b) A poll showed the approval rating to be 0.47(47%). A second poll based on 2000 randomly selected voters showed that 938 approved of the job the president was doing. Do the results of the second poll indicate that the proportion of voters who approve of the job the president is doing is significantly lower than the origins level? explain. Assume the alpha=0.01$ level of significance. Identify the null and alternative hypotheses for this test

Step 1 ：Define the null hypothesis as the proportion of voters who approve of the president's job is equal to 0.47, and the alternative hypothesis as the proportion is less than 0.47.

Step 2 ：Perform a one-sample z-test for proportions to test these hypotheses.

Step 3 ：Calculate the test statistic as \((p_{hat} - p_0) / \sqrt{(p_0 * (1 - p_0)) / n}\), where \(p_{hat}\) is the sample proportion, \(p_0\) is the hypothesized population proportion, and \(n\) is the sample size.

Step 4 ：Given that \(p_0 = 0.47\), \(n = 2000\), \(x = 938\), and \(alpha = 0.01\), calculate \(p_{hat} = 0.469\) and the test statistic \(z = -0.0896\).

Step 5 ：Compare the test statistic to the critical value for a one-tailed test at the 0.01 level of significance to determine whether to reject the null hypothesis.

Step 6 ：Given that the critical value is \(-2.3263\), and the test statistic is greater than the critical value, we do not reject the null hypothesis.

Step 7 ：Conclude that the data does not provide strong evidence to conclude that the proportion of voters who approve of the president's job is significantly lower than 0.47.

Step 8 ：Final Answer: \(\boxed{\text{No, the results of the second poll do not indicate that the proportion of voters who approve of the job the president is doing is significantly lower than the original level.}}\)