Calculate and interpret the covariance between x and y

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Statistics for Business Assignment -

Please answer all questions.

Question 1: A sample of eight observations of variables x (years of experience) and y (salary in $1,000s) is shown below:

x	5	3	7	9	2	4	6	8
y	20	23	15	11	27	21	17	14

a. Calculate and interpret the covariance between x and y.

b. Give a possible reason that the covariance is negative.

c. Calculate the coefficient of correlation, and comment on the relationship between x and y.

d. Give a possible reason that the correlation is negative.

Question 2: A company claims that 10% of the users of a certain sinus drug experience drowsiness. In clinical studies of this sinus drug, 81 of the 900 subjects experienced drowsiness.

a. We want to test their claim and find out whether the actual percentage is not 10%. State the appropriate null and hypotheses.

b. Is there enough evidence at the 5% significance level to infer that the competitor is correct?

c. Construct a 95% confidence interval estimate of the population proportion of the users of this allergy drug who experience drowsiness.

d. Explain how to use this confidence interval to test the hypotheses.

Question 3: Below are monthly rents paid by 30 students who live off campus.

a. Find the mean, median, and mode.

b. Do the measures of central tendency agree? Explain.

c. Calculate the standard deviation.

d. Are there outliers or unusual data values?

e. Using the Empirical Rule, do you think the data could be from a normal population?

730	730	730	930	700	570
690	1,030	740	620	720	670
560	740	650	660	850	930
600	620	760	690	710	500
730	800	820	840	720	700

Question 4: Three messenger services deliver to a small town in Oregon. Service A has 60% of all the scheduled deliveries, service B has 30%, and service C has the remaining 10%. Their on-time rates are 80%, 60%, and 40% respectively. Define event O as a service delivers a package on time.

a. Calculate P(A and O).

b. Calculate the probability that a package was delivered on time.

c. If a package was delivered on time, what is the probability that it was service A?

d. If a package was delivered 40 minutes late, what is the probability that it was service B?

e. If a package was delivered 40 minutes late, what is the probability that it was service C?

Reference no: EM132223663

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Total Marks: This assignment is worth 40 marks (40 % of the total marks in the unit). Instructions: Students are required to cover all stated requirements. Your answer must be both uploaded to Moodle in word file and handed over a printed copy. You need to support your answers with appropriate Harvard style references where necessary. Include a title/cover page containing the subject title and code and the name, student id numbers. Please save the document as STA101AT1_first name_Surename_Student Number Eg: STA101AT1_John_Smith_NA20170000. Each of the following question worth 10 marks, please answer all of them. If needed please use Harvard referencing style. There is no word limit, but it is necessary that you provide answers with explanations.

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