Question

A large food distributor claims that 45% of all individuals who purchase eggs from its grocery stores choose standard white eggs, 25% choose standard brown eggs, 20% choose organic eggs, and 10% choose free-range eggs. To investigate this claim, researchers collected data from a random sample of the distributor's customers in a large city. The results were 274 white, 159 brown, 126 organic, and 41 free-range egg purchases. Are the data from the sample consistent with the distributor's claim? Conduct an appropriate statistical test at the 5% significance level to support your conclusion. Make sure to include parameters, check conditions, and show calculations before formulating a conclusion.

Answer 1

To determine if the data from the sample is consistent with the food distributor's claim, we will conduct a chi-squared test of independence.

Step-by-step explanation:

To determine if the data from the sample is consistent with the food distributor's claim, we will conduct a chi-squared test of independence. This test is appropriate when analyzing categorical data.

The null hypothesis is that the observed frequencies are consistent with the expected frequencies based on the food distributor's claim.

First, we need to calculate the expected frequencies for each category. We multiply the total sample size (600) by the claimed percentages to obtain the expected counts: 270 white eggs, 150 brown eggs, 120 organic eggs, and 60 free-range eggs.

Next, we calculate the chi-squared statistic by summing the squared differences between the observed and expected frequencies, divided by the expected frequencies: 0.44.

Finally, we compare the chi-squared statistic to the critical value from the chi-squared distribution with (number of categories -1) degrees of freedom at the 5% significance level.

If the calculated chi-squared value is greater than the critical value, we reject the null hypothesis and conclude that the data is not consistent with the food distributor's claim.