Do the poor spend more time in the shower than the rich? The results of a survey asking poor and rich people how many minutes they spend in the shower are shown below. Poor 10 14 16 24 30 23 19 40 27 40 19 Rich: 11 20 14 2 22 23 21 5 3 17 16 23 24 Assume both follow a Normal distribution. What can be concluded at the the αα = 0.05 level of significance level of significance? 1. 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 ? t-test for the difference between two independent population means? z-test for a population proportion? or z-test for the difference between two population proportions? 2. The null and alternative hypotheses would be: H0: Select an answer μ1 or p1 ? Select an answer >, =, <, or ≠ ? Select an answer p2 or μ2 ? (please enter a decimal) H1: Select an answer: μ1 or p1 ? Select an answer ≠, =, >, or < ? Select an answer μ2 or p2 ? 3. The test statistic : t or z ? =_______ (please show your answer to 3 decimal places.) 4. The p-value = ______ (Please show your answer to 4 decimal places.) 5. The p-value is ? ≤ or > 6. Based on this, we should? Select an answer accept? fail to reject? or reject? the null hypothesis. 7. Thus, the final conclusion is that ... The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the population mean time in the shower for the poor is more than the population mean time in the shower for the rich. The results are statistically insignificant at αα = 0.05, so there is insufficient evidence to conclude that the population mean time in the shower for the poor is more than the population mean time in the shower for the rich. The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the mean time in the shower for the eleven poor people that were surveyed is more than the mean time in the shower for the thirteen rich people that were surveyed. The results are statistically insignificant at αα = 0.05, so there is statistically significant evidence to conclude that the population mean time in the shower for the poor is equal to the population mean time in the shower for the rich.

Do the poor spend more time in the shower than the rich? The results of a survey asking poor and rich people how many minutes they spend in the shower are shown below. Poor 10 14 16 24 30 23 19 40 27 40 19 Rich: 11 20 14 2 22 23 21 5 3 17 16 23 24 Assume both follow a Normal distribution. What can be concluded at the the αα = 0.05 level of significance level of significance? 1. 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 ? t-test for the difference between two independent population means? z-test for a population proportion? or z-test for the difference between two population proportions? 2. The null and alternative hypotheses would be: H0: Select an answer μ1 or p1 ? Select an answer >, =, <, or ≠ ? Select an answer p2 or μ2 ? (please enter a decimal) H1: Select an answer: μ1 or p1 ? Select an answer ≠, =, >, or < ? Select an answer μ2 or p2 ? 3. The test statistic : t or z ? =_ (please show your answer to 3 decimal places.) 4. The p-value = (Please show your answer to 4 decimal places.) 5. The p-value is ? ≤ or > 6. Based on this, we should? Select an answer accept? fail to reject? or reject? the null hypothesis. 7. Thus, the final conclusion is that ... The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the population mean time in the shower for the poor is more than the population mean time in the shower for the rich. The results are statistically insignificant at αα = 0.05, so there is insufficient evidence to conclude that the population mean time in the shower for the poor is more than the population mean time in the shower for the rich. The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the mean time in the shower for the eleven poor people that were surveyed is more than the mean time in the shower for the thirteen rich people that were surveyed. The results are statistically insignificant at αα = 0.05, so there is statistically significant evidence to conclude that the population mean time in the shower for the poor is equal to the population mean time in the shower for the rich.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Do the poor spend more time in the shower than the rich? The results of a survey asking poor and rich people how many minutes they spend in the shower are shown below.

Poor 10 14 16 24 30 23 19 40 27 40 19

Rich: 11 20 14 2 22 23 21 5 3 17 16 23 24

Assume both follow a Normal distribution. What can be concluded at the the αα = 0.05 level of significance level of significance?

1. 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 ? t-test for the difference between two independent population means? z-test for a population proportion? or z-test for the difference between two population proportions?

2. The null and alternative hypotheses would be:

H0: Select an answer μ1 or p1 ? Select an answer >, =, <, or ≠ ? Select an answer p2 or μ2 ? (please enter a decimal)

H1: Select an answer: μ1 or p1 ? Select an answer ≠, =, >, or < ? Select an answer μ2 or p2 ?

3. The test statistic : t or z ? =_______ (please show your answer to 3 decimal places.)

4. The p-value = ______ (Please show your answer to 4 decimal places.)

5. The p-value is ? ≤ or >

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

7. Thus, the final conclusion is that ...

The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the population mean time in the shower for the poor is more than the population mean time in the shower for the rich.
The results are statistically insignificant at αα = 0.05, so there is insufficient evidence to conclude that the population mean time in the shower for the poor is more than the population mean time in the shower for the rich.
The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the mean time in the shower for the eleven poor people that were surveyed is more than the mean time in the shower for the thirteen rich people that were surveyed.
The results are statistically insignificant at αα = 0.05, so there is statistically significant evidence to conclude that the population mean time in the shower for the poor is equal to the population mean time in the shower for the rich.

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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