Lighthouse Youth 8: Family Services aims to provide vital support and resources to the LGBTQ community in Cleveland, Ohio. They have recently started...

a.    The critical value is 3.841. Since the χ2 test statistic is above the critical value, we fail to reject the null hypothesis. There is insufficient evidence to claim that participation in the host home program and signs of depression are dependent on each other.

b.    The critical value is 0.004. Since the χ2 test statistic is above the critical value, we reject the null hypothesis. There is sufficient evidence to reject the claim that participation in the host home program and signs of depression are independent of each other.

c.    The critical value is 3.841. Since the χ2 test statistic is above the critical value, we reject the null hypothesis. There is sufficient evidence to reject the claim that participation in the host home program and signs of depression are independent of each other.

d.    The critical values are -3.841 and 3.841. Since the χ2 is outside of the critical value range, we fail to reject the null hypothesis. There is insufficient evidence to claim that participation in the host home program and signs of depression are dependent on each other.

e.    The critical value is 7.815. Since the χ2 is above the critical value, we reject the null hypothesis. There is sufficient evidence to reject the claim that participation in the host home program and signs of depression are independent of each other.

Lighthouse Youth 8: Family Services aims to provide vital support and resources to theLGBTQ community in Cleveland, Ohio. They have recently started a host home program to provide emergency housing to homeless LGBTQ youth. Through this program they hope todecrease rates of depression and suicide, which are disproportionately high among this population. After two years of providing this service, Lighthouse conducts a survey of 200community members to assess the effectiveness of this program. They surveyed members ofthe population and collected data on the depression status of those who needed housing butdid not use this program and compared this to the depression status of those who did use theprogram. A summary of the data is shown below. Using a significance level of 0.05,Lighthouse wants to test the claim that whether someone participates in the host home program is independent of whether they exhibit signs of depression. The researchers find thatthe chi-square test statistic for these data is 51.58. Find the critical value(s) for these data andinterpret the findings. Participated in host home program?Yes No Yes 12 80No 68 40 Depression