## Assignment Instructions

1. Test the hypothesis that as education increases the number of children one has decreases. Is there an association between education and the number of children?

2. The city council is considering a law that would ban smoking in all public facilities. A sample has been selected from the community and tested for support of the ordinance. Is there a statistically significant relationship between age and support for the anti-smoking law? Use the five-step model as a guide and write a sentence or two interpreting your results.

3. Does the number of times a person attends religious services (attend) vary by religious preference (relig)?

In selecting the appropriate test or procedure, you need to consider the question, the number of samples or categories being compared, and the level of measurement of the variables. To answer the question, you will need to use the GSS 2008 dataset (gss08pfp-a.sav). You can download it from the course’s website or get it from me. The dataset is identified as the “GSS dataset for Exam 3”.

Please submit your computer output with your neatly written answer.

## Assignment Solution

**Answer 1:
**

Null hypothesis: There exists no relationship between education and the number of children one has.

Alternate hypothesis: As education increases the number of children one has decreases.

Significance level: 5% alpha level is used.

The test statistic: The value of the correlation coefficient from the table given is -0.228 and its p-value (two-tailed) is 0. Dividing this p-value by 0, we can get a one-tailed p-value which is also equal to zero.

Decision: Since the p-value is less than 0.05 at a 5% alpha level, we reject the null hypothesis and since the value of the correlation coefficient is negative, we can conclude that as education increases the number of children one has decreases.

Interpretation: The negative value of the correlation coefficient shows that as education increases the number of children one has decreases. However, the value of the correlation coefficient at 0.228 is close to zero, suggesting that the relationship is not very strong.

**Answer 2:
**

Null hypothesis: There exists no relationship between age and support for the anti-smoking law.

Alternate hypothesis: There exists a relationship between age and support for the anti-smoking law.

Significance level; 5% alpha level is used.

Test statistic:

Chi-square statistic =

= 0.0602 + 0.073 + 0.4866 + 0.5895 = 1.2092

The p-value for chi-square=1.2092 at 1 ((2-1)*(2-1)) degrees of freedom is 0.2715.

Decision: Since the p-value is larger than 0.05 at a 5% alpha level, we cannot reject the null hypothesis.

Interpretation: The results in the above analysis conclude that we cannot reject the null hypothesis which means that there exists no relationship between age and support for the anti-smoking law.
**Answer 3:
**

Null hypothesis: The number of times a person attends religious services (attend) does not vary by religious preference (relig).

Alternate hypothesis: The number of times a person attends religious services (attend) vary by religious preference (relig).

Significance level; 5% alpha level is used.

Test statistic:

Since the “attend” variable is an ordinal scale variable with 0 meaning “never” and 8 meaning “More than once a week” and the religious preference (relig) variable is a categorical variable with many categories, we use chi-square statistic to conduct the analysis and the results from SPSS are presented below:

Value | df | Asymp. Sig. (2-sided) | |

Pearson Chi-Square | 482.136a | 88 | .000 |

Likelihood Ratio | 493.244 | 88 | .000 |

Linear-by-Linear Association | 84.248 | 1 | .000 |

N of Valid Cases | 1488 | 1 |

One of the important assumptions of Pearson chi-square states that at least 80% of the cells should have an expected count of more than 5. However, as stated in the table from SPSS, 74 cells (68.5%) have an expected count of less than 5, and thus, the Likelihood ratio test is used to test the hypothesis.

The results show that the p-value is close to zero.

Decision: Since the p-value is less than 0.05 at a 5% alpha level, we reject the null hypothesis.

Interpretation: The results in the above analysis conclude that we reject the null hypothesis which means that the number of times a person attends religious services (attend) varies by religious preference (relig).