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(Solved) ADM 2304 -- ASSIGNMENT 1 Due Date: Sunday, February 5, 2017 at midnight. Instructions: You may use Minitab or other software for any calculations....

Hello! This is a Stats assignment, it is fairly easy! Please check out the Assign1.pdf file for instructions and the rest of the files are suporting docs/data. I will give a generous tip if done properly and detailed.

ADM 2304 -- ASSIGNMENT 1

Due Date: Sunday, February 5, 2017 at midnight.

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.

3.

The data in the Minitab data files can be found in the file Assign1Data.xls.

4.

Remember to include your integrity statement. Your assignment should be uploaded to

Blackboard in pdf format.

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.

2. [ 10 marks ]

The file bmi.mtw contain the Body Mass Index (BMI) for a sample of men and a sample of

women. Two of the columns, OW_male and OW_female code the BMI values as:

0 - if BMI â‰¤ 25.4 (these are considered â€œnot overweightâ€);

1 - if BMI 25.5 (these are considered â€œoverweightâ€). (a) Test whether there is sufficient evidence to show that the proportion of overweight males

(proportion of males who are overweight) is different than the proportion of overweight females

in the population. Use the critical value approach and the 0.05 level of significance. Perform

the test manually after using Minitab to summarize the data (if you use descriptive statistics, the

mean coded value in each sample is the sample proportion).

(b) Explain how to find the p-value manually (indicate what probability has to be calculated).

(c) Finally calculate manually the 95% 2-sided confidence interval for the true difference between

the proportions of overweight males and overweight females.

(d) Explain how the results in parts (b) and (c) are consistent with your conclusion in part (a). 3. [ 5 marks ] (a) Test at the 0.05 level of significance whether the sample of male BMI observations is enough to

show that the mean BMI for males exceeds 25.5. Show your manual calculations (you may use

Minitab to summarize the sample data).

(b) Explain whether your test satisfies the underlying assumptions, with reference to a boxplot of

the sample data.

4. [10 marks]

The file OttawaMedianIncomes.mtw contains data on the median incomes (medinc) of

census dissemination areas in Ottawa. (a) Treating this set of data as the population, use Minitab to calculate the population mean for the

medinc variable. Set aside all population information until part (e).

(b) Examine a boxplot and histogram of the population data. Explain if the means of all possible

random samples of size 40 from this population would form a normal distribution.

Answer (c) and (d), without the information from (a) and (b).

(c) Now use Minitab (Calc Menu â€“ Random Data â€“ Sample from Columns) to draw twenty

samples of size n = 40 from the Ottawa medinc population. This procedure must be replicated

twenty times (note that if you open up the same sampling dialog box each time from the menu,

then you only have to replace the last destination column with the next one). For each sample,

use Minitab to calculate a 95% confidence interval estimate for the population mean, assuming

you do not know the population standard deviation (this interval estimation can be done in one

operation on all twenty columns, but not in Minitab Express).

(d) For your first sample, confirm the Minitab generated interval by calculating the interval

manually. Display the sample data using a boxplot and comment on whether the relevant

assumption regarding the population distribution is warranted given your sample (state clearly

the assumption needed to justify the interval estimation).

(e) Count the number of intervals out of your twenty that contain the true value of the population

mean from part (a).

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