Gun control has become a sensitive issue in the United States. In a recent 2016
ID: 3341270 • Letter: G
Question
Gun control has become a sensitive issue in the United States. In a recent 2016 survey conducted online, a randonm sample of adults was asked if they believed stricter laws were needed. The responses are coded in Excel as "Yes" if the respondent believed there should be stricter laws and "No" if they did not believe that stricter laws were needed Conduct a hypothesis test at the 5% level of significance to determine if the true proportion of people in the US. who support stricter gun control laws is a majority hat type of test should be used here? Briefly explain why using the variable situation and parameter b. Write the null and alternative hypotheses c. Check the conditions to ensure that the test from part (a) is appropriate to use d. Calculate the test statistic. (You may use Excel and just report the value, but be sure you can do the calculation by hand as well.) e. Use the Hypothesis Test Workbook to calculate the exact p-value. f. What is/are the critical value(s) of this test? g. Will you reject or fail to reject the null hypothesis? Explain why using the critical value or p-value. h. Write a conclusion in the context of the problem i. Suppose the proportion of people in favor of stricter gun control laws is actually .50. What type of decision did you make in part (g)? For parts (j) and (k), determine if the p-value would increase, decrease, or stay the same if the following changes had occurred. Assume all values other than the one being altered stay the same.Explanation / Answer
Given that,
possibile chances (x)=1055
sample size(n)=2008
success rate ( p )= x/n = 0.5254
success probability,( po )=0.5
failure probability,( qo) = 0.5
null, Ho:p=0.5
alternate, H1: p>0.5
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.64
since our test is right-tailed
reject Ho, if zo > 1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.5254-0.5/(sqrt(0.25)/2008)
zo =2.2762
| zo | =2.2762
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =2.276 & | z | =1.64
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: right tail - Ha : ( p > 2.27624 ) = 0.01142
hence value of p0.05 > 0.01142,here we reject Ho
ANSWERS
---------------
null, Ho:p=0.5
alternate, H1: p>0.5
test statistic: 2.2762
critical value: 1.64
decision: reject Ho
p-value: 0.01142
we have evidence that the people in U.S who support stricter gun control laws is majorty
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