Please save my life.. Instructions: 1. You may use Minitab or other software for

Question

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.

1. [ 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) A recent poll of 1500 respondents found that 29.3% support the Conservative party. Test whether this is sufficient evidence to conclude that the level of support has dropped since the election. Use the 5% level of significance and show your manual calculations.
(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%. What sample size would be required?
(c) Suppose that, in a random sample of 23 University of Ottawa (UOttawa) students, only 3 indicated a preference for the Conservatives. Test whether this is sufficient evidence to indicate that the level of support for the Conservatives among UOttawa students is lower than the 31.89% share of the popular vote in 2015. Use the .05 level of significance and show how you would calculate the p-value for this test.

Explanation / Answer

a) here null hypothesis: H0: mean proportion p=0.3189

and alternate hypothesis: Ha: mean proportion <0.3189

sample size n=1500

hence std error =(p(1-p)/n)1/2 =0.012

also phat =0.293

for 5% level of significance , rejection region is z<-1.6449

here zstat =(phat-p)/std error =-2.1523

as zstat is in rejection region, we reject null hypothesis  to conclude that the level of support has dropped since the election

b)for 95% CI, z =1.96

margion of error E=0.01

p=0.3189

hence sample size n=p(1-p)(Z/E)2 =8344

c) here p=0.3189 sample size n=23

std error =

hence std error =(p(1-p)/n)1/2 =0.097

also phat =3/23 =0.1304

for 5% level of significance , rejection region is z<-1.6449

here zstat =(phat-p)/std error =-1.9394

as zstat is in rejection region, we reject null hypothesis  to conclude that the level of support has dropped since the election

also for above zstat , p value from table =0.0262

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