On average, Americans have lived in 3 places by the time they are 18 years old. Is this average a different number for college students? The 63 randomly selected college students who answered the survey question had lived in an average of 3.06 places by the time they were 18 years old. The standard deviation for the survey group was 0.3. What can be concluded at the αα = 0.10 level of significance?For this study, we should use T test for a population mean or z test for a population proportion The null and alternative hypotheses would be: H0: H1: The test statistic t or z = (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 that the populaton mean is significantly different from 3 at αα = 0.10, so there is statistically significant evidence to conclude that the population mean number of places that college students lived in by the time they were 18 years old is different from 3.The data suggest that the population mean is not significantly different from 3 at αα = 0.10, so there is statistically insignificant evidence to conclude that the population mean number of places that college students lived in by the time they were 18 years old is different from 3.The data suggest that the sample mean is not significantly different from 3 at αα = 0.10, so there is statistically insignificant evidence to conclude that the sample mean number of places that college students lived in by the time they were 18 years old is different from 3.06.Interpret the p-value in the context of the study.If the population mean number of places that college students lived in by the time they were 18 years old is 3 and if you survey another 63 college students, then there would be a 11.74978814% chance that the sample mean for these 63 college students would either be less than 3 or greater than 3.06.There is a 11.74978814% chance of a Type I error.There is a 11.74978814% chance that the population mean number of places that college students lived in by the time they were 18 years old is not equal to 3.If the population mean number of places that college students lived in by the time they were 18 years old is 3 and if you survey another 63 college students then there would be a 11.74978814% chance that the population mean would either be less than 3 or greater than 3.06.Interpret the level of significance in the context of the study.There is a 10% chance that the population mean number of places that college students lived in by the time they were 18 years old is different from 3.There is a 10% chance that none of this is real since you have been hooked up to virtual reality since you were born.If the population mean number of places that college students lived in by the time they were 18 years old is 3 and if you survey another 63 college students, then there would be a 10% chance that we would end up falsely concluding that the population mean number of places that college students lived in by the time they were 18 years old is different from 3.If the population mean number of places that college students lived in by the time they were 18 years old is different from 3 and if you survey another 63 college students, then there would be a 10% chance that we would end up falsely concluding that the population mean number of places that college students lived in by the time they were 18 years old is equal to 3.

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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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On average, Americans have lived in 3 places by the time they are 18 years old. Is this average a different number for college students? The 63 randomly selected college students who answered the survey question had lived in an average of 3.06 places by the time they were 18 years old. The standard deviation for the survey group was 0.3. What can be concluded at the αα = 0.10 level of significance?

For this study, we should use T test for a population mean or z test for a population proportion
The null and alternative hypotheses would be:

H0:

H1:

The test statistic t or z = (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 that the populaton mean is significantly different from 3 at αα = 0.10, so there is statistically significant evidence to conclude that the population mean number of places that college students lived in by the time they were 18 years old is different from 3.
- The data suggest that the population mean is not significantly different from 3 at αα = 0.10, so there is statistically insignificant evidence to conclude that the population mean number of places that college students lived in by the time they were 18 years old is different from 3.
- The data suggest that the sample mean is not significantly different from 3 at αα = 0.10, so there is statistically insignificant evidence to conclude that the sample mean number of places that college students lived in by the time they were 18 years old is different from 3.06.
Interpret the p-value in the context of the study.
- If the population mean number of places that college students lived in by the time they were 18 years old is 3 and if you survey another 63 college students, then there would be a 11.74978814% chance that the sample mean for these 63 college students would either be less than 3 or greater than 3.06.
- There is a 11.74978814% chance of a Type I error.
- There is a 11.74978814% chance that the population mean number of places that college students lived in by the time they were 18 years old is not equal to 3.
- If the population mean number of places that college students lived in by the time they were 18 years old is 3 and if you survey another 63 college students then there would be a 11.74978814% chance that the population mean would either be less than 3 or greater than 3.06.
Interpret the level of significance in the context of the study.
- There is a 10% chance that the population mean number of places that college students lived in by the time they were 18 years old is different from 3.
- There is a 10% chance that none of this is real since you have been hooked up to virtual reality since you were born.
- If the population mean number of places that college students lived in by the time they were 18 years old is 3 and if you survey another 63 college students, then there would be a 10% chance that we would end up falsely concluding that the population mean number of places that college students lived in by the time they were 18 years old is different from 3.
- If the population mean number of places that college students lived in by the time they were 18 years old is different from 3 and if you survey another 63 college students, then there would be a 10% chance that we would end up falsely concluding that the population mean number of places that college students lived in by the time they were 18 years old is equal to 3.

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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