Answer:
(D) The P-value is below 0.01.
Step-by-step explanation:
Test statistic (z) = (p' - p) ÷ sqrt[p(1-p) ÷ n]
p' is sample proportion = 162/462 = 0.35
p is population proportion = 0.41
n is sample size = 462
z = (0.35 - 0.41) ÷ sqrt[0.41(1-0.41) ÷ 462] = -0.06 ÷ 0.023 = -2.61
From the standard normal distribution table, the cumulative area of the test statistic is found by taking the value of 2.6 under 0.01. The value (cumulative area) is 0.9945.
The test is a one-tailed test because the alternate hypothesis is expressed using the inequality less than.
P-value = 1 - 0.9955 = 0.0045
The P-value 0.0045 is below 0.01