Question

After spending months collecting data on ferrets the cryptozoologist has a suspicion that along the front range, ferrets make up 3% of the rodent population.

One month, in his catch and release traps, the CZ caught 2156 = n rodents and captures 188 = n ferrets. Is the CZ's suspicion about the proportion of rodents that are ferrets correct? ( use α =.05)

Answer 1

The following information is provided: The sample size is N = 188, the number of favorable cases is X = 2156, and the sample proportion is p = 11.4681, and the significance level is a = 0.05 X N 2156 188 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: p= 0.03 Ha :P + 0.03 This corresponds to a two-tailed test, for which a z-test for one population proportion needs to be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.05, and the critical value for a two-tailed test is ze 1.96. The rejection region for this two-tailed test is R = {z: 121 > 1.96} (3) Test Statistics The Z-statistic is mputed as follows: z = P - PO V po(1 – po)/n 11.4681 – 0.03 10.03(1 – 0.03)/188 919.36 .(4) Decision about the null hypothesis Since it is observed that |z= 919.36 > ze = 1.96, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p = 0, and since p= 0 < 0.05, it is concluded that the null hypothesis is rejected. (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population proportion p is different than po, at the a = 0.05 significance level.

please like ??