hi i just need the fill in the blanks not answered **10. The t test for two independent samples - One-tailed example using tables**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:- **H₀**: μ (couples living above the poverty level) ≤ μ (couples living below the poverty level)- **H₁**: μ (couples living above the poverty level) > μ (couples living below the poverty level)This is a **one-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 **68**. **Title: Understanding the Critical t-Score and Calculating the t Statistic**With a significance level ($\alpha$) of 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 **1.995**.**Note:** If your degrees of freedom (df) value is not included in the standard 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.**Calculating the t Statistic:**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.- **Pooled Variance:** _________- **Estimated Standard Error of the Difference in Means:** _________ **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.**Conclusion:**The t statistic **__________** lie in the critical region for a one-tailed hypothesis test. Therefore, the null hypothesis is **_____________**. The psychologist **________** concludes that couples living above the poverty level have greater relationship satisfaction than couples living below the poverty level.

The claim of the test is that the couples living above the poverty level will have greater relationship satisfaction than couples living below the poverty level. The hypothesis is, Null hypothesis: H0:μcouples living above the poverty level≤μcouples living below the poverty level Alternative hypothesis: H1:μcouples living above the poverty level>μcouples living below the poverty level The alternative indicated that the test is one tailed(Right tail) test. Thus, the test is one-tailed test. From the data, the values are n1=39,x¯1=51.1,s1=9,n2=31,x¯2=45.2,s2=12. The degrees of freedom is, df=n1+n2-2=39+31-2=68 Thus, the degrees of freedom is 68. The alpha value is 0.05. Computation of critical value: The critical value of t-distribution at 68 degrees of freedom can be obtained using the excel formula “=T.INV(0.05,68)”. The critical value is -1.6676 which is left tailed critical value, then the right tailed critical value is 1.6676. Thus, the critical t-score is 1.6676.The pooled variance is, sp2=n1-1s12+n2-1s22n1+n2-2=39-192+31-112239+31-2=7,39868=108.7941 Thus, the pooled variance is 108.7941. The estimated standard error of the difference in means is, SE=sp21n1+1n2=108.7941139+131=2.5098 Thus, the estimated standard error of the difference in means is 2.5098. The t statistic is, t=x¯1-x¯2SE=51.1-45.22.5098=5.92.5098=2.3508 Thus, the t statistic is 2.3508. Decision rule: If test statistic > critical value, then reject the null hypothesis. Otherwise, do not reject the null hypothesis. The t statistic does not(greater than) lie in the critical region for a one-tailed hypothesis test. Therefore, the null hypothesis is rejected. The psychologist can conclude that couples living above poverty level have greater relationship satisfaction than couples living below the poverty level.

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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 one- tailed test.

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 one- tailed test.

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

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Question

hi i just need the fill in the blanks not answered

**10. The t test for two independent samples - One-tailed example using tables**

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:

- **H₀**: μ (couples living above the poverty level) ≤ μ (couples living below the poverty level)
- **H₁**: μ (couples living above the poverty level) > μ (couples living below the poverty level)

This is a **one-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 **68**.

**Title: Understanding the Critical t-Score and Calculating the t Statistic**

With a significance level ($\alpha$) of 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 **1.995**.

**Note:** If your degrees of freedom (df) value is not included in the standard 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.

**Calculating the t Statistic:**
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.

- **Pooled Variance:** _________
- **Estimated Standard Error of the Difference in Means:** _________

**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.

**Conclusion:**
The t statistic **__________** lie in the critical region for a one-tailed hypothesis test.

Therefore, the null hypothesis is **_____________**.

The psychologist **________** concludes that couples living above the poverty level have greater relationship satisfaction than couples living below the poverty level.

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