Question

A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes to help the public schools. The opinion poll recently sampled 1500 voting age citizens. 622 of the sampled citizens were in favor of an increase in taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than 66%. At what level of significance will the null hypothesis not be rejected?

Answer 1

na ses The following null and alternative hypotheses need to be tested Ho:p<0.66 Ha:p 0.66 This corresponds to a right-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 α = 0.05, and the critical value for a right-tailed test is1.64. The rejection region for this right-tailed test is R 1.64) The z-statistic is computed as follows Po 0.4147-0.66 一一20.058 Since it is observed that20.058 1.64, it is then concluded that the null hypothesis is not rejected Using the P-value approach. The p-value is p = 1, and since p = 1 > 0.05, it is concluded that the null hypothesis is not rejected (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion p is greater than po, at the a 0.05 significance level. The 95% confidence interval for p is: 0.39 p 0.44

Wont be rejected at any level as p = 1