Answered: Hotels want to gather information about…

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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Hotels want to gather information about their rooms, they take a random sample of 52 rooms to produce a mean cost of $208.35 a night. If the population standard deviation of costs for a one-night stay is $47.45.

1. Construct a 99% confidence interval for the average cost per night in a hotel.

2. What is the value of your point estimate for part 1?

3. Construct a 95% confidence interval for the average cost per night in a hotel.

4. What is the value of your margin of error for part 3?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1

Solution:

Let X be the Cost for a one-night stay.

From the given information, x-bar=$208.35, n=52 and σ=$47.45.

The confidence level is 0.99.

Step 2

Then, a 99% confidence interval for the average cost per night in a hotel is

Step 3

The point is the sample mean.

Thus, the value of the point estimate for part 1 is $208.35.

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