Part 2: o rats take less time on average than hamsters to travel through a maze? The table below shows the times in seconds that the rats and hamsters took. Rats: 21, 28, 38, 34, 25, 42, 35, 32 Hamsters: 48, 43, 31, 39, 49, 27, 40, 40 Assume that both populations follow a normal distribution. What can be concluded at the αα = 0.01 level of significance level of significance? a. The p-value =_______ (Please show your answer to 4 decimal places.) The p-value is ? ≤ or > b. Based on this, we should? Select an answer fail to reject? accept? or reject? the null hypothesis. Thus, the final conclusion is that ... The results are statistically insignificant at αα = 0.01, so there is insufficient evidence to conclude that the population mean time to complete the maze for rats is less than the population mean time to complete the maze for hamsters. The results are statistically insignificant at αα = 0.01, so there is statistically significant evidence to conclude that the population mean time to complete the maze for rats is equal to the population mean time to complete the maze for hamsters. The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the mean time to complete the maze for the eight rats is less than the mean time to complete the maze for the eight hamsters. The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the population mean time to complete the maze for rats is less than the population mean time to complete the maze for hamsters. c. Interpret the p-value in the context of the study. There is a 2.56% chance of a Type I error. There is a 2.56% chance that the mean time to complete the maze for the 8 rats is at least 7.8 seconds less than the mean time to complete the maze for the 8 hamsters. If the sample mean time to complete the maze for the 8 rats is the same as the sample mean time to complete the maze for the 8 hamsters and if another 8 rats and 8 hamsters are observed then there would be a 2.56% chance of concluding that the mean time to complete the maze for the 8 rats is at least 7.8 seconds less than the mean time to complete the maze for the 8 hamsters. If the population mean time to complete the maze for rats is the same as the population mean time to complete the maze for hamsters and if another 8 rats and 8 hamsters are observed then there would be a 2.56% chance that the mean time to complete the maze for the 8 rats would be at least 7.8 seconds less than the mean time to complete the maze for the 8 hamsters. d. Interpret the level of significance in the context of the study. If the population mean time to complete the maze for rats is the same as the population mean time to complete the maze for hamsters and if another 8 rats and 8 hamsters are observed, then there would be a 1% chance that we would end up falsely concluding that the sample mean time to complete the maze for these 8 rats and 8 hamsters differ from each other. There is a 1% chance that the rat will eat the hamster. There is a 1% chance that the population mean time to complete the maze for rats and hamsters is the same. If the population mean time to complete the maze for rats is the same as the population mean time to complete the maze for hamsters and if another 8 rats and 8 hamsters are observed then there would be a 1% chance that we would end up falsely concluding that the population mean time to complete the maze for rats is less than the population mean time to complete the maze for hamsters

Part 2: o rats take less time on average than hamsters to travel through a maze? The table below shows the times in seconds that the rats and hamsters took. Rats: 21, 28, 38, 34, 25, 42, 35, 32 Hamsters: 48, 43, 31, 39, 49, 27, 40, 40 Assume that both populations follow a normal distribution. What can be concluded at the αα = 0.01 level of significance level of significance? a. The p-value =_______ (Please show your answer to 4 decimal places.) The p-value is ? ≤ or > b. Based on this, we should? Select an answer fail to reject? accept? or reject? the null hypothesis. Thus, the final conclusion is that ... The results are statistically insignificant at αα = 0.01, so there is insufficient evidence to conclude that the population mean time to complete the maze for rats is less than the population mean time to complete the maze for hamsters. The results are statistically insignificant at αα = 0.01, so there is statistically significant evidence to conclude that the population mean time to complete the maze for rats is equal to the population mean time to complete the maze for hamsters. The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the mean time to complete the maze for the eight rats is less than the mean time to complete the maze for the eight hamsters. The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the population mean time to complete the maze for rats is less than the population mean time to complete the maze for hamsters. c. Interpret the p-value in the context of the study. There is a 2.56% chance of a Type I error. There is a 2.56% chance that the mean time to complete the maze for the 8 rats is at least 7.8 seconds less than the mean time to complete the maze for the 8 hamsters. If the sample mean time to complete the maze for the 8 rats is the same as the sample mean time to complete the maze for the 8 hamsters and if another 8 rats and 8 hamsters are observed then there would be a 2.56% chance of concluding that the mean time to complete the maze for the 8 rats is at least 7.8 seconds less than the mean time to complete the maze for the 8 hamsters. If the population mean time to complete the maze for rats is the same as the population mean time to complete the maze for hamsters and if another 8 rats and 8 hamsters are observed then there would be a 2.56% chance that the mean time to complete the maze for the 8 rats would be at least 7.8 seconds less than the mean time to complete the maze for the 8 hamsters. d. Interpret the level of significance in the context of the study. If the population mean time to complete the maze for rats is the same as the population mean time to complete the maze for hamsters and if another 8 rats and 8 hamsters are observed, then there would be a 1% chance that we would end up falsely concluding that the sample mean time to complete the maze for these 8 rats and 8 hamsters differ from each other. There is a 1% chance that the rat will eat the hamster. There is a 1% chance that the population mean time to complete the maze for rats and hamsters is the same. If the population mean time to complete the maze for rats is the same as the population mean time to complete the maze for hamsters and if another 8 rats and 8 hamsters are observed then there would be a 1% chance that we would end up falsely concluding that the population mean time to complete the maze for rats is less than the population mean time to complete the maze for hamsters

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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Part 2:

o rats take less time on average than hamsters to travel through a maze? The table below shows the times in seconds that the rats and hamsters took.

Rats: 21, 28, 38, 34, 25, 42, 35, 32

Hamsters: 48, 43, 31, 39, 49, 27, 40, 40

Assume that both populations follow a normal distribution. What can be concluded at the αα = 0.01 level of significance level of significance?

a. The p-value =_______ (Please show your answer to 4 decimal places.) The p-value is ? ≤ or >

b. Based on this, we should? Select an answer fail to reject? accept? or reject? the null hypothesis.

Thus, the final conclusion is that ...

The results are statistically insignificant at αα = 0.01, so there is insufficient evidence to conclude that the population mean time to complete the maze for rats is less than the population mean time to complete the maze for hamsters.
The results are statistically insignificant at αα = 0.01, so there is statistically significant evidence to conclude that the population mean time to complete the maze for rats is equal to the population mean time to complete the maze for hamsters.
The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the mean time to complete the maze for the eight rats is less than the mean time to complete the maze for the eight hamsters.
The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the population mean time to complete the maze for rats is less than the population mean time to complete the maze for hamsters.

c. Interpret the p-value in the context of the study.

There is a 2.56% chance of a Type I error.
There is a 2.56% chance that the mean time to complete the maze for the 8 rats is at least 7.8 seconds less than the mean time to complete the maze for the 8 hamsters.
If the sample mean time to complete the maze for the 8 rats is the same as the sample mean time to complete the maze for the 8 hamsters and if another 8 rats and 8 hamsters are observed then there would be a 2.56% chance of concluding that the mean time to complete the maze for the 8 rats is at least 7.8 seconds less than the mean time to complete the maze for the 8 hamsters.
If the population mean time to complete the maze for rats is the same as the population mean time to complete the maze for hamsters and if another 8 rats and 8 hamsters are observed then there would be a 2.56% chance that the mean time to complete the maze for the 8 rats would be at least 7.8 seconds less than the mean time to complete the maze for the 8 hamsters.

d. Interpret the level of significance in the context of the study.

If the population mean time to complete the maze for rats is the same as the population mean time to complete the maze for hamsters and if another 8 rats and 8 hamsters are observed, then there would be a 1% chance that we would end up falsely concluding that the sample mean time to complete the maze for these 8 rats and 8 hamsters differ from each other.
There is a 1% chance that the rat will eat the hamster.
There is a 1% chance that the population mean time to complete the maze for rats and hamsters is the same.
If the population mean time to complete the maze for rats is the same as the population mean time to complete the maze for hamsters and if another 8 rats and 8 hamsters are observed then there would be a 1% chance that we would end up falsely concluding that the population mean time to complete the maze for rats is less than the population mean time to complete the maze for hamsters

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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