Question

4)According to the American Society for the Prevention of Cruelty to Animals 37% of cats entering shelters are adopted. A local cat lover wants to see if the percentage of cats adopted is different at her local shelters. She randomly selects the records for 80 cats from three different local shelters and finds that 40% were adopted. Does her sample give evidence that the adoption rate at her local shelters is different ? Use a significance level of ?=0.05.

a)State the hypotheses in symbols. (2points)

b)Run the test and report the test statistic and p-value. Be sure to write out what you entered in your calculator. (3points)

c)Write a full conclusion for this test in the context of the problem. (2points)

d)Find a 90% confidence interval for the proportion of cats adopted from the local shelters. Be sure to write out what you entered in your calculator. (3points)

e)Does this confidence interval support your conclusion in part (e)? Explain. (2points)

Answer 1

a) As we are testing here whether the percentage of cats adopted is different at her local shelters, therefore the null and the alternative hypothesis here are given as:

b) We are given the sample size here as n = 80 and the sample proportion as p = 0.4. The test statistic here is computed as:

Therefore 0.5558 is the test statistic value here.

As this is a two tailed test, the p-value here is computed from the standard normal tables as:
p = 2P(Z > 0.5558) = 2*0.2892 = 0.5784

Therefore 0.5784 is the required p-value here.

c) As the p-value here is 0.5784 > 0.05 which is the level of significance, therefore the test is not significant here and we cannot reject the null hypothesis here. therefore we have insufficient evidence here that the percentage of cats adopted is different at her local shelters

d) From standard normal tables, we have here:
P(-1.645 < Z < 1.645) = 0.9

Therefore the confidence interval here is obtained as:

This is the required 90% confidence interval here.

e) As the confidence interval does contain 0.37 here therefore we dont have sufficient evidence here that the proportion is different from 0.37, which is same as what we got from the hypothesis test.