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A survey investigating whether the proportion of today's high school seniors who own their own cars is higher than it was a decade ago finds a P-value of 0.017 . Is it reasonable to conclude that more high schoolers have cars? Explain.

He cheats? A friend of yours claims that when he tosses a coin he can control the outcome. You are skeptical and want him to prove it. He tosses the coin, and you call heads; it's tails. You try again and lose again. a. Do two losses in a row convince you that he really can control the toss? Explain. b. You try a third time, and again you lose. What's the probability of losing three tosses in a row if the process is fair? c. Would three losses in a row convince you that your friend controls the outcome? Explain. d. How many times in a row would you have to lose to be pretty sure that this friend really can control the toss? Justify your answer by calculating a probability and explaining what it means.

Candy Someone hands you a box of a dozen chocolatecovered candies, telling you that half are vanilla creams and the other half peanut butter. You pick candies at random and discover the first three you eat are all vanilla. a. If there really were 6 vanilla and 6 peanut butter candies in the box, what is the probability that you would have picked three vanillas in a row? b. Do you think there really might have been 6 of each? Explain. c. Would you continue to believe that half are vanilla if the fourth one you try is also vanilla? Explain.

Smartphones Many people have trouble setting up all the features of their smartphones, so a company has developed what it hopes will be easier instructions. The goal is to have at least \(96 \%\) of customers succeed. The company tests the new system on 200 people, of whom 188 were successful. Is this strong evidence that the new system fails to meet the company's goal? A student's test of this hypothesis is shown. How many mistakes can you find? $$ \begin{array}{l} \mathrm{H}_{0}: \hat{p}=0.96 \\ \mathrm{H}_{\mathrm{A}}: \hat{p} \neq 0.96 \\ \mathrm{SRS}, 0.96(200)>10 \\ \frac{188}{200}=0.94 ; S D(\hat{p})=\sqrt{\frac{(0.94)(0.06)}{200}}=0.017 \end{array} $$ \(z=\frac{0.96-0.94}{0.017}=1.18\) $$ \mathrm{P}=P(z>1.18)=0.12 $$

Obesity 2016 In \(2016,\) the Centers for Disease Control and Prevention reported that \(36.5 \%\) of adults in the United States are obese. A county health service planning a new awareness campaign polls a random sample of 750 adults living there. In this sample, 228 people were found to be obese based on their answers to a health questionnaire. Do these responses provide strong evidence that the \(36.5 \%\) figure is not accurate for this region? Correct the mistakes you find in a student's attempt to test an appropriate hypothesis. $$ \begin{array}{l} \mathrm{H}_{0}: \hat{p}=0.365 \\ \mathrm{H}_{\mathrm{A}}: \hat{p}<0.365 \\ \mathrm{SRS}, 750 \geq 10 \\ \frac{228}{750}=0.304 ; S D(\hat{p})=\sqrt{\frac{(0.304)(0.696)}{750}}=0.017 \end{array} $$ \(z=\frac{0.304-0.365}{0.017}=-3.588\) $$ \mathrm{P}=P(z>-3.588)=0.9998 $$ There is more than a \(99.98 \%\) chance that the stated percentage is correct for this region.

Dowsing In a rural area, only about \(30 \%\) of the wells that are drilled find adequate water at a depth of 100 feet or less. A local man claims to be able to find water by "dowsing"using a forked stick to indicate where the well should be drilled. You check with 80 of his customers and find that 27 have wells less than 100 feet deep. What do you conclude about his claim? a. Write appropriate hypotheses. b. Check the necessary assumptions and conditions. c. Perform the mechanics of the test. What is the P- value? d. Explain carefully what the P-value means in context. e. What's your conclusion?

In the 1980 s, it was generally believed that congenital abnormalities affected about \(5 \%\) of the nation's children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 384 children and found that 46 of them showed signs of an abnormality. Is this strong evidence that the risk has increased? a. Write appropriate hypotheses. b. Check the necessary assumptions and conditions. c. Perform the mechanics of the test. What is the P- value? d. Explain carefully what the P-value means in context. e. What's your conclusion? f. Do environmental chemicals cause congenital abnormalities?

Absentees The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In \(1996,34 \%\) of students had not been absent from school even once during the previous month. In a 2000 survey, responses from 8302 students showed that this figure had slipped to \(33 \%\). Officials would, of course, be concerned if student attendance were declining. Do these figures give evidence of a change in student attendance? a. Write appropriate hypotheses. b. Check the assumptions and conditions. c. Perform the test and find the P-value. d. State your conclusion. e. Do you think this difference is meaningful? Explain.

Contributions, please II We learned in Chapter 16 ?, Exercise 35 ? that the Paralyzed Veterans of America recently sent letters to a random sample of 100,000 potential donors and received 4781 donations. They've had a contribution rate of \(5 \%\) in past campaigns, but a staff member worries that the rate is lower now that they've redesigned their letter. Is there evidence that the \(4.78 \%\) they received is evidence of a real drop in the contribution rate? a. What are the hypotheses? b. Are the assumptions and conditions for inference met? c. Do you think the rate would drop? Explain.

Pollution A company with a fleet of 150 cars found that the emissions systems of 7 out of the 22 they tested failed to meet pollution control guidelines. Is this strong evidence that more than \(20 \%\) of the fleet might be out of compliance? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.