MATH 225N Week 7 Assignment Conduct a Hypothesis Test for Proportion – P-Value Approach

MATH 225N Week 7 Assignment Conduct a Hypothesis Test for Proportion – P-Value Approach Question A college administrator claims that the proportion of students that are nursing majors is greater than 40%. To test this claim, a group of 400 students are randomly selected and its determined that 190 are nursing majors. The following is the setup for this hypothesis test: H0:p=0.40 Ha:p0.40 Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places. The following table can be utilized which provides areas under the Standard Normal Curve: Correct answers: • P-value=0.001 Here are the steps needed to calculate the p-value for a hypothesis test for a proportion: 1. Determine if the hypothesis test is left tailed, right tailed, or two tailed. 2. Compute the value of the test statistic. 3. If the hypothesis test is left tailed, the p-value will be the area under the standard normal curve to the left of the test statistic z0 If the test is right tailed, the p-value will be the area under the standard normal curve to the right of the test statistic z0 If the test is two tailed, the p-value will be the area to the left of −|z0| plus the area to the right of |z0| under the standard normal curve For this example, the test is a right tailed test and the test statistic, rounding to two decimal places, is z=0.475−0.400.40(1−0.40)400‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√≈3.06. Thus the p-value is the area under the Standard Normal curve to the right of a z-score of 3.06. From a lookup table of the area under the Standard Normal curve, the corresponding area is then 1 - 0.999 = 0.001. z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 3.0 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 Required p-value = 0.001 Explanation: Formula to calculate the test statistic z is z=((1−p)∗p)/np^−p where p^=x/n=190/400=0.475,p=0.40,n=400 →((1−0.4)∗0.4)/4000.475−0.4 →0..075 ⇒3.06 P(z3.06) = 1-P(z3.06) ⇒ 1 - 0.999 [Find 3.0 in row and 0.06 in column in above table] ⇒ 0.001 Hence, p-value is 0.001 Determine the p-value for a hypothesis test for proportion