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. From a random sample of 59 dates, the mean record high daily temperature in a certain city has a mean of 86.32degrees°F. Assume the population standard deviation is 14.97degrees°F. The 90% confidence interval is (). (Round to two decimal places as needed.) The 95% confidence interval is (). (Round to two decimal places as needed.) Which interval is wider? Choose the correct answer below. A) The 90% confidence interval B) The 95% confidence interval Interpret the results. A. You can be 90% confident that the population mean record high temperature is between the bounds of the 90% confidence interval, and 95% confident for the 95% interval. B. You can be certain that the population mean record high temperature is either between the lower bounds of the 90% and 95% confidence intervals or the upper bounds of the 90% and 95% confidence intervals. C. You can be 90% confident that the population mean record high temperature is outside the bounds of the 90% confidence interval, and 95% confident for the 95% interval. D. You can be certain that the mean record high temperature was within the 90% confidence interval for approximately 53 of the 59 days, and was within the 95% confidence interval for approximately 56 of the 59 days.

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.

From a random sample of

dates, the mean record high daily temperature in a certain city has a mean of

86.32degrees°F.

Assume the population standard deviation is

14.97degrees°F.

The 90% confidence interval is

().

(Round to two decimal places as needed.)

The 95% confidence interval is

().

(Round to two decimal places as needed.)

Which interval is wider? Choose the correct answer below.

A) The 90% confidence interval

B) The 95% confidence interval

Interpret the results.

You can be 90% confident that the population mean record high temperature is between the bounds of the 90% confidence interval, and 95% confident for the 95% interval.

You can be certain that the population mean record high temperature is either between the lower bounds of the 90% and 95% confidence intervals or the upper bounds of the 90% and 95% confidence intervals.

You can be 90% confident that the population mean record high temperature is outside the bounds of the 90% confidence interval, and 95% confident for the 95% interval.

You can be certain that the mean record high temperature was within the 90% confidence interval for approximately

of the

days, and was within the 95% confidence interval for approximately

of the

days.

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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