ADM2304: Assignment 1
Due date: Sunday, October 6, 2024, at 11:59 pm (Brightspace)
Instructions
• You may use StatCrunch, MS Excel Analysis ToolPak, or other software for any calculations unless you are asked to use a specific software. You must show your manual calculations when asked. You may paste your output onto your assignment to show your use of software; however, this output does not replace any of the steps outlined below. This means that answers that are exclusively software output may receive only partial marks. Include your output when asked to confirm results.
• If you are performing a hypothesis test, make sure you state the hypotheses, the level of significance, the decision criteria/region, the test statistic, and/or the critical value or p-value (if requested), your decision (whether to reject or not to reject the null hypothesis), and a conclusion in managerial terms that answers the question posed. These steps must be completed in addition to any software output.
• The data for this assignment can be found in the file Assignment1.xlsx.
• Your assignment must be typed and uploaded to Brightspace in one single pdf file. You may upload several files, but only the most recent submission prior to the deadline will be graded.
Start each question on a different page and answer the questions in order.
• Late submissions will be accepted according to the late submission policy discussed in class and posted in the course outline on Brightspace.
• Remember to include your integrity statement. Assignments submitted without a signed in- tegrity statement will not be graded.
• IMPORTANT ADVICE FOR CALCULATIONS: Always use at least 2 decimal places all along your intermediate calculations and apply proper rounding at the end. It is recommended that all your calculations be done using Excel as this software always uses many decimal places in all calculations. Once you have the final answer, just round it properly.
Question 1. Grocery delivery service customer segmentation [23 marks]
A new grocery delivery service operating in Canada is investigating various customer segments to determine their profitability. One of the segments of interest is new customers who signed up for the service in 2023. The latest report from the company’s customer database shows that this population amounts to 600,000 customers, and they would like to know how many of them don’t use the app to place their orders but instead use their website or call customer support to do so. They commission a random survey of 700 customers in this population to investigate their usual ordering method and obtain the following summary results: app (420); website (120); customer support call (160).
a) [8 marks] The company will continue to invest in improving the app if at least 65% of customers currently use the app to place their orders. Test at 5% level of significance whether the proportion of customers who signed up in 2023 and use the app as their main ordering method meets the company’s threshold for continued investment in the app. Use both the critical value and p-value approach showing all the steps of hypotheses (hypotheses, decision region, test statistic, conclusion with justification, and managerial statement). (Manual Calculations)
b) [2 marks] Are the assumptions/conditions for the above test satisfied?
c) [4 marks] Calculate manually an appropriate 95% confidence interval for the population proportion of customers who signed up in 2023 and use the app to place their orders. Interpret the confidence interval. Does this interval allow you to make the same conclusion as in part a) above? Explain.
(Manual Calculations)
d) [5 marks] Using a two-sided 95% confidence interval for the population proportion of customers who signed up in 2023 and use the app to place their orders, calculate an estimate of the size of this customer segment. [HINT: calculate a range of values rounded to the nearest thousand for the estimate]
e) [4 marks] The company’s senior management would like a more precise range estimate of the size for this customer segment to strengthen their business case, and they are prepared to commission a larger survey. How large a sample size would be needed to estimate, within 2%, the true proportion with 95% confidence? What would be a new estimate of the size of this customer segment (rounded to the nearest thousand) assuming the new survey would obtain the sameˆ(p)? (Manual Calculations)
Question 2. Remote Learning Policies [19 marks]
A teachers’ union representing public school educators is claiming that the current policy mandating a 3-day per week in-person teaching requirement is not in line with current practices in private schools. They have commissioned a national survey to compare remote learning policies between public and private schools. The survey looked at two independent random samples of schools: 90 and 170 in the public and private sectors, respectively. They found that 58 public schools impose a 3-day per week in-person teaching requirement compared to 110 private schools.
a) [12 marks] Test whether schools in these two sectors are equally likely to impose a 3-day per week in- person teaching requirement. Use the critical value and p-value approach and a 5% level of significance. Make sure to include all the steps of hypothesis testing. [Hint: let p1 be the proportion of public schools and p2 the proportion of private schools who impose a 3-day per week in-person teaching requirement.] (Manual calculations and StatCrunch)
b) [5 marks] Calculate and interpret an appropriate 95% confidence interval for the true difference between the proportions of public and private schools that impose a 3-day per week in-person teaching requirement. (Manual calculations and StatCrunch)
c) [2 marks] Explain how your conclusions in parts a) and b) are consistent.
Question 3. Worldwide Movie Gross Values [22 marks]
The file Assign1Data.xlsx contains worldwide gross values in dollars (3650 records) originating from a dataset of popular movies.
a) [1 mark] Treating this set of data as population data, use StatCrunch to calculate the population mean and population standard deviation for the ’Worldwide Gross ($M)’ variable. (StatCrunch/EXCEL)
b) [3 marks] Examine a histogram and boxplot of this variable and explain if the means of all possible random samples of size 50 from this population would form. a normal distribution.
c) [8 marks] A random sample of 15 worldwide gross values has been drawn and displayed in the sheet Size 15 Sample in the Assign1Data.xlsx file. Use this sample to test whether the population mean is different from the value calculated in part a) above. Use the critical value and the p-value approach and a 5% level of significance. Assume that the population standard deviation is unknown, and the shape of the population worldwide gross values follows a normal distribution, notwithstanding your answer to part b). (Manual calculations and StatCrunch)
d) [5 marks] Using the same sample as in part c) above, build a 95% confidence interval for the population mean. Does the interval include the population mean calculated in part a) above? Explain why or why not. (Manual calculations and StatCrunch)
f) [5 marks] Now, use the StatCrunch/EXCEL sampling routine to draw 25 samples of size n = 50 from the population data. Report the 25 means of these samples. Calculate the mean and standard deviation of these sample means and compare them with the theoretical values (i.e., μ and √n/σ) as claimed by the sampling distribution. Are they equal? Why or why not? Justify.