Question

a company is started by four friends. the company was ericas idea, so she wants to fill 70% of the orders. jen, heather, and tonya each agree to fill 10% of the orders. after a successful first year, erica wants to determine if the distribution of the number of orders filled is adhering to the agreed - upon percentages. she decides to test: ( h_{0}: p_{erica}=0.7,p_{jen}=0.1,p_{heather}=0.1,p_{tonya}=0.1 ) ( h_{a} ): not all of the pis are as stated. to do so, she selects a random sample of 100 orders from the large number of orders that were filled and determines who filled the order. she finds that erica filled 56 orders, jen filled 18, heather filled 14, and tonya filled 12. the chi - square test statistic for goodness of fit is ( chi^{2}=11.20 ) and the p - value is between 0.01 and 0.02. because the p - value is less than 0.05, erica rejects the null hypothesis. because the null hypothesis is rejected, she would like to know which term contributed the significance of the test. complete a follow - up analysis. which term contributed the most to the significance of this test? were there more or fewer orders being filled by this person than expected? erica, more than expected erica, fewer than expected jen, more than expected jen, fewer than expected

Explanation:

Step1: Calculate expected values

Expected value for Erica: \(E_{Erica}=n\times p_{Erica}=100\times0.7 = 70\)
Expected value for Jen: \(E_{Jen}=n\times p_{Jen}=100\times0.1 = 10\)
Expected value for Heather: \(E_{Heather}=n\times p_{Heather}=100\times0.1 = 10\)
Expected value for Tonya: \(E_{Tonya}=n\times p_{Tonya}=100\times0.1 = 10\)

Step2: Calculate \((O - E)^2/E\) for each person

For Erica: \(\frac{(56 - 70)^2}{70}=\frac{(- 14)^2}{70}=\frac{196}{70}=2.8\)
For Jen: \(\frac{(18 - 10)^2}{10}=\frac{8^2}{10}=\frac{64}{10}=6.4\)
For Heather: \(\frac{(14 - 10)^2}{10}=\frac{4^2}{10}=\frac{16}{10}=1.6\)
For Tonya: \(\frac{(12 - 10)^2}{10}=\frac{2^2}{10}=\frac{4}{10}=0.4\)

Answer:

Jen, more than expected.