Reference no: EM133830139
Statistics for Managers
Question 1
A sample of 250 people was asked to identify their preferred mode of transportation; 175 stated that their preferred mode of transportation was driving a car. Construct a 90% confidence interval for the population proportion of people who consider driving a car as their preferred mode of transportation. Follow the steps below.
Specify the formula for the 90% confidence interval for the population proportion of people who prefer driving a car.
Calculate the lower and upper limits of the 90% confidence interval for the population proportion of people who prefer driving a car.
Check the validity of any required conditions.
A market researcher wishes to determine the sample size needed to estimate the proportion of coffee drinkers who prefer the Starbucks coffee brand. How many coffee drinkers should be surveyed if the researcher wants to estimate the proportion of coffee drinkers within 0.03 with 90% confidence? (Use p=q=0.5). Do you need urgent help? Get Solution Now!
Question 2
A company that manufactures office chairs advertises that the average lifespan of its product is 9 years. However, the company has recently received several customer complaints stating that the actual lifespan of the chairs is shorter than what is claimed. To investigate these claims, the company decides to collect a random sample of 30 office chairs. The sample reveals an average lifespan of 8.4 years, with a standard deviation of 1.2 years.
Required:
At the 95% level of confidence, test whether the customers' claim that the average lifespan is less than 9 years is valid. Use the 6-step hypothesis testing procedure discussed in the course.
Explain why it would be inappropriate to draw a conclusion by simply comparing the claimed mean (9 years) to the sample mean (8.4 years) without conducting a formal hypothesis test.
Question 3
A large food manufacturing company has recently introduced a new product line in three different types of retail environments: Supermarkets, Convenience Stores, and Online Platforms. The company wants to determine if there are any significant differences in the average sales revenue generated by the new product in these three retail environments. To explore this, the company collects sales data from a random sample of 10 months' worth of sales for each retail environment.
The summary statistics of the sales revenue (in thousands of dollars) for each retail environment are as follows:
Sales Revenue Data Summary:
|
Month
|
Super markets
|
Convenience Stores
|
Online Platforms
|
|
January
|
75
|
65
|
50
|
|
February
|
80
|
70
|
58
|
|
March
|
72
|
62
|
62
|
|
April
|
95
|
80
|
72
|
|
May
|
60
|
56
|
48
|
|
June
|
82
|
78
|
64
|
|
July
|
68
|
74
|
59
|
|
August
|
78
|
63
|
66
|
|
September
|
90
|
81
|
70
|
|
October
|
85
|
77
|
55
|
ANOVA: Single Factor SUMMARY
|
|
Count
|
Sum
|
Average
|
Variance
|
|
Super markets
|
10
|
785
|
78.5
|
107.61
|
|
Convenience store
|
10
|
706
|
70.6
|
75.60
|
|
Online sales
|
10
|
604
|
60.4
|
63.60
|
ANOVA
|
Source of Variation
|
SS
|
df
|
MS
|
Fvalue
|
Fcrit
|
|
Between
Groups
|
1646.87
|
2
|
?
|
?
|
?
|
|
Within
Groups
|
?
|
27
|
?
|
|
|
|
Total
|
1646.87
|
29
|
|
Required:
Using the 6-step process of hypothesis testing learned in this unit, copy the ANOVA table above into your answer box, complete the missing values, and at 5% significance level, decide whether there are any significant differences in the average sales revenue across the three retain environments.
Discuss the assumptions that need to be met for the one-way ANOVA to provide valid results.
If any of the assumptions of ANOVA listed above are violated, what alternative methods or adjustments would you consider ensuring valid results? (Hint: Address each assumption separately).
Question 4
Explain how Type I and Type II errors could arise during both parametric and non- parametric statistical analyses.
How might these errors impact business decisions, and suggest the steps that a company can take to mitigate them?
Question 5
A service company tracks the number of repair and maintenance service calls it performs each month. The company wants to forecast the number of service calls for October to prepare for staffing and inventory needs. The company has tracked the number of service calls for the last nine months, as shown below.
|
Month
|
Calls
|
|
January
|
35
|
|
February
|
38
|
|
March
|
34
|
|
April
|
37
|
|
May
|
39
|
|
June
|
40
|
|
July
|
39
|
|
August
|
41
|
|
September
|
43
|
|
|
|
Required:
Forecast the number of service calls that the company will perform in October using the Trendline Equation method.
Forecast the number of service calls for October (Month 10) using a three-period weighted moving average with weights of 0.6, 0.3, and 0.1. Compare this forecast from the Weighted average with the forecast obtained from the trendline method.