Homework Help is Here – Start Your Trial Now!
Math
Statistics
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.   Suppose a social psychologist sets out to look at the role of sexual orientation in relationship longevity. He decides to measure marital satisfaction in a group of homosexual couples and a group of heterosexual couples. He 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 homosexual couples as among heterosexual couples. The psychologist thinks that homosexual couples will have less relationship satisfaction than heterosexual couples. He identifies the null and alternative hypotheses as: H₀: μhomosexual coupleshomosexual couples     μheterosexual couplesheterosexual couples   H₁: μhomosexual coupleshomosexual couples     μheterosexual couplesheterosexual couples   This is a     tailed test.   The psychologist collects the data. A group of 31 homosexual couples scored an average of 21.7 with a sample standard deviation of 9 on the Marital Satisfaction Inventory. A group of 30 heterosexual couples scored an average of 25.5 with a sample standard deviation of 12. Use the t distribution table. To use the table, you will first need to calculate the degrees of freedom. The degrees of freedom are    .   The t distribution   Proportion in One Tail             0.25 0.10 0.05 0.025 0.01 0.005   Proportion in Two Tails Combined           df 0.50 0.20 0.10 0.05 0.02 0.01 1 1.000 3.078 6.314 12.706 31.821 63.657 2 0.816 1.886 2.920 4.303 6.965 9.925 3 0.765 1.638 2.353 3.182 4.541 5.841 4 0.741 1.533 2.132 2.776 3.747 4.604 5 0.727 1.476 2.015 2.571 3.365 4.032 6 0.718 1.440 1.943 2.447 3.143 3.707 7 0.711 1.415 1.895 2.365 2.998 3.499 8 0.706 1.397 1.860 2.306 2.896 3.355 9 0.703 1.383 1.833 2.262 2.821 3.250 10 0.700 1.372 1.812 2.228 2.764 3.169 11 0.697 1.363 1.796 2.201 2.718 3.106 12 0.695 1.356 1.782 2.179 2.681 3.055 13 0.694 1.350 1.771 2.160 2.650 3.012 14 0.692 1.345 1.761 2.145 2.624 2.977 15 0.691 1.341 1.753 2.131 2.602 2.947 16 0.690 1.337 1.746 2.120 2.583 2.921 17 0.689 1.333 1.740 2.110 2.567 2.898 18 0.688 1.330 1.734 2.101 2.552 2.878 19 0.688 1.328 1.729 2.093 2.539 2.861 20 0.687 1.325 1.725 2.086 2.528 2.845 21 0.686 1.323 1.721 2.080 2.518 2.831 22 0.686 1.321 1.717 2.074 2.508 2.819 23 0.685 1.319 1.714 2.069 2.500 2.807 24 0.685 1.318 1.711 2.064 2.492 2.797 25 0.684 1.316 1.708 2.060 2.485 2.787 26 0.684 1.315 1.706 2.056 2.479 2.779 27 0.684 1.314 1.703 2.052 2.473 2.771 28 0.683 1.313 1.701 2.048 2.467 2.763 29 0.683 1.311 1.699 2.045 2.462 2.756 30 0.683 1.310 1.697 2.042 2.457 2.750 40 0.681 1.303 1.684 2.021 2.423 2.704 60 0.679 1.296 1.671 2.000 2.390 2.660 120 0.677 1.289 1.658 1.980 2.358 2.617 ∞ 0.674 1.282 1.645 1.960 2.326 2.576   0.50 0.20 0.10 0.05 0.02 0.01   With α = 0.05, 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.)   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.)   Calculate the t statistic. The t statistic is      The t statistic    lie in the critical region for a one-tailed hypothesis test. Therefore, the null hypothesis is    . The psychologist    conclude that homosexual couples have less relationship satisfaction than heterosexual couples.

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.   Suppose a social psychologist sets out to look at the role of sexual orientation in relationship longevity. He decides to measure marital satisfaction in a group of homosexual couples and a group of heterosexual couples. He 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 homosexual couples as among heterosexual couples. The psychologist thinks that homosexual couples will have less relationship satisfaction than heterosexual couples. He identifies the null and alternative hypotheses as: H₀: μhomosexual coupleshomosexual couples     μheterosexual couplesheterosexual couples   H₁: μhomosexual coupleshomosexual couples     μheterosexual couplesheterosexual couples   This is a     tailed test.   The psychologist collects the data. A group of 31 homosexual couples scored an average of 21.7 with a sample standard deviation of 9 on the Marital Satisfaction Inventory. A group of 30 heterosexual couples scored an average of 25.5 with a sample standard deviation of 12. Use the t distribution table. To use the table, you will first need to calculate the degrees of freedom. The degrees of freedom are    .   The t distribution   Proportion in One Tail             0.25 0.10 0.05 0.025 0.01 0.005   Proportion in Two Tails Combined           df 0.50 0.20 0.10 0.05 0.02 0.01 1 1.000 3.078 6.314 12.706 31.821 63.657 2 0.816 1.886 2.920 4.303 6.965 9.925 3 0.765 1.638 2.353 3.182 4.541 5.841 4 0.741 1.533 2.132 2.776 3.747 4.604 5 0.727 1.476 2.015 2.571 3.365 4.032 6 0.718 1.440 1.943 2.447 3.143 3.707 7 0.711 1.415 1.895 2.365 2.998 3.499 8 0.706 1.397 1.860 2.306 2.896 3.355 9 0.703 1.383 1.833 2.262 2.821 3.250 10 0.700 1.372 1.812 2.228 2.764 3.169 11 0.697 1.363 1.796 2.201 2.718 3.106 12 0.695 1.356 1.782 2.179 2.681 3.055 13 0.694 1.350 1.771 2.160 2.650 3.012 14 0.692 1.345 1.761 2.145 2.624 2.977 15 0.691 1.341 1.753 2.131 2.602 2.947 16 0.690 1.337 1.746 2.120 2.583 2.921 17 0.689 1.333 1.740 2.110 2.567 2.898 18 0.688 1.330 1.734 2.101 2.552 2.878 19 0.688 1.328 1.729 2.093 2.539 2.861 20 0.687 1.325 1.725 2.086 2.528 2.845 21 0.686 1.323 1.721 2.080 2.518 2.831 22 0.686 1.321 1.717 2.074 2.508 2.819 23 0.685 1.319 1.714 2.069 2.500 2.807 24 0.685 1.318 1.711 2.064 2.492 2.797 25 0.684 1.316 1.708 2.060 2.485 2.787 26 0.684 1.315 1.706 2.056 2.479 2.779 27 0.684 1.314 1.703 2.052 2.473 2.771 28 0.683 1.313 1.701 2.048 2.467 2.763 29 0.683 1.311 1.699 2.045 2.462 2.756 30 0.683 1.310 1.697 2.042 2.457 2.750 40 0.681 1.303 1.684 2.021 2.423 2.704 60 0.679 1.296 1.671 2.000 2.390 2.660 120 0.677 1.289 1.658 1.980 2.358 2.617 ∞ 0.674 1.282 1.645 1.960 2.326 2.576   0.50 0.20 0.10 0.05 0.02 0.01   With α = 0.05, 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.)   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.)   Calculate the t statistic. The t statistic is      The t statistic    lie in the critical region for a one-tailed hypothesis test. Therefore, the null hypothesis is    . The psychologist    conclude that homosexual couples have less relationship satisfaction than heterosexual couples.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
See similar textbooks
icon
Related questions
Topic Video
Question
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.
 
Suppose a social psychologist sets out to look at the role of sexual orientation in relationship longevity. He decides to measure marital satisfaction in a group of homosexual couples and a group of heterosexual couples. He 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 homosexual couples as among heterosexual couples.
The psychologist thinks that homosexual couples will have less relationship satisfaction than heterosexual couples. He identifies the null and alternative hypotheses as:
H₀: μhomosexual coupleshomosexual couples     μheterosexual couplesheterosexual couples
 
H₁: μhomosexual coupleshomosexual couples     μheterosexual couplesheterosexual couples
 
This is a     tailed test.
 
The psychologist collects the data. A group of 31 homosexual couples scored an average of 21.7 with a sample standard deviation of 9 on the Marital Satisfaction Inventory. A group of 30 heterosexual couples scored an average of 25.5 with a sample standard deviation of 12. Use the t distribution table. To use the table, you will first need to calculate the degrees of freedom.
The degrees of freedom are    .
 
The t distribution
  Proportion in One Tail          
  0.25 0.10 0.05 0.025 0.01 0.005
  Proportion in Two Tails Combined          
df 0.50 0.20 0.10 0.05 0.02 0.01
1 1.000 3.078 6.314 12.706 31.821 63.657
2 0.816 1.886 2.920 4.303 6.965 9.925
3 0.765 1.638 2.353 3.182 4.541 5.841
4 0.741 1.533 2.132 2.776 3.747 4.604
5 0.727 1.476 2.015 2.571 3.365 4.032
6 0.718 1.440 1.943 2.447 3.143 3.707
7 0.711 1.415 1.895 2.365 2.998 3.499
8 0.706 1.397 1.860 2.306 2.896 3.355
9 0.703 1.383 1.833 2.262 2.821 3.250
10 0.700 1.372 1.812 2.228 2.764 3.169
11 0.697 1.363 1.796 2.201 2.718 3.106
12 0.695 1.356 1.782 2.179 2.681 3.055
13 0.694 1.350 1.771 2.160 2.650 3.012
14 0.692 1.345 1.761 2.145 2.624 2.977
15 0.691 1.341 1.753 2.131 2.602 2.947
16 0.690 1.337 1.746 2.120 2.583 2.921
17 0.689 1.333 1.740 2.110 2.567 2.898
18 0.688 1.330 1.734 2.101 2.552 2.878
19 0.688 1.328 1.729 2.093 2.539 2.861
20 0.687 1.325 1.725 2.086 2.528 2.845
21 0.686 1.323 1.721 2.080 2.518 2.831
22 0.686 1.321 1.717 2.074 2.508 2.819
23 0.685 1.319 1.714 2.069 2.500 2.807
24 0.685 1.318 1.711 2.064 2.492 2.797
25 0.684 1.316 1.708 2.060 2.485 2.787
26 0.684 1.315 1.706 2.056 2.479 2.779
27 0.684 1.314 1.703 2.052 2.473 2.771
28 0.683 1.313 1.701 2.048 2.467 2.763
29 0.683 1.311 1.699 2.045 2.462 2.756
30 0.683 1.310 1.697 2.042 2.457 2.750
40 0.681 1.303 1.684 2.021 2.423 2.704
60 0.679 1.296 1.671 2.000 2.390 2.660
120 0.677 1.289 1.658 1.980 2.358 2.617
∞ 0.674 1.282 1.645 1.960 2.326 2.576
  0.50 0.20 0.10 0.05 0.02 0.01
 
With α = 0.05, 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.)
 
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.)
 
Calculate the t statistic. The t statistic is   
 
The t statistic    lie in the critical region for a one-tailed hypothesis test. Therefore, the null hypothesis is    . The psychologist    conclude that homosexual couples have less relationship satisfaction than heterosexual couples.
Expert Solution
Step 1

The following hypothesis can be formed

H0: μhomosexual=μheterosexualHA: μhomosexual<μheterosexual

This is a left tailed test.

 

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Discrete Probability Distributions
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
SEE MORE TEXTBOOKS