The average American gets a haircut every 40 days. Is the average different for college students? The data below shows the results of a survey of 13 college students asking them how many days elapse between haircuts. Assume that the distribution of the population is normal. 36, 34, 39, 44, 30, 41, 30, 35, 26, 29, 39, 42, 27 What can be concluded at the the αα = 0.05 level of significance level of significance? For this study, we should use (t-test for a population mean, z-test for a population proportion) The null and alternative hypotheses would be: H0: (symbol) (symbol) __ H1: (symbol) (symbol) The test statistic (symbol) = _ (please show your answer to 3 decimal places.) The p-value = ___(Please show your answer to 3 decimal places.) The p-value is (symbol) αα Based on this, we should (accept, fail to reject, reject) the null hypothesis. Thus, the final conclusion is that ... The data suggest the populaton mean is significantly different from 40 at αα = 0.05, so there is sufficient evidence to conclude that the population mean number of days between haircuts for college students is different from 40. The data suggest the population mean number of days between haircuts for college students is not significantly different from 40 at αα = 0.05, so there is insufficient evidence to conclude that the population mean number of days between haircuts for college students is different from 40. The data suggest the population mean is not significantly different from 40 at αα = 0.05, so there is sufficient evidence to conclude that the population mean number of days between haircuts for college students is equal to 40.

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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The average American gets a haircut every 40 days. Is the average different for college students? The data below shows the results of a survey of 13 college students asking them how many days elapse between haircuts. Assume that the distribution of the population is normal.

36, 34, 39, 44, 30, 41, 30, 35, 26, 29, 39, 42, 27

What can be concluded at the the αα = 0.05 level of significance level of significance?

For this study, we should use (t-test for a population mean, z-test for a population proportion)
The null and alternative hypotheses would be:

H0: (symbol) (symbol) ____

H1: (symbol) (symbol) ____

The test statistic (symbol) = _____ (please show your answer to 3 decimal places.)
The p-value = _____(Please show your answer to 3 decimal places.)
The p-value is (symbol) αα
Based on this, we should (accept, fail to reject, reject) the null hypothesis.
Thus, the final conclusion is that ...
- The data suggest the populaton mean is significantly different from 40 at αα = 0.05, so there is sufficient evidence to conclude that the population mean number of days between haircuts for college students is different from 40.
- The data suggest the population mean number of days between haircuts for college students is not significantly different from 40 at αα = 0.05, so there is insufficient evidence to conclude that the population mean number of days between haircuts for college students is different from 40.
- The data suggest the population mean is not significantly different from 40 at αα = 0.05, so there is sufficient evidence to conclude that the population mean number of days between haircuts for college students is equal to 40.

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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