### Confidence Interval Estimation for Average Spending**Problem Context:**Scarlett and Heather own an upscale restaurant in Dayton, Ohio, and want to study the spending habits of their customers. The results from a sample of 20 customers are as follows:- **Sample Mean ($\bar{x}$)**: $38.54- **Sample Standard Deviation**: $7.26The task is to construct a 95% confidence interval estimate for the population mean amount spent per customer in the restaurant.**Diagram Explanation:**1. **Bell Curve:** - The image features a bell-shaped curve which typically represents a normal distribution. This is used to visualize how data (such as spending amounts) is distributed around the mean value.2. **Table of Answers:** - This is a table with columns labeled "Answers," providing structured spaces to fill out key statistical elements: - **Point Estimate**: The sample mean, representing the central value of the estimate. - **Alpha (α)**: Represents the significance level. In a 95% confidence interval, $ \alpha = 0.05 $. - **Critical Value**: Typically derived from a standard normal or t-distribution table depending on the sample size and variance knowledge. - **Standard Error**: Calculated using the sample standard deviation divided by the square root of the sample size. - **Margin of Error**: Derived from multiplying the critical value and the standard error. - **Confidence Interval Limits**: The range within which the true population mean is expected to lie, calculated as the sample mean ± the margin of error.These components together help in determining the confidence interval, providing an estimated range for the average amount customers spend at the restaurant.

Answered: 3. Scarlett and Heather own an upscale…

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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In a survey, 21 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $41 and standard deviation of $6. Find the margin of error at a 90% confidence level.
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In a survey, 26 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $40 and standard deviation of $6. Find the margin of error at a 90% confidence level.
In a survey, 41 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $36 and standard deviation of $4. Find the margin of error for a 95% confidence level.
The Health Care Cost Institute tracks health care expenditures for beneficiaries under theage of 65 who are covered by employer-sponsored private health insurance (Health CareCost Institute website, November 4, 2012). The data contained in the DATAfile namedDrugCost are consistent with the institute’s findings concerning annual prescription costsper employee. Analyze the data using Excel and answer the following questions.a. Develop a 90% confidence interval for the annual cost of prescription drugs.b. Develop a 90% confidence interval for the amount of out-of-pocket expense peremployee.c. What is your point estimate of the proportion of employees who incurred no prescription drug costs?
A researcher is studying the average cost of traveling for a college student. As part of their research, they would like to learn more about the average yearly money spent to travel to and from home by air. In a random sample of 130 students, the mean travel cost by air was $1180 with a standard deviation of $535. Use these sample data to answer the following questions. What sample size would be needed to construct a 95% confidence interval to estimate the average air travel cost for a college student with a margin of error of ±$50? You will need to do calculations by hand.
2. A food truck serves lunch every Tuesday and Thursday on the plaza in front of Van Metre Hall on the GMU Arlington campus. The number of customers varies every day, so it wants to order supplies based on the average number of customers served per day. The truck recorded how many customers were served on 40 randomly selected days, and obtained a sample mean and sample standard deviation of 145 and 17, respectively. Construct a 90% confidence interval for the mean number of customers served per day.
A researcher is studying the average cost of traveling for a college student. As part of their research, they would like to learn more about the average yearly money spent to travel to and from home by air. In a random sample of 130 students, the mean travel cost by air was $1180 with a standard deviation of $535. Use these sample data to answer the following questions. Construct a 95% confidence interval to estimate the mean travel cost by air. Remember to include all relevant Minitab output and to identify your answer. You should not need to do any calculations by hand.

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