Question

A survey of Internet users reported that 15% downloaded music onto their computers. The filing of lawsuits by the recording industry may be a reason why this percent has decreased from the estimate of 31% from a survey taken two years before. Suppose we are not exactly sure about the sizes of the samples. Perform the calculations for the significance tests and 95% confidence intervals under each of the following assumptions. (Use previous − recent. Round your test statistics to two decimal places and your confidence intervals to four decimal places.)

(i) Both sample sizes are 1000.

Z = _______

95% C.I. ( _______, _______ )

(ii) Both sample sizes are 1600.

Z= _______

95% C.I. ( _______, _______ )

(iii) The sample size for the survey reporting 31% is 1000 and the sample size for the survey reporting 15% is 1600.

Z= _______

95% C.I. ( _______, _______ )

Summarize the effects of the sample sizes on the results.

We see in (i) and (ii) that smaller samples result in larger z (stronger evidence) and narrower intervals, while larger samples have the reverse effect. The results of (iii) show that the effect of varying unequal sample sizes is more complicated.

We see in (i) and (ii) that smaller samples result in smaller z (stronger evidence) and wider intervals, while larger samples have the reverse effect. The results of (iii) show that the effect of varying unequal sample sizes is more complicated.     

We see in (i) and (ii) that smaller samples result in larger z (weaker evidence) and smaller intervals, while larger samples have the reverse effect. The results of (iii) show that the effect of varying unequal sample sizes is more complicated.

We see in (i) and (ii) that smaller samples result in smaller z (weaker evidence) and narrower intervals, while larger samples have the reverse effect. The results of (iii) show that the effect of varying unequal sample sizes is more complicated.

We see in (i) and (ii) that smaller samples result in smaller z (weaker evidence) and wider intervals, while larger samples have the reverse effect. The results of (iii) show that the effect of varying unequal sample sizes is more complicated.

Answer 1

Solutlont a1e sizes Botn sample 150 o 210 valuues G P(1- P P,(- slandord tu oIS (- s) o 311-0 31) ooD TStandasd Meirgin oI .6xO.o18 5 O0362. tnterve Contidence -o-13 38, o1962 gamplej 00 46 2 40 24 O 1 50 P, (-P o 311-6.3I oIS(-o15) 1600

value Margin Limit s confidence Interu el, o 114 01 310 A2 24D LE EO31 Mi1000 Stardard &tTOY : valuc f ox Margiw Intervel -tE Conkidence 1264,O ME o962 o1238 000 66362 I000 009 .02860 1314 30 1600 : 1264 2 to00