161.101 - 2018 Summer Semester: Assignment 3 [40 marks]

due Tuesday 5 February 2019 at 11.55pm

Q1. Hypothesis test - Difference in means [6 marks]

A company that manufactures terracotta roof shingles wishes to test the strength and resistance to wear of its products. It takes two brands of tiles, namely “Bondi” and “Vincentia”, and tests samples of them by repeatedly scraping them with an abrasive material. The amount of tile particles lost due to the test are measured (in grams) and are recorded in the file RoofShingles.xls. We wish to know if one brand of tiles is more resistant to wear than the other (lower numbers mean that tile was more resistant to wear).

a)State, in words and in symbols, the hypothesis to be tested.

b)Using the Test for two means Excel template, perform the hypothesis test, report the test statistic and the p-value, and state your conclusion clearly in context.

Q2. Hypothesis test – Difference in proportions [8 marks]

A research group in the United States performed a study to investigate the problem of binge drinking among university students. Specifically, they were interested in whether there was any difference in the proportions of male and female students who binge drink.

The table below lists the results of their survey.

Group n X (number of binge drinkers)

1.Male 7,180 1,630

2.Female 9,916 1,684

Total 17,096 3,314

a)Calculate the sample proportions of binge drinkers for males and females.

b)State, in words and symbols, the hypothesis to be tested.

c)Using the Test for two proportions Excel template, perform the hypothesis test, report the test statistic and the p-value, and state your conclusion clearly in context.

Q3. Contingency tables [6 marks]

A mid-sized insurance company is implementing an employee health program. As part of it, they assess the health of current employees, in particular whether or not they smoke. The contingency table below displays the smoking status (current, former, never) of the 466 employees categorized by job type (manager, clerical, technical). We wish to test whether job type is independent of smoking status.

Job Type

Smoking Status Manager Technical Clerical

Current 22 43 51

Former 21 28 92

Never 19 68 122

a)Formally state, using symbols and words, the hypothesis to be tested.

b)Using the Chi-squared test Excel template, perform the hypothesis, report the test statistic and the p-value, and state your conclusion clearly in context.

Q4. Regression [10 marks]

Research was conducted to investigate if the flow of investors’ money into stock mutual funds is related to the flow of money into bond mutual funds. The data set BondsStocks.xlsx contains data on net new money flowing into stock and bond mutual funds in the years 1985 to 2000 in billions of US dollars. “Net” means that funds flowing out are subtracted from those flowing in. If more money leaves than arrives, the net flow will be negative. To eliminate the effect of inflation, all dollar amounts are in “real dollars” with constant buying power equal to that of a dollar in the year 2000.

a)Construct an appropriate scatterplot, and describe what the scatterplot suggests about the relationship between Bonds (response variable) and Stocks (explanatory variable).

b)Use the Excel Regression 1 template to find the least squares regression line for predicting Bonds based on Stocks.

c)Interpret, in context, the slope coefficient of the model.

d)Report, and interpret the meaning of, the value of R Square.

e)Use the linear model to predict the response when Stocks = 300.

Q5. Time Series [10 marks]

The Excel file AirPassengers.xlsx contains the number of international airline passengers from 1949 to 1960.

a)Construct a time series plot of the variable Passengers versus Date. Describe the main features of the time series.

b)A moving average MA(5) smoother, and an exponential Exp(0.2) smoother were constructed in Excel, a screenshot of which is shown below. Using Excel, or by hand, calculate the value of the missing numbers A and B.

c)Using the Month variable, fit a regression model to predict the number of passengers. Report the coefficients of the fitted model, and forecast the number of passengers, in January 1961 (Month=144). What are the pros and cons of this forecast?

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