Question

1. 15 pts) Below is a 2x2 contingency table presenting data related to grade level and owning a cell phone.

Cell Phone?	11th grade	12th grade	Total
Yes	59	50	109
No	6	3	9
Total	65	53	118

Conduct a hypothesis test to determine if having a cell phone is independent of one’s grade level.

1. (3 pts) State the hypotheses.

2. (3 pt) State the test statistic.

3. (3 pt) State the p-value.

4. (3 pt) State your decision.

5. (3 pts) State your conclusion.

Answer 1

Since the level of significance is not provided assuming it to be 5%.

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: H0​: The two variables are independent i.e. having a cell phone is independent of one’s grade level Ha​: The two variables are dependent i.e. having a cell phone is not independent of one’s grade level This corresponds to a Chi-Square test of independence. Degrees of Freedom The number of degrees of freedom is df = (2 - 1) * (2 - 1) = 1 Critical value and Rejection Region Based on the information provided, the significance level is α=0.05, the number of degrees of freedom is df = (2 - 1) * (2 - 1) = 1, so the critical value is 3.8415. Then the rejection region for this test becomes R={χ2:χ2>3.8415}. (2)Test Statistics The Chi-Squared statistic is computed as follows: (3)P-value The corresponding p-value for the test is p=Pr(χ2​>0.5282)=0.4673 (4)Decision about the null hypothesis Since it is observed that χ2=0.5282<χ2_c​rit=3.8415, it is then concluded that the null hypothesis is NOT rejected. (5)Conclusion It is concluded that the null hypothesis Ho is NOT rejected. Therefore, there is NOT enough evidence to claim that the two variables having a cell phone and grade level are dependent, at the 0.05 significance level. Conditions: a. The sampling method is simple random sampling. b. The data in the cells should be counts/frequencies c. The levels (or categories) of the variables are mutually exclusive.

Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!