Most engaged couples expect or at least hope that they will have high levels of marital satisfaction. However, because 54% of first marriages end in divorce, social scientists have begun investigating influences on marital satisfaction. [Data source: This data was obtained from the National Center for Health Statistics.]   Suppose a social psychologist sets out to look at the role of race in relationship longevity. She decides to measure marital satisfaction in a group of African American couples and a group of Latino couples. She chooses the Marital Satisfaction Inventory, because it refers to “partner” and “relationship” rather than “spouse” and “marriage,” which makes it useful for research wit

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Take your time answer the questions, this is all one question, please answer correctly, thank you very much, will write an wonderful review when solutions are done. For the following question, this is all part of the same question, they are not different questions, its just that this question is long and the screenshots were not allowing to fully get the question, so their are two images along with a text. This question has 3 parts underneath this text is the first part of the quesiton then the images are the second and third part. Bartleby allows me only to insert two images so that is why I cant put all of the question in the same screenshot. Thank you :)

Most engaged couples expect or at least hope that they will have high levels of marital satisfaction. However, because 54% of first marriages end in divorce, social scientists have begun investigating influences on marital satisfaction. [Data source: This data was obtained from the National Center for Health Statistics.]
 
Suppose a social psychologist sets out to look at the role of race in relationship longevity. She decides to measure marital satisfaction in a group of African American couples and a group of Latino couples. She chooses the Marital Satisfaction Inventory, because it refers to “partner” and “relationship” rather than “spouse” and “marriage,” which makes it useful for research with both traditional and nontraditional couples. Higher scores on the Marital Satisfaction Inventory indicate greater satisfaction. There is one score per couple. Assume that these scores are normally distributed and that the variances of the scores are the same among African American couples as among Latino couples.

 

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24
25
26
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30
40
60
120
0.690
0.689
0.688
0.688
0.687
0.686
0.686
0.685
0.685
0.684
0.684
0.684
0.683
0.683
0.683
0.681
0.679
0.677
0.674
0.50
1.337 1.746 2.120 2.583 2.921
2.110 2.567 2.898
2.552 2.878
1.333 1.740
1.330 1.734 2.101
1.328 1.729 2.093
2.539
2.861
1.325 1.725 2.086
2.528 2.845
1.323 1.721 2.080 2.518 2.831
1.321 1.717 2.074 2.508 2.819
2.500 2.807
1.319 1.714 2.069
1.318
1.711
2.064
2.492
2.797
1.316 1.708 2.060
2.485
2.787
1.315 1.706 2.056
2.479
2.779
1.314 1.703 2.052 2.473 2.771
1.313 1.701 2.048
2.467 2.763
1.311 1.699 2.045
2.462
2.756
1.310 1.697 2.042
2.457
1.303 1.684 2.021
2.423
1.296 1.671 2.000
2.390
2.358
1.289 1.658
1.282 1.645
0.10
1.980
1.960 2.326
0.20
0.05
0.02
With a = 0.01, the critical t-score (the value for a t-score that separates the tail from the main body of the distribution, forming the critical region)
is
▼. (Note: If your df value is not included in this table, look up the critical values for both surrounding df values and select the larger
t value to use as your critical t-score. If you fail to reject the null hypothesis, you can later check the smaller t value to decide whether to
interpolate. However, for the purposes of this problem, you can just assume that if your t statistic is not more extreme than the larger t value,
you will not reject the null hypothesis. Also, the table includes only positive t values. Since the t distribution is symmetrical, for a one-tailed test
where the alternative hypothesis is less than, simply negate the t value provided in the table.)
Calculate the t statistic. The t statistic is
to calculate the t statistic.)
The t statistic
psychologist
2.750
2.704
2.660
2.617
2.576
0.01
To calculate the t statistic, you first need to calculate the estimated standard error of the difference in means. To calculate this estimated
standard error, you first need to calculate the pooled variance. The pooled variance is
▼. The estimated standard error of the
difference in means is
▼. (Hint: For the most precise results, retain four decimal places from your calculation of the pooled variance
to calculate the standard error.)
.(Hint: For the most precise results, retain four decimal places from your previous calculation
▼lie in the critical region for a one-tailed hypothesis test. Therefore, the null hypothesis is
conclude that African American couples have less relationship satisfaction than Latino couples.
. The
Transcribed Image Text:16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 0.690 0.689 0.688 0.688 0.687 0.686 0.686 0.685 0.685 0.684 0.684 0.684 0.683 0.683 0.683 0.681 0.679 0.677 0.674 0.50 1.337 1.746 2.120 2.583 2.921 2.110 2.567 2.898 2.552 2.878 1.333 1.740 1.330 1.734 2.101 1.328 1.729 2.093 2.539 2.861 1.325 1.725 2.086 2.528 2.845 1.323 1.721 2.080 2.518 2.831 1.321 1.717 2.074 2.508 2.819 2.500 2.807 1.319 1.714 2.069 1.318 1.711 2.064 2.492 2.797 1.316 1.708 2.060 2.485 2.787 1.315 1.706 2.056 2.479 2.779 1.314 1.703 2.052 2.473 2.771 1.313 1.701 2.048 2.467 2.763 1.311 1.699 2.045 2.462 2.756 1.310 1.697 2.042 2.457 1.303 1.684 2.021 2.423 1.296 1.671 2.000 2.390 2.358 1.289 1.658 1.282 1.645 0.10 1.980 1.960 2.326 0.20 0.05 0.02 With a = 0.01, the critical t-score (the value for a t-score that separates the tail from the main body of the distribution, forming the critical region) is ▼. (Note: If your df value is not included in this table, look up the critical values for both surrounding df values and select the larger t value to use as your critical t-score. If you fail to reject the null hypothesis, you can later check the smaller t value to decide whether to interpolate. However, for the purposes of this problem, you can just assume that if your t statistic is not more extreme than the larger t value, you will not reject the null hypothesis. Also, the table includes only positive t values. Since the t distribution is symmetrical, for a one-tailed test where the alternative hypothesis is less than, simply negate the t value provided in the table.) Calculate the t statistic. The t statistic is to calculate the t statistic.) The t statistic psychologist 2.750 2.704 2.660 2.617 2.576 0.01 To calculate the t statistic, you first need to calculate the estimated standard error of the difference in means. To calculate this estimated standard error, you first need to calculate the pooled variance. The pooled variance is ▼. The estimated standard error of the difference in means is ▼. (Hint: For the most precise results, retain four decimal places from your calculation of the pooled variance to calculate the standard error.) .(Hint: For the most precise results, retain four decimal places from your previous calculation ▼lie in the critical region for a one-tailed hypothesis test. Therefore, the null hypothesis is conclude that African American couples have less relationship satisfaction than Latino couples. . The
The psychologist thinks that African American couples will have less relationship satisfaction than Latino couples. She identifies the null and
alternative hypotheses as:
Ho: HAfrican American couples
H₁: HAfrican American couples
This is a
tailed test.
The degrees of freedom are
The t distribution
The psychologist collects the data. A group of 25 African American couples scored an average of 26.3 with a sample standard deviation of 8 on
the Marital Satisfaction Inventory. A group of 23 Latino couples scored an average of 20.3 with a sample standard deviation of 9. Use the t
distribution table. To use the table, you will first need to calculate the degrees of freedom.
df
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Latino couples
Latino couples
Proportion in One Tail
0.25
Proportion in Two Tails Combined
0.50
1.000
0.816
0.765
0.741
0.727
0.718
0.711
0.706
0.703
0.700
0.697
0.695
0.694
0.692
0.691
0.10
0.05 0.025
0.01
0.005
0.02
0.20 0.10
0.05
3.078 6.314 12.706 31.821 63.657
1.886 2.920 4.303
6.965
9.925
1.638 2.353 3.182 4.541
5.841
3.747 4.604
4.032
3.707
3.499
1.533 2.132 2.776
1.476 2.015 2.571 3.365
1.440 1.943 2.447 3.143
1.415 1.895 2.365 2.998
1.397 1.860 2.306 2.896
1.383 1.833 2.262 2.821
2.228 2.764 3.169
2.718
3.355
3.250
1.372 1.812
1.363 1.796 2.201
3.106
1.356 1.782 2.179
2.681
3.055
2.650
3.012
1.350 1.771 2.160
1.345 1.761 2.145
2.624 2.977
1.341 1.753 2.131
2.602
2.947
0.01
Transcribed Image Text:The psychologist thinks that African American couples will have less relationship satisfaction than Latino couples. She identifies the null and alternative hypotheses as: Ho: HAfrican American couples H₁: HAfrican American couples This is a tailed test. The degrees of freedom are The t distribution The psychologist collects the data. A group of 25 African American couples scored an average of 26.3 with a sample standard deviation of 8 on the Marital Satisfaction Inventory. A group of 23 Latino couples scored an average of 20.3 with a sample standard deviation of 9. Use the t distribution table. To use the table, you will first need to calculate the degrees of freedom. df 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Latino couples Latino couples Proportion in One Tail 0.25 Proportion in Two Tails Combined 0.50 1.000 0.816 0.765 0.741 0.727 0.718 0.711 0.706 0.703 0.700 0.697 0.695 0.694 0.692 0.691 0.10 0.05 0.025 0.01 0.005 0.02 0.20 0.10 0.05 3.078 6.314 12.706 31.821 63.657 1.886 2.920 4.303 6.965 9.925 1.638 2.353 3.182 4.541 5.841 3.747 4.604 4.032 3.707 3.499 1.533 2.132 2.776 1.476 2.015 2.571 3.365 1.440 1.943 2.447 3.143 1.415 1.895 2.365 2.998 1.397 1.860 2.306 2.896 1.383 1.833 2.262 2.821 2.228 2.764 3.169 2.718 3.355 3.250 1.372 1.812 1.363 1.796 2.201 3.106 1.356 1.782 2.179 2.681 3.055 2.650 3.012 1.350 1.771 2.160 1.345 1.761 2.145 2.624 2.977 1.341 1.753 2.131 2.602 2.947 0.01
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