A large investment company is interested in analysing the efficacy of launching a brand of frozen food products. As part of their feasibility study, they obtain data on a sample of 856 potential customers and categorise them according to their gender and average weekly spending. The data is provided in the Excel file labelledAssignment 2 data.xlsx.Please refer to the worksheet labelledFrozen Food.

Assume that weekly spending is normally distributed with a mean of $27.10 and standard deviation of $2.20. If the company has 5000 customers per year purchasing frozen food, how many of them would spend more than $30 per week on average on frozen food?

Based on the data given, we take a small sample of male customers. Refer to the worksheet labelledFrozen Food - Sample. Calculate the 95% confidence interval estimate of the average amount of spending by male customers. Remember to interpret the estimated interval. Show all working.

Those who spend more than $30 per week on average are categorised as "High Spenders" and those otherwise as "Low Spenders". The Marketing Manager of the company claims that spending habits are influenced by gender. Is there evidence to support the claim? Use a 5% level of significance and the p-value approach.Briefly explain why you have chosen this type of test.(We encourage you to use Microsoft Excel)

Questions 2 - 4 are based on the data onEmployment by industry. This data can be found intwo worksheets:Regions-Employment and Australia-Employmentin theAssignment 2 data.xlsx. The worksheetRegions-Employmentcontains employment information on 45 regions in 18 different industries in Australia and the worksheetAustralia-Employmentcontains information on employment for each industry in Australia as a whole. The worksheets have columns containing the following variables

This data file provides information on Australian employment among regions and industries in May 2020. The data set contains employment information by 19 industry categories based 45 regions in Australia.It is a slightly modified version of theEmployment by Industry (Excel) (64.9KB)file from the linkhttps://lmip.gov.au/default.aspx?LMIP/Downloads/EmploymentRegion.

Description of Variables

Region Name- Name of regions (population above 100,000 persons).

State/Territory -State or territory in Australia.

Industry-Industry categories.

Employment Total -Total employment by an industry category.

Employed Full-Time- Full-time employment total.

Employed Part-Time -Part-time employment total.

Employed - Male- Male employment total.

Employed - Female -Female employment total.

Five-year Growth- Employment growth in previous five years. Negative growths present declines in employment.

Employment Distribution (%) -Percentage employment of an industry in the region

Assume the data in the worksheetRegion-Employmentis a random sample from Australia for all industry categories. You are required to calculate the 99% confidence interval estimate of the average employment distribution (%) of the Retail Trade industry. The lower limit is?

(Please keepall workings/calculations to at least 4 decimal places. State yourfinal answer to 2 decimal placesanduse appropriate units)

The Mining industry is an important contributor to the Australian economy. It contributes about 8 per cent to Australia's GDP and around 60 per cent of exports. Refer to the data on this sector.

Calculate the 99% confidence interval estimate of the average employment distribution (%) of the Mining industry.Show all working and interpret the interval obtained.

At the 1% level of significance, test whether the average employment distribution (%) of the industry is different to the employment distribution (%) of the Mining industry in all of Australia. Show all working. You can use either the p-value or critical value approach.

Interpret a type I error in the context of the question above.

Compare the results of Question 3a and Question 3b. Briefly explain the conclusions

We wish to analyse the relationship between the female employment total, the part-time employment total and five-year employment growth in theAgriculture, Forestry and Fishingindustry.

UsingALLrelevant simple linear regression tools you have used in this unit, analyse the relationship between the female employment total and the part-time employment total.

Predict the number of females employed when there are 1000 people employed part-time in a region. Using all relevant available information from part (a), discuss the likely validity of this prediction.

We now investigate the relationship between female employment total, part-time employment total and Five-year growth.

Generate a regression output of female employment on part-time employment and Five-year growth. Interpret the estimated slope coefficients.

Has the coefficient of determination increased in comparison to your model in (a)? Explain why/why not.

At the 1% level of significance, test if the overall model is significant.

This is a general concept question and is not related to the data set provided. "Correlation does not imply causality" is an important concept when referring to regression. Briefly describe this concept. Provide one example of how it may occur. Your answer in this section does not need to be related to the data set provided for the assignment.