STAT1060 – Assignment 2

STAT1060 – Assignment 2 STATISTICAL ANALYSIS TO SUPPORT DECISION MAKING

Total marks: 46, Weight: 20% Due time and date: 23.59AEDT, Sunday end of Week 11

Student:

Name:

Question 1 (6 Marks)

Australia’s employment statistics are an important indicator of socio-economic status. The levels of full or part-time employment, unemployment and labour force participation indicates the strength of the local economy and social characteristics of the population. The data is provided in the file Question1.xlsx for the city of Newcastle employment status: Columns A and B contain the employment status and their percentage for the year 2016.

  1. Identify the type of variable in the data (Continuous, Discrete, Ordinal or Nominal) and justify your answer? [2 Marks]
    The type of variable in such e
  2. Name the appropriate graphical display to use for the variable type you have identified in part (i)? [1 Mark]
  3. Use Excel to create an appropriate graph to display the data provided. [1 Mark]
  4. Comment on the key finding from this graph. [2 Marks]

Question 2 (4 Marks)

Hungry Jack’s restaurant in Australia claims that the mean waiting time of customer’s service is normally distributed with a mean of three minutes and a standard deviation of one minute. Use the empirical rule to answer the following questions. Shade in (roughly) the areas in the curves, corresponding to your answers

  1. What is the probability that the waiting time of customer’s service is less than 2 minutes? [1 Mark]
  2. What is the probability that the waiting time of customer’s service is more than 5 minutes? [1 Mark]
  3. What is the probability that the waiting time of customer’s service is between 2 minutes and 4 minutes? [1 Mark]
  4. Find the waiting time of customer’s service, which is on the 2.5 % (approximately) of the distribution? [1 Mark]

Question 3 (6 Marks)

The data in Excel file Question3.xlsx was collected by the market research department randomly selecting 100 customers waiting time from the Hungry Jack’s restaurant in the city of Newcastle. The variable ‘waiting time’ is the numerical value attained from the survey questions. Management expected the mean waiting time to be about 3 minutes. Provide a hypothesis test, at a 5% significance level, to test if the population mean waiting time is 3 minutes. [6 Marks]

Question 4 (14 Marks)

Hungry Jack’s restaurant in the city of Newcastle offering home delivery is interested in comparing delivery times of their products during two periods of the day: afternoon and evening. Management is concerned that the road traffic may affect the delivery times. Management is interested in comparing the delivery times (in minutes) for afternoon and evening. A random sample of 25 orders for each period of the day: is provided in the Excel file Question4.xlsx: Columns A is afternoon and B is evening

  1. Use Excel to construct a histogram of afternoon delivery times for 25 orders. How would you describe the shape? Include your histogram after finding a suitable number of bins. [2 Marks]
  2. (ii) Use Excel to construct a histogram of evening delivery times for 25 orders. How would you describe the shape? Include your histogram after finding a suitable number of bins. [2 Marks]
  3. Use Excel to find the mean, median, standard deviation and interquartile ranges of the afternoon delivery times. Repeat for the evening delivery times. Do not simply include raw output. [2 Marks]
  4. Using your output created in parts (i)-(iii), give a brief statement comparing the afternoon delivery times and evening delivery times. [2 marks]
  5. Explain, using support from a hypothesis test, if delivery times differ across these two periods. Perform hypothesis testing at the 5% significance level, and discuss the result. Assume the data were taken from different restaurants for afternoon and evening delivery times. (Hint) Research question: Is there a difference between the average delivery times for afternoon and evening? [6 Marks]

Question 5 (6 Marks)

Management at the Hungry Jack’s restaurant in the city of Newcastle set discount pricing strategy for more sales. The difference* (with promotion and without promotion) in sales of Chicken burgers is listed in Excel file Question5.xlsx.

Difference* = days with promotion – days without promotion Use Excel to test whether there is a difference, at 5% significance level, between the mean difference in sales of Chicken burgers for days with promotion and days without promotion. Comment on the result. Note: Both measurements were taken from same restaurant. [6 Marks]

Question 6 (10 Marks)

The data in Excel file Question6.xlsx was collected by the marketing research department randomly selecting 100 customers’ menu preferences from the Hungry Jack’s restaurant in the city of Newcastle. A study was conducted to investigate the type/s of burgers and customers preferences regarding the size of burgers at Hungry Jack’s restaurant.

  1. Use Excel file Question6.xlsx to create a cross-tab (contingency table) from two qualitative variables in Excel. [1 Mark]
  2. What is the probability that a randomly selected customer bought the beef burger? [1 Mark]
  3. What is the probability that a randomly selected customer bought the chicken burger and large size? [1 Mark]
  4. What is the probability that a randomly selected customer bought the chicken burger given medium size burger? [1 Mark]
  5. Use Excel to conduct the appropriate formal hypothesis test at the 5% significance level to see if there is a statistically significant relationship between preferences for the type/s of burgers and the customer’s preferences regarding the size of burgers. Use P-value approach to answer the research question. [6 Marks]

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