Question

1. 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. Using a 0.10 significance level determine if the percentage of microchipped dogs returned is significantly lower in this region?

2. what is the z stat and p value ?
3. Do we reject or retain ?
4. Please write a statement that summarizes your findings from the hypothesis test above

Answer 1

Ho : p = 0.53 Vs H1 : p < 0.53

Test statistic Z

Z = (p^ - p)/sqrt[p*(1-p)/n]

Where p^ = 98/200 = 0.49

Z = ( 0.49-0.53)/[0.53*0.47/200]

Z = -1.13

p-value = P( Z < -1.13)

p-value = 0.1292

Decision rule : if p-value < a we reject the null hypothesis otherwise we retain the null hypothesis

Our p-value = 0.1292 > 0.10

Decision : we retain the null hypothesis

Conclusion : There is no sufficient evidence to support the claim the percentage of microchipped dogs returned is significantly lower in this region