The research department of Petco did a study to determine if there was a differe
ID: 3200271 • Letter: T
Question
The research department of Petco did a study to determine if there was a difference in the proportion of adults who preferred dogs as a pet vs the proportion of children who preferred dogs as a pet. At the .05 significance level, is there a significant difference in the proportions of the preference for dogs as a pet between Adults vs Children? (Use z or t value of 1.31) 120 out of 200 Adults preferred dogs as a pet. 165 out of 250 Children who preferred dogs as a pet. What is the Rejection Region? Reject Ho if z > 2.58 Reject Ho if z < -1.65 Reject Ho if -1.28 > z > 1.28 Reject Ho if -1.96 > z > 1.96
Explanation / Answer
Solution:
p1 = 120/200 = 0.60
n1 = 200
p2 = 165/250 = 0.66
n2 = 250
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P1 = P2
Alternative hypothesis: P1 P2
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the proportion from population 1 is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.
Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).
p = (p1 * n1 + p2 * n2) / (n1 + n2)
p = 0.63333
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.04572
z = (p1 - p2) / SE
z = - 1.31234
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Since we have a two-tailed test, the P-value is the probability that the z-score is less than - 1.31 or greater than 1.31.
Thus, the P-value = 0.0951 + 0.0951 = 0.1902
Rejection re/ion:-
zcritical = 1.96
Reject Ho if -1.96 > z > 1.96
Interpret results. Since the P-value (0.1902) is more than significance level (0.05) so we have to accept the nul hypothesis.
From this we can conclude we do not have sufficient evidence in the favor of the claim that there a significant difference in the proportions of the preference for dogs as a pet between Adults vs Children.