Question

In: Statistics and Probability

A cereal manufacturer is planning to develop a new product. The product does not require adding...

A cereal manufacturer is planning to develop a new product. The product does not require adding milk because each piece has milk substitute inside of it. All the consumer needs to do is add water. The product is scheduled to be rolled out nationally next year. The marketing manager has to decide how to market the new product. There are three different marketing strategies that the firm is looking at. They want to emphasize all three points, but they also realize that they need to choose one as the primary hook before the national launch. The product is presently being sold in only the Columbus, Detroit and Pittsburgh markets. The marketing manager decides to launch three different advertising campaigns. In the Columbus market, convenience will be the main hook. In the Detroit market, quality will be the main hook. In the Pittsburgh market, the product's low price, due to the fact that no milk purchase is necessary, will be the main hook. Weekly sales were recorded for 20 weeks following the beginning of the campaigns. The data are below. (Answers must use excel). (A) State the null hypothesis and the alternative hypothesis. (B) Run the appropriate test to see if one campaign differs from the others. (C) What do you find? (D) If you find that there is a difference, in which pair(s) is it located? Bold and format with two digits after the decimal point the cells you looked at to make this decision. This will require running a test for each possible pair of data.

Convenience Quality Price
529 804 630
658 630 531
793 774 443
514 717 526
663 679 602
719 604 502
711 620 619
606 697 689
461 706 675
529 615 512
498 492 691
663 719 733
604 787 628
495 699 776
485 572 561
557 523 572
353 584 469
557 634 581
542 580 639
614 624 532

Solutions

Expert Solution

a)

As we want to see if the weekly sale is different for at least one of the state from the others, so the appropriate test would be -

Null Hypothesis - H0: All the states have same population mean of weekly sales.

Alternate Hypothesis - H1: At least one of the state has different population mean of weekly sales from the others.

Symbolically, it can be written as -

Null Hypothesis - H0:

Alternate Hypothesis - H1: for at least one pair of (i, j), .

Where , and are the population mean of weekly sales for the states Columbus, Detroit and Pittsburgh respectively.

__________________________

b)

We would need to conduct an ANOVA test for this hypothesis. We can use Excel's 'Data Analysis' toolpak to access the 'Anova: Single Factor' option as shown -

Then, you enter the field values as shown -

Make sure to mark the check box for 'Labels in First Row' as we have labels in first row.

Output obtained from excel is as shown -

Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
Convenience 20 11551 577.55 10775.00
Quality 20 13060 653 7238.11
Price 20 11911 595.55 7913.21
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 62114.7 2 31057.35 3.59 0.03 3.16
Within Groups 492599.9 57 8642.10
Total 554714.6 59

-------------------------------------------

C)

As the p-value of test = 0.03, is less than significance level of = 0.05, so we reject the null hypothesis and conclude that there is enough evidence in the data to support the claim that the population mean of at least one state is different from the remaining two.

-------------------------------------------

D) To further check which two population means are different from each other, we need to perform a post-hoc test.

Tukey's HSD test can be conducted for difference of means using the test statistic critical value 'q' = 3.40-

Note that, you can get the critical value of 'd' from Tukey's critical value table corresponding to 3 treatments and error degrees of freedom = 57.

Following table shows comparison of differences of mean from the HSD value and conclusion -

Difference Value Critical Value Decision
|| 75.45 70.6763 Significant
|| 57.45 70.6763 Not Significant
|| 18 70.6763 Not Significant

As the difference between the means of population 1 (Columbus - Convenience strategy) and population 2 (Detroit - Quality Strategy) is greater than the critical value of test statistic, so this difference is significant.

And as the average value of 'Quality' strategy = 653 is more than the average value of 'Convenience' strategy = 577.55, so we can say that the most effective strategy is the 'Quality' strategy that was used in Detroit.

_____________________________________


Related Solutions

The company is considering adding a new product line that will require an investment of $1,454,000....
The company is considering adding a new product line that will require an investment of $1,454,000.       Management estimates that this investment will have a 10-year life and generate future net cash       inflows of $310,000 the first year, $280,000 the second year and $240,000 each year thereafter for       eight years. Compute the payback period. (Hint: the payback period does not use the time value                  of money charts.)
Joe’s Hardware is adding a new product line that will require an investment of $ 1,476,000....
Joe’s Hardware is adding a new product line that will require an investment of $ 1,476,000. Managers estimate that this investment will have a​ 10-year life and generate net cash inflows of $ 310,000 the first​ year, $ 280,000 the second​ year, and $ 230,000 each year thereafter for eight years. Compute the payback period. Round to one decimal place.
Williams Corp is a manufacturer that is considering adding a new product line - either tillers...
Williams Corp is a manufacturer that is considering adding a new product line - either tillers for tractors (Proposal A) or trailers for trucks (Proposal B). To do so, it will need to invest in new equipment. Williams Corp. has gathered the following information about each proposal: Proposal A's equipment will cost $8,390,000 and is expected to result in annual net cash inflows of $1,530,000 over nine years, with zero residual value at the end of nine years. Proposal B's...
A manufacturer of breakfast cereal is to release a new cereal called Smores. Before Smores is...
A manufacturer of breakfast cereal is to release a new cereal called Smores. Before Smores is to be distributed in grocery stores across the country, the manufacturer conducts a study to determine if (i) the height of the shelf in which the cereal is to be displayed and (ii) the type of display will effect sales of the cereal. A statistician was hired to design an experiment to investigate if - and if so, how - does the (i) shelf-height...
A cereal manufacturer has two new brands of cereal which it would like to produce. Because...
A cereal manufacturer has two new brands of cereal which it would like to produce. Because resources are limited, the cereal manufacturer can only afford to produce one of the new brands. A marketing study produced the following probability distributions for the amount of sales for each of the new brands of cereal. Table A - Cereal A Sales P(Sales) -$150,000 0.2 $200,000 0.3 $300,000 0.3 $400,000 0.2 Table B - Cereal B Sales P(Sales) -$10,000 0.40 $300,000 0.40 $600,000...
A manufacturer is planning to produce and sell a new product. It would cost $20 million...
A manufacturer is planning to produce and sell a new product. It would cost $20 million at Year 0 to buy the equipment necessary to manufacture the product. The project would require net working capital at the beginning of each year in an amount equal to 15% of the year's projected sales; for example, NWC0 = 15%(Sales1). The product would sell for $30 per unit, and believes that variable costs would amount to $15 per unit. After Year 1, the...
A manufacturer is planning to produce and sell a new product. It would cost $20 million...
A manufacturer is planning to produce and sell a new product. It would cost $20 million at Year 0 to buy the equipment necessary to manufacture the product. The project would require net working capital at the beginning of each year in an amount equal to 15% of the year's projected sales; for example, NWC0 = 15%(Sales1). The product would sell for $30 per unit, and believes that variable costs would amount to $15 per unit. After Year 1, the...
You work for a breakfast cereal manufacturer. Your job is to decide if the new machinery...
You work for a breakfast cereal manufacturer. Your job is to decide if the new machinery is overfilling the cereal boxes. You take a sample of 37 randomly selected boxes and find that the mean weight for the sample is 1.6 lbs with sample standard deviation 0.3 lbs. The boxes are supposed to weigh 1.5 lbs. Conduct a hypothesis test at the α = 0.01 significance level. Be sure to state your conclusion in context.
A food manufacturer claims that eating its new cereal as part of a daily diet lowers...
A food manufacturer claims that eating its new cereal as part of a daily diet lowers total blood cholesterol levels. The table shows the total blood cholesterol levels​ (in milligrams per deciliter of​ blood) of seven patients before eating the cereal and after one year of eating the cereal as part of their diets. Use technology to test the mean difference. Assume the samples are random and​ dependent, and the population is normally distributed. At alphaαequals=0.050.05​, can you conclude that...
Empire Industries is considering adding a new product to its lineup. This product is expected to...
Empire Industries is considering adding a new product to its lineup. This product is expected to generate sales for four years after which time the product will be discontinued. What is the project's net present value if the firm wants to earn a 13 percent rate of return? YEAR CASH FLOW ($) 0 -62,000 1 16,500 2 23,800 3 27,100 4 23,300
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT