91影视

Cell-phone passwords A consumer organization suspects that less than half of parents know their child鈥檚 cell-phone password. The Pew Research Center asked a random sample of parents if they knew their child鈥檚 cell-phone password. Of the $1060$parents surveyed, $551$reported that they knew the password. Explain why it isn鈥檛 necessary to carry out a significance test in this setting.

Proposition XA political organization wants to determine if there is convincing evidence that a majority of registered voters in a large city favor Proposition X. In an SRS of $1000$registered voters, $482$favor the proposition. Explain why it isn鈥檛 necessary to carry out a significance test in this setting.

Gregor Mendel $(1822-1884)$, an Austrian monk, is considered the father of genetics. Mendel studied the inheritance of various traits in pea plants. One such trait is whether the pea is smooth or wrinkled. Mendel predicted a ratio of $3$smooth peas for every $1$wrinkled pea. In one experiment, he observed $423$smooth and $133$wrinkled peas. Assume that the conditions for inference are met.

a. . State appropriate hypotheses for testing Mendel鈥檚 claim about the true proportion of smooth peas.

b. Calculate the standardized test statistic and P-value.

c. Interpret the P-value. What conclusion would you make?

Teen drivers A state鈥檚 Division of Motor Vehicles (DMV) claims that $60\%$

of all teens pass their driving test on the first attempt. An investigative reporter examines an SRS of the DMV records for $125$teens; $86$of them passed the test on their first try. Is there convincing evidence at the $伪=0.05$significance level that the DMV鈥檚 claim is incorrect?

We want to be rich In a recent year, $73\%$of first-year college students responding to a national survey identified 鈥渂eing very well-off financially鈥� as an important personal goal. A state university finds that $132$of an SRS of $200$of its first-year students say that this goal is important. Is there convincing evidence at the $伪=0.05$significance level that the proportion of all first-year students at this university who think being very well-off is important differs from the national value of 73%?

Teen drivers Refer to Exercise 51.

a. Construct and interpret a 95% confidence interval for the true proportion p of all teens in the state who passed their driving test on the first attempt. Assume that the conditions for inference are met.

b. Explain why the interval in part (a) provides more information than the test in Exercise 51.

Refer to Exercise $52$.

a. Construct and interpret a $95\%$confidence interval for the true proportion p of all first year students at the university who would identify being very well-off as an important personal goal. Assume that the conditions for inference are met.

b. Explain why the interval in part (a) provides more information than the test in Exercise 52.

Do you Tweet? The Pew Internet and American Life Project asked a random sample of U.S. adults, 鈥淒o you ever 鈥� use Twitter or another service to share updates about yourself or to see updates about others?鈥� According to Pew, the resulting 95% confidence interval is (0.123, 0.177).11 Based on the confidence interval, is there convincing evidence that the true proportion of U.S. adults who would say they use Twitter or another service to share updates differs from 0.17? Explain your reasoning.

Losing weight A Gallup poll found that 59% of the people in its sample said 鈥淵es鈥� when asked, 鈥淲ould you like to lose weight?鈥� Gallup announced: 鈥淔or results based on the total sample of national adults, one can say with 95% confidence that the margin of (sampling) error is 卤3 $卤3$percentage points.鈥�12 Based on the confidence interval, is there convincing evidence that the true proportion of U.S. adults who would say they want to lose weight differs from 0.55? Explain your reasoning

Reporting cheating What proportion of students are willing to report cheating by other students? A student project put this question to an SRS of 172 undergraduates at a large university: 鈥淵ou witness two students cheating on a quiz. Do you go to the professor?鈥� The Minitab output shows the results of a significance test and a 95% confidence interval based on the survey data.13

a. Define the parameter of interest.

b. Check that the conditions for performing the significance test are met in this case.

c. Interpret the P-value.

d. Do these data give convincing evidence that the population proportion differs from $0.15$? Justify your answer with appropriate evidence.