b) A poll showed the approval rating to be 0.46 (46%). A second poll based on 2000 randomly selected voters showed that 902 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 original level? Explain. Assume the a = 0.1 level of significance
Determine the P- value for this hypothesis test

Step 1 ：We are given a null hypothesis that the proportion of voters who approve of the president's job is 0.46. The alternative hypothesis is that the proportion is less than 0.46. We are given a sample size of 2000 and a sample proportion of 902/2000 = 0.451. We are asked to determine the P-value for this hypothesis test.

Step 2 ：The P-value is the probability of obtaining a result as extreme as, or more extreme than, the observed data, under the assumption that the null hypothesis is true. In this case, we are looking for the probability of obtaining a sample proportion of 0.451 or less, given that the true population proportion is 0.46.

Step 3 ：To calculate the P-value, we can use the formula for the Z-score of a sample proportion, which is \((p_{hat} - p_0) / \sqrt{(p_0 * (1 - p_0)) / n}\), where \(p_{hat}\) is the sample proportion, \(p_0\) is the population proportion under the null hypothesis, and n is the sample size. The P-value is then the area to the left of this Z-score in the standard normal distribution.

Step 4 ：Given that \(p_0 = 0.46\), \(p_{hat} = 0.451\), and \(n = 2000\), we calculate the Z-score to be approximately -0.808.

Step 5 ：The P-value is approximately 0.21, which is greater than the significance level of 0.1. This means that we do not reject the null hypothesis. There is not enough evidence to conclude that the proportion of voters who approve of the president's job is significantly lower than 0.46.

Step 6 ：Final Answer: The P-value for this hypothesis test is approximately \(\boxed{0.21}\).