Goodness of Fit Test: Videos & Practice Problems

A survey is conducted to determine the distribution of preferred fruit among a group of people. The fruits considered in the survey are apples, bananas, oranges, grapes, and pears. Based on past studies, it is expected that the preference for each fruit is equal, with each fruit having a $20\%$ chance of being chosen.
$H_0$: $p_{\text{apple}}=p_{\text{banana}}=p_{\text{orange}}=p_{\text{grape}}=p_{\text{pear}}=0.2$
$H_1$: At least one of the proportions is different from the others.

Test the hypothesis at the $\alpha =0.05$ level of significance.