ch15 - Chapter 15 Solutions 15.1 The most important reason...

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Chapter 15 Solutions 15.1. The most important reason is (c); this is a convenience sample consisting of students with a particular interest in Flmmaking which may make their opinions different from those of “typical” college-age adults. Anything we learn from this sample will not extend to the larger population The other two reasons are valid (but less important) issues. Reason (a)—the size of the course, and large margin of error—would make the interval less informative, even if the sample were representative of the population. Reason (b)—nonresponse—is a potential problem with every survey, but there is no particular reason to believe it is more likely in this situation. 15.2. (a) The 95% conFdence interval is x ± 1 . 96 σ/ 880 = 1 . 92 ± 0 . 1209 = 1 . 80 to 2.04 motorists. (b) The large sample size means that, because of the central limit theorem, the sampling distribution of x is roughly Normal even if the distribution of responses is not. (c) Only people with listed phone numbers were represented in the sample, and the low response rate (10 . 9% . = 5029 45 , 956 ) means that even that group may not be well represented by this sample. 15.3. Any number of things could go wrong with this convenience sample. Depending on the time of day or the day of the week, certain types of shoppers would or would not be present. 15.4. (a) The three conFdence intervals are given in the table on the right: x ± z n . = 26 . 8 ± 0 . 2933 z . (b) The margins of error, given in the “m.e.” column, increase as conFdence level increases. Conf. Level z m.e. Interval 90% 1.645 0.4824 26.32 to 27.28 95% 1.960 0.5748 26.23 to 27.37 99% 2.576 0.7555 26.04 to 27.56 15.5. With z = 1 . 96 and σ = 7 . 5, the margin of error is z n = 14 . 7 / n . (a) and (b) The margins of error are given in the table. (c) Mar- gin of error decreases as n increases. (SpeciFcally, it is halved each time n quadruples.) n m.e. 100 1.47 400 0.735 1600 0.3675 15.6. (a) Not included: this is a flaw in the sampling design. (b) Not included: this error arises from the sampling process. (c) Included: this random error is the only error addressed by conFdence interval methods. 15.7. (a) z = 544 518 114 / 50 . = 1 . 61—not signiFcant at the 5% level ( P = 0 . 0537). (b) z = 545 518 114 / 50 . = 1 . 67—signiFcant at 5% level ( P = 0 . 0475), 178
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Solutions 179 15.8. The full applet output for n = 5is below on the left; on the right are the Normal curves drawn for n = 15 and n = 40. The reported P -values agree with the “hand-computed” values z = 4 . 8 5 0 . 5 / n and P = P ( Z < z ) given in the table on the right. nz P 5 0.89 0.1867 15 1.55 0.0606 40 2.53 0.0057 15.9. The conFdence intervals are given in the table on the right. In each case, the interval is 4 . 8 ± 1 . 960 µ 0 . 5 n . n Interval 5 4.362 to 5.238 15 4.547 to 5.053 40 4.645 to 4.955 15.10. (a) In a sample of size 500, we expect to see about 5 people who have a P -value of 0.01 or less [5 = ( 500 )( 0 . 01 ) ]. These four might have ESP, or they may simply be among the “lucky” ones we expect to see. (b) The researcher should repeat the procedure on these four to see whether they again perform well.
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This note was uploaded on 11/23/2010 for the course STAT 2325151 taught by Professor T during the Spring '10 term at Waters College.

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ch15 - Chapter 15 Solutions 15.1 The most important reason...

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