Reference no: EM133777022

Statistics for Managers

Question 1

A logistics company conducted a study to measure the average delivery time for packages in a specific region. They collected data from a random sample of 25 deliveries and found that the average delivery time was 42.5 minutes. The population standard deviation of 4.8 minutes was recorded previously.

Required:
Assuming the delivery times follow a normal distribution, calculate the 99% confidence interval for the mean delivery time.

Question 2

Professor Kim is conducting a study on the weekly study habits of university students in a specific program. The findings from this study aim to identify trends in study behaviours and potentially inform academic support services.

To estimate the average hours spent studying per week, Professor Kim selects a random sample of 15 students from the program. After collecting the data, the sample mean study time is found to be 14 hours. Given that the population standard deviation of 3.5 hours was recorded in the previous study and assume data follows Normal distribution.

Required:
Using the 6-step hypothesis testing method discussed in this course, assess whether Professor Kim can conclude, with 99% confidence, that the population mean weekly study time is less than 16 hours.

Question 3

A national furniture retailer has expanded across three key markets: metropolitan areas, suburban areas, and rural regions. To explore whether there are significant differences in sales revenue based on location, the company performed an analysis of variance (ANOVA).

ANOVA: Single Factor		Count	Sum	Average	Variance
SUMMARY	Metropolitan	12	4820	401.67	7200.33
	Suburban	12	4680	390	6700
	Rural	12	3200	266.67	3200

ANOVA	Source of Variation	SS	df	MS	F value	F crit
	Between Groups	A	B	D	F	G
	Within Groups	188104	C	E
	Total	322390	35

Required:
Using the 6-step process of hypothesis testing learned in this unit, complete the ANOVA table above A-G and at 5% significance level, decide whether there are any significant differences between the sales revenue across 3 locations.

Question 4

A business consulting firm is helping a chain of restaurants analyse customer satisfaction scores across three types of locations: Region A, Region B, and Region C. The firm has collected feedback data from customers in each region to determine whether satisfaction levels vary significantly based on location.

Required:
Describe three scenarios where a parametric test should be applied to compare the satisfaction scores between the three regions and three situations where a non-parametric test would be more appropriate due to the characteristics of the data or the assumptions.

Question 5

A global electronics company recorded its smartphone shipments for 5 of the last 6 months of 2023, as shown below. Use two forecasting methods; Linear Trend Equation and Weighted Moving Average (with weights of 0.5, 0.3 and 0.2) to predict December shipments and determine which method is more accurate. Provide all steps of your calculations.

Month	Smartphones Shipped (1000s of Units)
July	180
August	190
September	210
October	240
November	280
December	?