Suppose that insurance companies did a survey. They randomly surveyed 440 drivers and found that 330 claimed they always buckle up. We are interested in the population proportion of drivers who claim they always buckle up. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a (1) Enter an exact number as an integer, fraction, or decimal. * = 330 (ii) Enter an exact number as an integer, fraction, or decimal. 1= 440 ii) Round your answer to four decimal places. p' = -75 (rounded to four decimal places) Part (b) In words, define the random variables X and P' O X is the proportion of people in the sample who do not buckle up, and P' is the number of people who do not buckle up. O X is the ho buckle up. O X is the number of peop ample who do not buckle up. X is the number of people who ion of people in the sample who buckle up. Correct! The random variable of interest, X, is the number of people who buckle up. and P' represents the proportion of the sample who buckle up. Part (c) Which distribution should you use for this problem? (Round your answer to four decimal places.) P' ~ N |.75 .9750 Explain your choice. O The binomial distribution should be us e two outcomes, buckle up or do not buckle up. O The Stude dard deviation. O The Student's t-distribution should be used because vnpq S 10, which implies a small sample The normal distribution should be used sted in proportions and the sample size is large. Correct! We use the standard normal distribution to create confidence intervals about the population proportion. Part (d) Construct a 95% confidence interval for the population proportion who claim they always buckle up. 1) State the confidence interval. (Round your answers to four decimal places.) 7095 .7905 (ii) Sketch the graph. = 025 C.L. = 95 = 025 7095 7905 P' (i) Calculate the error bound. (Round your answer to four decimal places.) .0405 Part (e) if this survey were done by telephone, list three difficulties the companies might have in obtaining random results. Individuals may not tell the truth about buckling up one will not be included. Only peop be included in the survey effect the population. Individuals may choose to participate or not participate in the phone surveypharmaceutical company makes tranquilizers. It is assumed that the dis 1 a hospital used the drug on a random sample of 9 pa : 2.6; 2.9; 3.1; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4. NOTE: If you are using a Student's t-distribution, you may assume sumption, though.) Part (a ) (i) Round your answer to two decimal places. * = 2.52 (rounded to two decimal places) (i) Round your answer to two decimal places 5 x = .35 (rounded to two decimal pl (ii) Enter an exact number as an integer, fraction, or decimal. n =9 (iv) Enter an exact number as an integer, fraction, or decimal. n - 1=B Part (b) In words, define the random variable X. time, in hours, of the effectiveness of a tranquilizer O the number of patients that were g ranquilizer O the number of tranquilizers the hospital used for each patient O time, in minutes, of the effectiveness of a tranquilizer Correct: The pharmaceutical company Ic Interested In how many hours a tranquilizer Is effective. Part (c) In words, define the random variable X. O the average number of tranquilizers used for each patient the average length, in ha ness period of tranquilizers O the average length, in minutes, of the effectiveness period of tranquilizers O the average number of tranqui company dispenses to hospitals Correct The pharmaceutical company Ic Interested In the average number of hours a tranquilizer Is effective. - Part (d) Which distribution should you use for this problem? (Enter your answer in the form 2 or fay where of is the degrees of freedom.) tcit Explain your choice. The Student's I-distribu on is known and the sample size is small. O The standard normal distribution ndard deviation is known. O The standard not deviation is known. O The Student's Correct Only cample data Is given for nine camples; exiation le a cample clandard deviation Part (9) Construct a 95% confidence interval for the population mean length of time. (i) State the confidence interval. (Round your answers to two decimal places.) 2.26 2.79 ") Sketch the graph. a _ 025 C.L. =95 2 025 2.26 2.79 X 27 (i) Calculate the error bound. (Round your answer to two decimal places.) - Part (1) What does it mean to be "95% confident" in this problem? O This means that the chances of a tranquilizer bei O This mear We are 95% confident that the This Correoti 8636 con nath of effectiveness of tranquilizers