**Concept:** Calculating the Test Statistic for a Sample Proportion

**Concept:** Calculating the Test Statistic for a Sample Proportion: Intro

**Problem:** UPS claims all orders ship within the same day, but knows that the percentage is actually closer to 95%. Out of a

random sample of 100 items from a particular branch, 90 were shipped within the same day. Is there enough evidence to

conclude that this branch’s proportion of items shipped within the same day is less than expected? Test using a significance

level of 4%.

**Problem:** AMC Theaters has claimed that, on average, half of the people who attend the theater purchase something

else at the concession stands. A manager gets a bonus if their theater gets a significantly higher proportion of customers to

purchase concessions products than the average theater. Out of 144 randomly selected theater-goers, a theater had 80 of

them purchase concessions products. Can this theater’s manager claim his bonus using an α = .01?

**Problem:** Physics majors are said to be better candidates for medical school. Out of any science degree, the average

rate for students to apply and get admitted is .55. A random sample of 225 physics ma jors who applied to medical schools

was collected. 142 of these students eventually went to medical school. Is there evidence to suggest that physics majors

have a higher chance of getting into medical school? Use a .10 significance level.