Question

You are contacted by the top cookie-selling Girl Scout troop in the city. As part of their sales plan for next year’s cookie selling season, they need to know (with 99% confidence, or α = 0.01) if the types of cookies purchased by their customers depends on where the scouts sell them. Here is their confidential sales data from last year:

Answer 1

Answer:

The types of cookies purchased by the customers depends on where the scouts sell them.

Step-by-step explanation:

The data provided is:

Sales                                                   Type of Cookie Sold

Method                                                        

                   Thin Mints        Tagalongs          Do-si-dos         Trefoils        Samoas

    At

parents’        472                   641                    350                  223               401

workplace  

  Door

  -to-              840                  1092                   673                    511               542

  Door  

Community   683                     742                   491                     420             374

  Events

A Chi-square test for goodness of fit will be used to determine whether the types of cookies purchased by the customers depends on where the scouts sell them.

The hypothesis can be defined as:

H₀: The observed frequencies are same as the expected frequencies.

Hₐ: The observed frequencies are not same as the expected frequencies.

The test statistic is given as follows:

$\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}$

The formula to compute the expected frequency is:

$E_{i}=\frac{i^{th}\ \text{Row Total}\times i^{th}\ \text{Column Total}}{N}$

Consider the Excel output for the expected frequency values.

The Chi-square test statistic value is:

$\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}=56.788$

The degrees of freedom is:

df = (r - 1)(c - 1)

   = (3 - 1)(5 - 1)

   = 2 × 4

   = 8

The p-value is:

$P(\chi^{2}_{8}>56.788)$

*Use a Chi-square table.

The p-value of the test is very small.

The null hypothesis will be rejected at 1% level of significance.

Conclusion:

There is enough evidence to support the claim that the types of cookies purchased by the customers depends on where the scouts sell them.