10 questions

23 minutes

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1. After a frost warning was issued, the owner of a large orange grove asked his workers to spray all his trees with water. The water was supposed to freeze and form a protective covering of ice around the orange blossom. Nevertheless, the owner suspected that some trees suffered considerable damage due to the frost. To estimate the proportion of trees that suffered more than 50 percent damage due to the frost, he took a random sample of 100 trees from his grove. What is the response variable in this experiment?

2. For which of the following purposes would it be most unreasonable to use a census?

3. A student organization at a university is interested in estimating the proportion of students in favor of showing movies biweekly instead of monthly. How many students should be sampled to get a 90 percent confidence interval with a width of at most 0.08?

4. A small kiosk at the Atlanta airport carries souvenirs in the price range of $3.99 to $29.99, with a mean price of $14.75. The airport authorities decide to increase the rent charged for a kiosk by 5 percent. To make up for the increased rent, the kiosk owner decides to increase the prices of all items by 50 cents. As a result, which of the following will happen?

5. Two hundred students were classified by sex and hostility level (low, medium, high), as measured by an HLT-test. The results were the following:

If the hostility level among students were independent of their sex, then how many female students would we expect to show the medium HLT score?

6. After receiving several complaints from his customers about the store being closed on Sundays, a storekeeper decided to conduct a survey. He randomly selected 100 female customers and 120 male customers, and asked them, "Are you interested in shopping at this store on Sundays?" He counted the number of customers answering "yes" and constructed a 95 percent confidence interval for the difference by subtracting the proportions of female from the proportion of male customers in favor of shopping on Sundays. The resulting interval was (–0.23, –0.18). Which of the following is a correct interpretation of the interval?

7. A company is interested in comparing the mean sales revenue per salesperson at two different locations. The manager takes a random sample of 10 salespeople from each location independently and records the sales revenue generated by each person during the last four weeks. He decides to use a t-test to compare the mean sales revenue at the two locations. Which of the following assumptions is necessary for the validity of the t-test?

8. A skeptic decides to conduct an experiment in ESP in which a blindfolded subject calls out the color of a card dealt from a regular deck of cards (half the cards are red; the other half, black). One hundred cards are dealt from a well-shuffled pack, with each card being replaced after a deal. Using a 5 percent level of significance, what is the lowest number of cards that the subject needs to call out correctly in order to show that he is doing better than he would if he were simply guessing?

9. A manufacturer of motor oil is interested in testing the effects of a newly developed additive on the lifespan of an engine. Twenty-five different engine types are selected at random and each one is tested using oil with the additive and oil without the additive. What type of analysis will yield the most useful information?

10. A chi-squared test of independence is to be performed on a 3 × 4 contingency table. How many degrees of freedom does this test have?