Question

The government of Preon (a small island nation) was voted in at the last election with 70% of the votes. That was 2 years ago, and ever since then the government has assumed that their approval rating has been the same. Some recent events have affected public opinion and the government suspects that their approval rating might have changed. They decide to run a hypothesis test for the proportion of people who would still vote for them. The null and alternative hypotheses are: Ho: p = 0.70 Ha: p 0.70 The level of significance used in the test is a = 0.1. A random sample of 115 people are asked whether or not they would still vote for the government. The proportion of people that would is equal to 0.757. a) Calculate the test statistic (z) for this hypothesis test. Give your answer to 3 decimal places. z = b) According to this test statistic, you should the null hypothesis.

Answer 1

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho:p = 0.70 Ha:p + 0.70 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 = 0.10, and the critical value for a two-tailed test is zc 1.64. The rejection region for this two-tailed test is R= {z : [2] > 1.64} (3) Test Statistics The Z-statistic is computed as follows: z = P – Po V Po(1 – po)/n 0.75 -0.70 0.70(1 – 0.70)/115 1.334 (4) Decision about the null hypothesis < ze = 1.64, it is then concluded that the Since it is observed that |z1 = 1.3: null hypothesis is not rejected.

please like ??