1.A researcher is interested in the proportion, of adults who use online banking. Of the 30 randomly sampled adults, 24 responded that they use online banking. Assume the conditions are satisfied.

A)Construct and interpret a 90% confidence interval.

B)What happens to the width of the 90% CI if the sample size was increased to 100 but the sample proportion remains the same at 80%? Briefly explain your answer.

2.A seasonal regression model was fitted to Quarterly sales data ($000) for a national company specializing in green cleaning products with the following resulting regression model:

Estimated Sales = 121 - 31Q₁52Q₂65Q₃+ 0.60t

3.The manufacturers of an exercise machine claim that using their machine for only a few minutes a day will result in an average weight loss of 4 kilograms per week. A consumer group does not believe the weight loss would be 4 kilograms per week.

The consumer group took a random sample of 49 volunteers to use the exercise machine in accordance with the manufacturer's instructions. They found an average weight loss of 3.4 kilograms with a standard deviation of 2.8 kilograms. Is this sufficient evidence that the consumer group is correct? Use a 10% level of significance.You are told that the calculated test statistic is 1.5.

4.If thep-valueis less than in atwo-tailedtest

Select one:

Noconclusionshouldbereached

Thenullhypothesisshouldbe rejected

A one-tailedtest shouldbeused

Thenullhypothesisshouldnotberejected

5.Whichofthefollowingisnotanexampleofa seasonal effect?

Select one:

Movementsincasualemploymentnumbers in thelead-uptoChristmas&NewYear

Theplunge intheuraniumprice followinganuclearaccident inJapan

Visitor numberstothe Victoriansnowfieldsin winter

Increasedelectricityconsumptionin summerduetoair-conditionerusage

Where t is time in quarters, with origin March 2016

Q₁is a dummy for the March quarter

Q₂is a dummy for the June quarter

Q₃is a dummy for the September quarter.

A)Interpret the coefficient of t.

B)Forecast the sales for June 2025.

6.Thewidthof aconfidence interval (CI) estimateforamean willbe

Select one:

Narrower for99%CI thanfor a90%CI

Widerfor asamplesizeof100 thanasample sizeof50

Narrower for99%CI thanfor a95%CI

Narrower for a90%CIthanfor a95%CI

7.Inasimple linearregressionmodel, the intercept(b0) represents

Select one:

Change intheestimated averageYperunitchange inX

Thevariationaroundthesampleregressionline

The estimatedvalueofYwhenX=0

ThepredictedvalueofY

8.Residual analysis is used to

Select one:

Test the significance of the model

Test the significance of the intercept

Forecast the dependent variable

Check the assumptions of the regression model

9.To assess the reliability of a forecast in a multiple linear regression, other than checking the X variable values are within the sample data range, we should also use which of the following?

Select one:

R squared

The F statistic

The standard error of the slope

Adjusted R squared

10.Suppose that a random variable X is normally distributed with mean 96 and standard deviation 18. If a random sample of size 36 is taken, what is the z value whenx

xis 148?

Please give your answer correctly rounded to two decimal places.

11.A recent newspaper article claims that the mean number of screens per household is greater than 14.8. A random sample of 33 households had a sample mean of 18.6 screens.Assume that the population standard deviation is known to be 2.1 screens. Please give the value of the calculated test statistic, to two decimal places.

12.What is the value of the lower confidence limit for a 95% confidence interval for the population mean number of laptops owned by households, if a random sample of 48 households had a sample mean of 1.7 laptops.Assume the population standard deviation is 0.9 laptops?Please give your answer to two decimal places.Do NOT give units with your answer.

13.Regression was used to model quarterly electricity costs ($) for a household.

Estimated Electricity Cost = 156.75+ 3.85t + 40.31 Q1 6.86Q2 +15.89Q4

With t is in quarters and the origin is att = 0 June 2020

Q1, Q2, Q4 are dummy variables for March, June and December, respectively.

Q3 is the dummy variable for the September quarter and is the benchmark for this model.

What is the value that measures the trend of electricity cost of this household for this model?

Please give your answer correctly rounded to two decimal places.