Is memory ability before a meal better than after a meal? Ten people were given memory tests before their meal and then again after their meal. The data is shown below. A higher score indicates a better memory ability. Score on the Memory Test Before a Meal 66 68 58 70 62 58 81 77 74 66 After a Meal 64 68 52 61 57 71 73 75 66 60 Assume a Normal distribution. What can be concluded at the the αα = 0.01 level of significance? For this study, we should use Select an answer t-test for a population mean t-test for the difference between two dependent population means z-test for the difference between two population proportions t-test for the difference between two independent population means z-test for a population proportion The null and alternative hypotheses would be: H0:H0: Select an answer p1 μ1 μd Select an answer < ≠ = > Select an answer p2 0 μ2 (please enter a decimal) H1:H1: Select an answer μd p1 μ1 Select an answer > < = ≠ Select an answer p2 μ2 0 (Please enter a decimal) The test statistic ? z t = (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 Select an answer accept fail to reject reject the null hypothesis. Thus, the final conclusion is that ... The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the population mean memory score before a meal is higher than the population mean memory score after a meal The results are statistically insignificant at αα = 0.01, so there is statistically significant evidence to conclude that the population mean memory score before a meal is equal to the population mean memory score after a meal. The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the ten memory scores from the memory tests that were taken before a meal are higher on average than the ten memory scores from the memory tests that were taken after a meal. The results are statistically insignificant at αα = 0.01, so there is insufficient evidence to conclude that the population mean memory score before a meal is higher than the population mean memory score after a meal. Interpret the p-value in the context of the study. If the sample mean memory score for the 10 people who took the test before a meal is the same as the sample mean memory score for the 10 people who took the test after a meal and if another 10 people are given a memory test before and after a meal then there would be a 7% chance of concluding that the mean memory score for the 10 people who took the test before a meal is at least 3.3 points higher than the mean memory score for the 10 people who took the test after a meal. There is a 7% chance of a Type I error. If the population mean memory score before a meal is the same as the population mean memory score after a meal and if another 10 people are given a memory test before and after a meal then there would be a 7% chance that the mean memory score for the 10 people who took the test before a meal would be at least 3.3 points higher than the mean memory score for the 10 people who took the test after a meal. There is a 7% chance that the mean memory score for the 10 people who took the test before a meal is at least 3.3 points higher than the mean memory score for the 10 people who took the test after a meal. Interpret the level of significance in the context of the study. There is a 1% chance that the population mean memory score is the same before and after a meal. There is a 1% chance that your memory is so bad that you have already forgotten what this chapter is about. If the population mean memory score before a meal is the same as the population mean memory score after a meal and if another 10 people are given a memory test before and after a meal, then there would be a 1% chance that we would end up falsely concuding that the sample mean memory scores before and after a meal for these 10 people who were part of the study differ from each other. If the population mean memory score before a meal is the same as the population mean memory score after a meal and if another 10 people are given a memory test before and after a meal, then there would be a 1% chance that we would end up falsely concuding that the population mean memory score before a meal is higher than the population mean memory score after a meal

Is memory ability before a meal better than after a meal? Ten people were given memory tests before their meal and then again after their meal. The data is shown below. A higher score indicates a better memory ability. Score on the Memory Test Before a Meal 66 68 58 70 62 58 81 77 74 66 After a Meal 64 68 52 61 57 71 73 75 66 60 Assume a Normal distribution. What can be concluded at the the αα = 0.01 level of significance? For this study, we should use Select an answer t-test for a population mean t-test for the difference between two dependent population means z-test for the difference between two population proportions t-test for the difference between two independent population means z-test for a population proportion The null and alternative hypotheses would be: H0:H0: Select an answer p1 μ1 μd Select an answer < ≠ = > Select an answer p2 0 μ2 (please enter a decimal) H1:H1: Select an answer μd p1 μ1 Select an answer > < = ≠ Select an answer p2 μ2 0 (Please enter a decimal) The test statistic ? z t = (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 Select an answer accept fail to reject reject the null hypothesis. Thus, the final conclusion is that ... The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the population mean memory score before a meal is higher than the population mean memory score after a meal The results are statistically insignificant at αα = 0.01, so there is statistically significant evidence to conclude that the population mean memory score before a meal is equal to the population mean memory score after a meal. The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the ten memory scores from the memory tests that were taken before a meal are higher on average than the ten memory scores from the memory tests that were taken after a meal. The results are statistically insignificant at αα = 0.01, so there is insufficient evidence to conclude that the population mean memory score before a meal is higher than the population mean memory score after a meal. Interpret the p-value in the context of the study. If the sample mean memory score for the 10 people who took the test before a meal is the same as the sample mean memory score for the 10 people who took the test after a meal and if another 10 people are given a memory test before and after a meal then there would be a 7% chance of concluding that the mean memory score for the 10 people who took the test before a meal is at least 3.3 points higher than the mean memory score for the 10 people who took the test after a meal. There is a 7% chance of a Type I error. If the population mean memory score before a meal is the same as the population mean memory score after a meal and if another 10 people are given a memory test before and after a meal then there would be a 7% chance that the mean memory score for the 10 people who took the test before a meal would be at least 3.3 points higher than the mean memory score for the 10 people who took the test after a meal. There is a 7% chance that the mean memory score for the 10 people who took the test before a meal is at least 3.3 points higher than the mean memory score for the 10 people who took the test after a meal. Interpret the level of significance in the context of the study. There is a 1% chance that the population mean memory score is the same before and after a meal. There is a 1% chance that your memory is so bad that you have already forgotten what this chapter is about. If the population mean memory score before a meal is the same as the population mean memory score after a meal and if another 10 people are given a memory test before and after a meal, then there would be a 1% chance that we would end up falsely concuding that the sample mean memory scores before and after a meal for these 10 people who were part of the study differ from each other. If the population mean memory score before a meal is the same as the population mean memory score after a meal and if another 10 people are given a memory test before and after a meal, then there would be a 1% chance that we would end up falsely concuding that the population mean memory score before a meal is higher than the population mean memory score after a meal

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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Score on the Memory Test

Before a Meal	66	68	58	70	62	58	81	77	74	66
After a Meal	64	68	52	61	57	71	73	75	66	60

Assume a Normal distribution. What can be concluded at the the αα = 0.01 level of significance?

For this study, we should use Select an answer t-test for a population mean t-test for the difference between two dependent population means z-test for the difference between two population proportions t-test for the difference between two independent population means z-test for a population proportion

The null and alternative hypotheses would be:

H0:H0: Select an answer p1 μ1 μd Select an answer < ≠ = > Select an answer p2 0 μ2 (please enter a decimal)

H1:H1: Select an answer μd p1 μ1 Select an answer > < = ≠ Select an answer p2 μ2 0 (Please enter a decimal)

The test statistic ? z t = (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 Select an answer accept fail to reject reject the null hypothesis.
Thus, the final conclusion is that ...
- The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the population mean memory score before a meal is higher than the population mean memory score after a meal
- The results are statistically insignificant at αα = 0.01, so there is statistically significant evidence to conclude that the population mean memory score before a meal is equal to the population mean memory score after a meal.
- The results are statistically significant at αα = 0.01, so there is sufficient evidence to conclude that the ten memory scores from the memory tests that were taken before a meal are higher on average than the ten memory scores from the memory tests that were taken after a meal.
- The results are statistically insignificant at αα = 0.01, so there is insufficient evidence to conclude that the population mean memory score before a meal is higher than the population mean memory score after a meal.
Interpret the p-value in the context of the study.
- If the sample mean memory score for the 10 people who took the test before a meal is the same as the sample mean memory score for the 10 people who took the test after a meal and if another 10 people are given a memory test before and after a meal then there would be a 7% chance of concluding that the mean memory score for the 10 people who took the test before a meal is at least 3.3 points higher than the mean memory score for the 10 people who took the test after a meal.
- There is a 7% chance of a Type I error.
- If the population mean memory score before a meal is the same as the population mean memory score after a meal and if another 10 people are given a memory test before and after a meal then there would be a 7% chance that the mean memory score for the 10 people who took the test before a meal would be at least 3.3 points higher than the mean memory score for the 10 people who took the test after a meal.
- There is a 7% chance that the mean memory score for the 10 people who took the test before a meal is at least 3.3 points higher than the mean memory score for the 10 people who took the test after a meal.
Interpret the level of significance in the context of the study.
- There is a 1% chance that the population mean memory score is the same before and after a meal.
- There is a 1% chance that your memory is so bad that you have already forgotten what this chapter is about.
- If the population mean memory score before a meal is the same as the population mean memory score after a meal and if another 10 people are given a memory test before and after a meal, then there would be a 1% chance that we would end up falsely concuding that the sample mean memory scores before and after a meal for these 10 people who were part of the study differ from each other.
- If the population mean memory score before a meal is the same as the population mean memory score after a meal and if another 10 people are given a memory test before and after a meal, then there would be a 1% chance that we would end up falsely concuding that the population mean memory score before a meal is higher than the population mean memory score after a meal

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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