sales is____________.

The upper limit (in $1000) of 98% confidence interval for average sales is_____________.

Based on your lower and upper limits of a 98% confidence interval for average sales, is it plausible that the average sales (in $1000) for all such stores be 65 in Week 1 of December? Yes or No

because

_____65 is between lower and upper values.

_____65 is NOT between lower and upper values.

______65 is a value in the given data.

______65 is NOT a value in the given data.

__X____None of these.

Part 2: One Sample t-Test

a. Use Excel to perform a one-sample t test to test the claim that the average sales (in $1000) for all such stores is different from 65 in Week 1 of December.

The p-value for this test is (rounded to 4 decimal places)_______________

At 0.02 significance level, the correct conclusion for this test is

_____There is enough evidence that the average sales (in $1000) for all such stores is different from 65 in Week 1 of December

____There is NO enough evidence that the average sales (in $1000) for all such stores is different from 65 in Week 1 of December

__X__None of these.

b. Select ONLY the necessary requirements (or assumptions) met in this analysis to confirm that our results from the one-sample t procedures are valid. Make sure to use Excel to create a histogram and boxplot for the data.

__x___There is a random sample of data.

_____There is NO random sample of data.

___x__The sample is large enough.

_____It is given that the population has a Normal distribution.

__x___The histogram and boxplot shows it is safe to assume sample is selected from a population with a Normal distribution.

___x___The boxplot shows the sample has no outliers.

______None of these.

c. Do your conclusions based on confidence interval and p-value indicate the same thing?

____Yes, because we use matching confidence level and significance level.

__x__No, they don't have to be same.