The average house has 13 paintings on its walls. Is the mean different for houses owned by teachers? The data show the results of a survey of 12 teachers who were asked how many paintings they have in their houses. Assume that the distribution of the population is normal.12, 14, 14, 14, 15, 14, 14, 14, 12, 13, 15, 14What can be concluded at the αα = 0.01 level of significance?For this study, we should use The null and alternative hypotheses would be: H0:H0: H1:H1: The test statistic = (please show your answer to 3 decimal places.)The p-value = (Please show your answer to 4 decimal places.)The p-value is ααBased on this, we should the null hypothesis.Thus, the final conclusion is that ...The data suggest the population mean is not significantly different from 13 at αα = 0.01, so there is sufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is equal to 13.The data suggest that the population mean number of paintings that are in teachers' houses is not significantly different from 13 at αα = 0.01, so there is insufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is different from 13.The data suggest the populaton mean is significantly different from 13 at αα = 0.01, so there is sufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is different from 13.Interpret the p-value in the context of the study.If the population mean number of paintings that are in teachers' houses is 13 and if you survey another 12 teachers, then there would be a 2.1% chance that the sample mean for these 12 teachers would either be less than 12 or greater than 14.There is a 2.1% chance of a Type I error.If the population mean number of paintings that are in teachers' houses is 13 and if you survey another 12 teachers then there would be a 2.1% chance that the population mean would either be less than 12 or greater than 14.There is a 2.1% chance that the population mean number of paintings that are in teachers' houses is not equal to 13.Interpret the level of significance in the context of the study.If the population mean number of paintings that are in teachers' houses is different from 13 and if you survey another 12 teachers, then there would be a 1% chance that we would end up falsely concuding that the population mean number of paintings that are in teachers' houses is equal to 13.There is a 1% chance that the population mean number of paintings that are in teachers' houses is different from 13.If the population mean number of paintings that are in teachers' houses is 13 and if you survey another 12 teachers, then there would be a 1% chance that we would end up falsely concuding that the population mean number of paintings that are in teachers' houses is different from 13.There is a 1% chance that teachers are so poor that they are all homeless.

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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 house has 13 paintings on its walls. Is the mean different for houses owned by teachers? The data show the results of a survey of 12 teachers who were asked how many paintings they have in their houses. Assume that the distribution of the population is normal.

12, 14, 14, 14, 15, 14, 14, 14, 12, 13, 15, 14

What can be concluded at the αα = 0.01 level of significance?

For this study, we should use
The null and alternative hypotheses would be:

H0:H0:

H1:H1:

The test statistic = (please show your answer to 3 decimal places.)
The p-value = (Please show your answer to 4 decimal places.)
The p-value is αα
Based on this, we should the null hypothesis.
Thus, the final conclusion is that ...
- The data suggest the population mean is not significantly different from 13 at αα = 0.01, so there is sufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is equal to 13.
- The data suggest that the population mean number of paintings that are in teachers' houses is not significantly different from 13 at αα = 0.01, so there is insufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is different from 13.
- The data suggest the populaton mean is significantly different from 13 at αα = 0.01, so there is sufficient evidence to conclude that the population mean number of paintings that are in teachers' houses is different from 13.
Interpret the p-value in the context of the study.
- If the population mean number of paintings that are in teachers' houses is 13 and if you survey another 12 teachers, then there would be a 2.1% chance that the sample mean for these 12 teachers would either be less than 12 or greater than 14.
- There is a 2.1% chance of a Type I error.
- If the population mean number of paintings that are in teachers' houses is 13 and if you survey another 12 teachers then there would be a 2.1% chance that the population mean would either be less than 12 or greater than 14.
- There is a 2.1% chance that the population mean number of paintings that are in teachers' houses is not equal to 13.
Interpret the level of significance in the context of the study.
- If the population mean number of paintings that are in teachers' houses is different from 13 and if you survey another 12 teachers, then there would be a 1% chance that we would end up falsely concuding that the population mean number of paintings that are in teachers' houses is equal to 13.
- There is a 1% chance that the population mean number of paintings that are in teachers' houses is different from 13.
- If the population mean number of paintings that are in teachers' houses is 13 and if you survey another 12 teachers, then there would be a 1% chance that we would end up falsely concuding that the population mean number of paintings that are in teachers' houses is different from 13.
- There is a 1% chance that teachers are so poor that they are all homeless.

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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