Answered: In a study of speed dating, male…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 30PPS

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Question

In a study of speed dating, male subjects were asked to rate the attractiveness of their female dates, and a sample of the results is listed below (1=not attractive; 10=extremely attractive). Construct a confidence interval using a 99%confidence level. What do the results tell about the mean attractiveness ratings of the population of all adult females?

5,8,3,8,5,5,6,7,9,8,6,9

What is the confidence interval for the population mean μ?

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

Obtain the 99% confidence interval for the population mean μ.

The 99% confidence interval for the population mean μ is obtained below as follows:

The formula for the Confidence interval for mean is:

Use EXCEL Procedure to obtain values for the given samples.

Follow the instruction to obtain the value of mean and SD:

Open EXCEL
Go to Data>Data Analysis.
Choose Descriptive Statistics.
Enter the input range as $A$1:$A$13.
Check the Labels in the first row.
Check the option Summary statistics
Click OK.

EXCEL output:

From the EXCEL output, the value of mean is 6.5833 and the standard deviation is 1.8809

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