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:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]
The formula to compute the expected frequency is:
[tex]E_{i}=\frac{i^{th}\ \text{Row Total}\times i^{th}\ \text{Column Total}}{N}[/tex]
Consider the Excel output for the expected frequency values.
The Chi-square test statistic value is:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}=56.788[/tex]
The degrees of freedom is:
df = (r - 1)(c - 1)
= (3 - 1)(5 - 1)
= 2 × 4
= 8
The p-value is:
[tex]P(\chi^{2}_{8}>56.788)<0.00001[/tex]
*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.
