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Deb's Specialty Coffees and Desserts

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Deb is the owner and manager of Deb's Specialty Coffees and Desserts, a small Oregon firm that roasts coffee beans and retails bulk beans to grocery stores, as well as desserts targeted to health conscious consumers. Deb is curious as to whether her new publicity campaign will help boost sales in the stores that carry her products. During a recent month, she hired unemployed State workers to provide free samples to grocery shoppers in one of the chains of Oregon grocery stores that she supplies. She hopes that the cost of the campaign will be more than offset by increased unit sales. The total cost to Deb is $1,500 each month for the cost of supplies, renting space in the stores, and salaries for handing out the free samples.
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Side by side refer the Excel sheet:

We can use the Z-test to compare the means of the population control group and the experimental group.

Z-Statistics =
Here,
is the mean of the control group and is the mean of the experimental group, S12 and S22 is the standard deviation of control group and the experimental group respectively.

=

= -4.30072
At 0.05 and 0.01 level of significance we have the t-table values as -1.6707 and -2.3901 respectively. So we can accept the null hypothesis an increase was realized.

1. How large an increase was realized? How confident can she be in the results?

Solution:

The experimental group is 36.2643 more than the control group. She can be 99.99% confident in the results.

2. Was there a real difference between the two chains of grocery stores?

Solution:
Yes, there is a real difference between the two chains of grocery stores.

3. How much confidence can be placed in the results of the analysis?

The 99 % confidence can be placed in the results of the analysis.

4. Calculate and explain descriptive statistics and variation for these data sets.

Mean for the control group and the experimental group:

We know that mean of any data set can be found out using the formula,

,
the standard deviation for the data set is given by,

The following table gives the mean and the standard deviation for the given data.

X1-bar 153.5571
X2-bar 189.8214
S1 25.61086
S2 39.25423

5. Discuss similarities and differences. What is the most efficient way to compare the two data sets?

The control group and the experimental group vary in their mean and also in the standard deviation, but the number of data in the each set is 31.

To compare the two set of data, we can go with the testing the difference between the two means. Since mean is the representative of both the sample.

ANOVA:

Sum of Squares for between can be found out using the formula,

Hypotheses
The null hypothesis will be that all population means are equal, the alternative hypothesis is that at least one mean is different.
In the following, lower case letters apply to the individual samples and capital letters apply to the entire set collectively. That is, n is one of many sample sizes, but N is the total sample size.
Grand Mean
The grand mean of a set of samples is the total of all the data values divided by the total sample size. This requires that you have all of the sample data available to you, which is usually the case, but not always. It turns out that all that is necessary to find perform a one-way analysis of variance are the number of samples, the sample means, the sample variances, and the sample sizes.
Another way to find the grand mean is to find the ...

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