STA101 Business Statistics

Subject Code :
STA101
Country :
AU
University :
The University Of Sydney

Step 1

Answer all four questions. They are about how statistics can be used to make key business decisions. Pretend you are a business consultant for the businesses in the questions. Process the data. Advise the businesses.

Keep your workings brief. Round all final numerical answers to two decimal places or round them to the closestwhole numbers (if the data is discrete).

Where is the data you will use? See the Excel spreadsheet found inMoodle →Assessments →Individual assignment

Step 2

Compose a report of around 1,000 words or less. It must contain your workings, answers and your interpretations of the answers, including any recommendations you might provide for the businesses concerned. Pretend you are to deliver it to your boss,who is not familiar with statistics, and who needs to understand what your analysis means. Better still: imagine yourreader is a 10-year-old kid. Explain what you did, what the numbers mean and what the findings are in simple words so the reader will say, “Ah! So that’s what all of this is about!”

Let your creative juices flowlike fine wine. Craft your response however you like. But the steps must be correctly and systematically laid out, and the reader must understand what the statistics mean.

Step 3

Attach a signed or initialled student declaration form on the front of your report. On the first page, write a title that describes your study and below it your name. See the ‘sample report’ on Moodle. Inside, divide the report into these sections:

1. Introduction

2. Chi-squared test

3. Normal distribution

4.Hypothesis testing I

5. Hypothesis testing II

6. Conclusion (summarise your advice and recommendations for the businesses)

Step 4

Submit report as a MS Word file on Turnitin via the link at Moodle > Assessments > Individual assignment (35%).STA101 Business Statistics ICMS

Questions

1. Chi-squared test: Kevin ‘The Caffeine’ G., the tea entrepreneur Noticing that there are hardly any cafes in Sydney that specialise in selling tea, an entrepreneur called Kevin plans to start one. If Starbucks could serve a dozen different kinds of coffee, he believes he could do the same with tea and succeed wildly.

He could open his first shop either in Manly -whose residents are predominantly white – orin places like Chatswood, where there are large Asian communities. Where might he easily make money? Kevin carries out a market survey. He wishes to know is whether hot beverages such as tea is dependent on ethnicity. Suppose there is a relationship

between ethnicity and choice of hot beverages, and that there is evidence Asians are far more likely to go for tea than coffee and other hot beverages. Or suppose there is no relationship. Either way, Kevin could make a better decision regarding his café’s location (or other related business strategies). Kevin collected a representative sample of Asian and non-Asian adults living across Sydney, inquiring them about the type of hot beverage they are most likely to purchase. For the survey data see ‘Data Dossier’ in Moodle > Assessments >p between ethnicity and choice of hot beverage people purchase? What should Kevin do about selecting a location for his tea shop?”

Report:

(i) the null and alternative hypotheses

(ii) the expected values, all χ

values, including the total and critical χ

(iii) whether you will keep or reject the null hypothesis (and why), andwhat your advice for Kevin would be

2. Normal distribution: The Bread Brothers’ Bakery

Triplet brothers Jayden, Jirameth and Jonathon run a bakery in a corner of Manly. It’s open 52 weeks of the year.From their records, they know they get about 500 customers per week (the population mean, μ). They also calculated thepopulation standard deviation: σ = 200 customers per week. They also learnt that each of their customers spends onaverage $10 at their shop. They pay a weekly rent of $1,462. All the data have a normal distribution.There could be weeks during which business is poor(e.g., in winter), and their revenue might be insufficient to coverthecost ofrent.How many weeks in a year might their weekly revenues fail to cover their weekly rent? nAdvise them:“Dudes! You are likely to be _______weeks in a year when you will have insufficient money to pay your weekly rent and will need to borrow money. Have a contingency plan!”

Illustrate the situation for the brothers with a hand-drawn normal distribution curvewith the appropriate numbers andshaded area (snap a photo of it, paste/insert it in MS Word).

3. Hypothesis testing I (using one sample): The restaurant with the slippery floor Leonie owns a chain of five Greek restaurants. Not all is well in the operation of her business. The kitchen and waiting staff have been breaking a lot of kitchenware and tableware due to slippages and other accidents. She obtained sample rubber mats from a salesman called Andre and covered parts of the kitchen floor and dining area of one of her restaurants, in the hope of reducing accidents that cause breakages. In the past, Leonie remembers the number of kitchenware and tableware that were broken in each restaurant was about 20 items a month on average. With the rubber mats in place, Leonie kept track of the number of breakages that happened each month for a sample of n = 36 random months. See ‘Data Dossier’ in Moodle > Assessments > Individual assignment (35%).

Advise Leonie: is there evidence that with the rubber mats (all other factors remain the same: the same waiters andwaitresses etc.), the number of breakages has decreased significantly? Should she invest in rubber mats for herrestaurants to solve the problem?

Report:

(i) the null and alternative hypotheses

(ii) whether this involves a one-tailed test or two-tailed test, and what the critical t-score is

(iii) the calculated t-score

(iv) whether you should keep or reject the null hypothesis

(v) whether Leonie should invest in rubber mats to reduce significantly the number of broken kitchenwareand tableware in her restaurants

4. Hypothesis testing II (using two samples): The bar that wants to introduce a Ladies’ Night Does offering women free drinks on certain nights at nightclubs and bars (called ‘Ladies’ Night’) result in a significant increase in sales of drinks on those nights, compared to other nights?Is it a good idea for these businesses to thereforehave Ladies’ Nights?

The owners of OS Barin Sydney, Will, Tom, Nick and Cooper,want to statistically examine whether there really is a significant improvement in the sales of drinks. If there is, they might host a Ladies’ Night at OS Bar. You help them with this task.

Focusing on Sydney as the target population, you gather sales data from a representative sample of 40 bars and nightclubs across Sydney. You recorded the average sales (in dollars, $) made at these bars and nightclubs when they had Ladies’ Night, and when they did not (the regular nights).

You run a t-test fortwo samples of data on Excel, using the Data Analysis add-in. Which one will you choose? The independent-samples t-test (known in Data Analysis as the t-test assuming unequal variances), or the paired samples test

Posted on : January 2nd, 2020

STA101 Business Statistics

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