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10. The t test for two independent samples - One-tailed example using tables Aa Aa 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 National Center for Health Statistics.] Suppose a social psychologist sets out to look at the role of economic hardship in relationship longevity. She decides to measure marital satisfaction in a group of couples living above the poverty level and a group of couples living below the poverty level. 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 couples living above the poverty level as among couples living below the poverty level. The psychologist thinks that couples living above the poverty level will have greater relationship satisfaction than couples living below the poverty level. She identifies the null and alternative hypotheses as: Ho: Hcouples living above the poverty level Pcouples living below the poverty level H1: Pcouples living above the poverty level Pcouples living below the poverty level This is a tailed test. The psychologist collects the data. A group of 39 couples living above the poverty level scored an average of 51.1 with a sample standard deviation of 9 on the Marital Satisfaction Inventory. A group of 31 couples living below the poverty level scored an average of 45.2 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

10. The t test for two independent samples - One-tailed example using tables Aa Aa 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 National Center for Health Statistics.] Suppose a social psychologist sets out to look at the role of economic hardship in relationship longevity. She decides to measure marital satisfaction in a group of couples living above the poverty level and a group of couples living below the poverty level. 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 couples living above the poverty level as among couples living below the poverty level. The psychologist thinks that couples living above the poverty level will have greater relationship satisfaction than couples living below the poverty level. She identifies the null and alternative hypotheses as: Ho: Hcouples living above the poverty level Pcouples living below the poverty level H1: Pcouples living above the poverty level Pcouples living below the poverty level This is a tailed test. The psychologist collects the data. A group of 39 couples living above the poverty level scored an average of 51.1 with a sample standard deviation of 9 on the Marital Satisfaction Inventory. A group of 31 couples living below the poverty level scored an average of 45.2 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

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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10. The t test for two independent samples - One-tailed example using tables Aa Aa 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 National Center for Health Statistics.] Suppose a social psychologist sets out to look at the role of economic hardship in relationship longevity. She decides to measure marital satisfaction in a group of couples living above the poverty level and a group of couples living below the poverty level. 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 couples living above the poverty level as among couples living below the poverty level. The psychologist thinks that couples living above the poverty level will have greater relationship satisfaction than couples living below the poverty level. She identifies the null and alternative hypotheses as: Ho: Pcouples living above the poverty level Pcouples living below the poverty level H1: Pcouples living above the poverty level Pcouples living below the poverty level This is a tailed test. The psychologist collects the data. A group of 39 couples living above the poverty level scored an average of 51.1 with a sample standard deviation of 9 on the Marital Satisfaction Inventory. A group of 31 couples living below the poverty level scored an average of 45.2 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
Transcribed Image Text:10. The t test for two independent samples - One-tailed example using tables Aa Aa 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 National Center for Health Statistics.] Suppose a social psychologist sets out to look at the role of economic hardship in relationship longevity. She decides to measure marital satisfaction in a group of couples living above the poverty level and a group of couples living below the poverty level. 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 couples living above the poverty level as among couples living below the poverty level. The psychologist thinks that couples living above the poverty level will have greater relationship satisfaction than couples living below the poverty level. She identifies the null and alternative hypotheses as: Ho: Pcouples living above the poverty level Pcouples living below the poverty level H1: Pcouples living above the poverty level Pcouples living below the poverty level This is a tailed test. The psychologist collects the data. A group of 39 couples living above the poverty level scored an average of 51.1 with a sample standard deviation of 9 on the Marital Satisfaction Inventory. A group of 31 couples living below the poverty level scored an average of 45.2 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
With a = .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 (Hint: For the most precise results, retain four decimal places from your previous calculation to calculate the t statistic.) The t statistic lie in the critical region for a one-tailed hypothesis test. Therefore, the null hypothesis is The psychologist conclude that couples living above the poverty level have greater relationship satisfaction than couples living below the poverty level.
Transcribed Image Text:With a = .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 (Hint: For the most precise results, retain four decimal places from your previous calculation to calculate the t statistic.) The t statistic lie in the critical region for a one-tailed hypothesis test. Therefore, the null hypothesis is The psychologist conclude that couples living above the poverty level have greater relationship satisfaction than couples living below the poverty level.
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