You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals.A random sample of 55 home theater systems has a mean price of $115.00.Assume the population standard deviation is $19.70. Construct a 90% confidence interval for the population mean.The 90% confidence interval is ( | ).(Round to two decimal places as needed.)Construct a 95% confidence interval for the population mean.The 95% confidence interval is ( | ).(Round to two decimal places as needed.)Interpret the results. Choose the correct answer below.A. With 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said thatthe population mean price lies in the second interval. The 95% confidence interval is narrower than the 90%.B. With 90% confidence, it can be said that the sample mean price lies in the first interval. With 95% confidence, it can be said that thesample mean price lies in the second interval. The 95% confidence interval is wider than the 90%.C. With 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said thatthe population mean price lies in the second interval. The 95% confidence interval is wider than the 90%.

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Description: You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If conve

As the population standard deviation is known, we will use z distribution. The value of z at a 90%…

Answered: Construct a 90% confidence interval for…

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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You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals.

A random sample of 55 home theater systems has a mean price of $115.00.

Assume the population standard deviation is $19.70.

Construct a 90% confidence interval for the population mean.
The 90% confidence interval is ( | ).
(Round to two decimal places as needed.)
Construct a 95% confidence interval for the population mean.
The 95% confidence interval is ( | ).
(Round to two decimal places as needed.)
Interpret the results. Choose the correct answer below.
A. With 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said that
the population mean price lies in the second interval. The 95% confidence interval is narrower than the 90%.
B. With 90% confidence, it can be said that the sample mean price lies in the first interval. With 95% confidence, it can be said that the
sample mean price lies in the second interval. The 95% confidence interval is wider than the 90%.
C. With 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said that
the population mean price lies in the second interval. The 95% confidence interval is wider than the 90%.

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 + ...

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