Question

A researcher is interested in investigating whether living situation and pet ownership are dependent. The table below shows the results of a survey. Frequencies of Living Situation and Pet Single Family Couple 85 81 93 Cat 116 70 90 Various 37 51 46 None 53 53 32 What can be concluded at the a=0.10 significance level? Dog a. What is the correct statistical test to use? Goodness-of-Fit Independence Homogeneity Paired t-test b. What are the null and alternative hypotheses? HO: The distribution of pets is not the same for each living situation. The distribution of pets is the same for each living situation. Pet ownership and living situation are independent. Pet ownership and living situation are dependent. Pet ownership and living situation are dependent. The distribution of pets is the same for each living situation Pet ownership and living situation are independent. The distribution of pets is not the same for each living situation. C. The test-statistic for this data (Please show your answer to three decimal places.) d. The p-value for this sample (Please show your answer to four decimal places.) e. The p-value is Select an answer

Answer 1

Ans.

(a) Correct statistical test - Independence

(b). Null and Alternative hypothesis:-

H₀ : Pet ownership and living situation are independent.

H₁ : Pet ownership and living situation are dependent.

Note:- We test this question using MINITAB:-

Steps:-

1    Choose Stat > Tables > Chi-Square Test (Table in Worksheet).

2    In Columns containing the table, enter the columns containing the contingency table data. Click OK.

Result:-

Chi-Square Test: Single, Family, Couple Expected counts are printed below observed counts Chi-Square contributions are printed below expected counts Total 259 Dog Single Family 85 81 93.39 81.84 0.754 0.009 Couple 93 83.77 1.018 Cat 276 6 116 99.52 2.728 70 87.21 3.397 90 89.26 0.006 Various 134 37 48.32 2.652 51 42.34 1.770 46 43.34 0.163 None 138 53 49.76 0.211 53 43.61 2.024 32 44.63 3.575 Total 291 255 261 807 Chi-Sq = 18.307, DF = 6, P-Value = 0.0055

(c). Test Statistics:-

Chi-square = 18.307

(d). P-value:-

P-value = 0.0055

(e) P-value is less than $\alpha=0.10$

Reject H₀