Problem 4 (13 points) Gun control has become a sensitive issue in the United Sta

Question

Problem 4 (13 points) Gun control has become a sensitive issue in the United States. In a recent 2014 survey conducted online, 762 people responded that there should be stricter gun control laws while 438 people would be opposed to stricter gun control laws. Conduct a hypothesis test at the 10% level of significance to determine ifthe true proportion of people in the U.S. who support stricter gun control laws is greater than 0.60. a. What type of test should be used here? Briefly explain why. (2 points) Type of Test: Reason b. Write the null and alternative hypotheses. HO: c Check the conditions to ensure that the test from part (a) is appropriate to use. d. Calculate the test statistic. (You may use Minitab and just report the value, but be sure you can do the calculation by hand as well.)

Explanation / Answer

Preparatory Work

Let X = number of people who respond that there should be stricter gun control laws.

Then, given that a total of 1200 people responded either way, X ~ B(1200, p) where p = probability that a person would respond that there should be stricter gun control laws, which is also equivalent to proportion of people responding in favour of stricter gun control laws.

Part (a)

We want to test if true proportion of people in the US who favour stricter gun control laws is more than 0.6.

This, in test terminology means testing the null hypothesis: p = 0.6 against the alternative: p > 0.6.

The appropriate test is a Z-test, which is based on Normal approximation to Binomial.

Note that the question is concerned with only the proportion favouring and hence, non-favouring proportion will not come into the picture.

Part (b)

As already indicated above, H0: p = 0.6     Vs HA: p > 0.6 ANSWER

Part (c)

Again, as already indicated above, the suggested Z-test is based on Normal approximation to Binomial, which is governed by the twin condition, np 5 and np(1 - p) 5. In the given question, n = 1200, p = 0.6 and hence (1- p) = 0.4. Twin condition is fulfilled. ANSWER

Part (d)

Test statistic is Z = (X – np)/{np(1 - p)} = (762 - 720)/ 288 = 42/16.97 = 2.475 ANSWER

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.