One of the questions in a study of marital satisfaction of dual-career couples was to rate the statement, "I'm pleased with the way we divide the responsibilities for childcare." The ratings went from 1 (strongly agree) to 5 (strongly disagree). The table below contains ten of the paired responses for husbands and wives. Conduct a hypothesis test at the 5% level to see if the mean difference in the husband's versus the wife's satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife). Wife's score 3 2 2 3 4 2 1 1 2 4 Husband's score 2 2 1 3 2 1 1 1 2 4 NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part 1) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. Part 2) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) ? = Part 3) Explain how you determined which distribution to use.

Given data, Difference d = husband score –wife score Wife score Husband score difference 3 2 -1 2 2 0 2 1 -1 3 3 0 4 2 -2 2 1 -1 1 1 0 1 1 0 2 2 0 4 4 0 d¯=∑din=-510=-0.5sd=∑di-d¯2n-1=0.7071 Mean = -0.5 Standard deviation = 0.7071 Hypotheses: H0:μd≥0H1:μd<0 Test statistic: t=d¯-μdsdn=-0.5-00.707110=-2.236 p-value: Degree of freedom=n-1=10-1=9 thus, p-value is 0.0261. Decision rule: If p-value ≤α, then reject the null hypothesis. Otherwise, do not reject the null hypothesis. Conclusion: Here, p-value (0.0261) is less than the level of significance (0.05). Therefore, reject the null hypothesis. We can conclude that mean difference in the husband's versus the wife's satisfaction level is negative.

Answered: One of the questions in a study of marital satisfaction of dual-career couples was to rate the statement, "I'm pleased with the way we divide the…

MATLAB: An Introduction with Applications

6th Edition

ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

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Hypothesis Testing- 2 samples

One of the questions in a study of marital satisfaction of dual-career couples was to rate the statement, "I'm pleased with the way we divide the responsibilities for childcare." The ratings went from 1 (strongly agree) to 5 (strongly disagree). The table below contains ten of the paired responses for husbands and wives. Conduct a hypothesis test at the 5% level to see if the mean difference in the husband's versus the wife's satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife).

Wife's score	3	2	2	3	4	2	1	1	2	4
Husband's score	2	2	1	3	2	1	1	1	2	4

NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Part 1) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value.

Part 2) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.

(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
? =

Part 3) Explain how you determined which distribution to use.

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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