Please give me right answer and don\'t copay and paste.. please save my life.. I
ID: 2921579 • Letter: P
Question
Please give me right answer and don't copay and paste.. please save my life..
Instructions:
1. You may use Minitab or other software for any calculations. However, you must show your manual calculations when asked. You may paste your output onto your assignment to show your use of Minitab; however, this output does not replace any of the steps outlined below. This means that answers that are exclusively Minitab output may receive only one mark.
2. If you are performing a hypothesis test, make sure you state the hypotheses, the level of significance, the rejection region, the test statistic (and p-value, if requested), your decision (whether to reject or not to reject the null hypothesis), and a conclusion in managerial terms that answers the question posed. These steps must be completed in addition to any Minitab output.
2. [ 10 marks ]
In the 2015 federal election, 39.47% of the electorate voted for the Liberal party, 31.89% for the Conservative party, 19.71% for the NDP, 4.66% for the Bloc Quebecois, and 3.45% for the Green party.
(a) An August poll of 1150 respondents found that 35% would support the Conservative party. Test whether this is sufficient evidence to conclude that the level of support has changed since the election. Use the 1% level of significance and show your manual calculations (you do not need to calculate the summary statistics manually).
(b) Suppose you want to estimate the national level of support for the Conservatives using a 95% 2-sided confidence interval with a margin of error of ±1.5%. What sample size would be required?
(c) To test whether the level of support for the Conservatives among U of O students is lower than the 31.89% share of the popular vote in 2015, you found 3 out of 23 randomly selected University of Ottawa students supported the Conservatives. Use the 5% level of significance and show how you would calculate the p-value for this test.
Explanation / Answer
(a) H0 : p = 0.3189
Ha : p 0.3189
Number of respondents = 1150
p^ = 0.35
Standard error of the proportion = sqrt [p0 * (1- p0)/ N] = sqrt [ 0.3189 * 0.6811 / 1150] = 0.0137
so Test statistic
Z = (0.35 - 0.3189)/ 0.0137 = 2.27
p- value = 2 * Pr(Z > 2.27)= 2 * (1 - 0.9884) = 0.0232
so Critical value of Z for 1% significance level for 2 - sided test Zcr = 2.575
so we cannot reject the null hypothesis and conclude that support for conservatives hasn't changed.
(b) Margin of error = Test statistic * standard error of the proportion
Here Margin of error = 0.015
Test statistic for significance level 0.05 = 1.96
Sample size = N
0.015 = 1.96 * sqrt [0.3189 * 0.6811 / N]
sqrt [ N / 0.3189 * 0.6811 ] = 130.66667
N = 3709
(c) Here H0 : pOttawa = p0
Ha : pottawa < p0
Sample proportion p^ = 3/23 = 0.1304
standard error of the proportion se0 = sqrt [0.3189 * 0.6811 / 23] = 0.0972
Test Statistic
Z = (pottawa - p0 )/ se0
Z = (0.1304 - 0.3189)/ 0.0972 = -1.94
Here the test is one - sided test
p- value = Pr(Z < -1.94) = 0.0262 < 0.05 so significant.
So, level of support for the conservatives among University of Ottawa students is lower than the 31.89% share of the popular vote.