Question

Recent studies have shown that 53% percent of microchipped dogs when lost are returned to their owners. A local shelter suspects that this percentage is much lower in their region. A random sample of 200 microchipped dogs reported lost was selected. In this sample only 98 were returned. Please write a statement that summarizes your findings from the hypothesis test above.

Answer 1

Solution:
Given in the question
A local shelter suspects that this percentage is much lower in their region
So null and alternate hypothesis can be written as
Null hypothesis H0: p = 0.53
Alternate hypothesis Ha: p < 0.53
Number of sample = 200
Here we will use the Z test as np(0.53*200) = 106 and n(1-p) = (1-0.53)*200 = 94
as we can see that np and n(1-p) are greater 10. So we will use the Z test
Sample proportion (p^)= 98/200 = 0.49
First, we will use the Z test statistic which can be calculated as
Z- test stat = (p^ - p)/sqrt(p*(1-p)/n) = (0.49 - 0.53)/sqrt(0.53*(1-0.53)/200) = -0.04/0.035 = -1.13
From Z table we found p-value as this is left tailed test so P-value = 0.1292
So if we take significance level alpha = 0.05, then we are failed to reject the null hypothesis as the p-value is greater than alpha value(0.1292>0.05). So we don't have significant evidence to support the claim that this percentage is much lower in their region.