Math 227 - Statistics » Winter 2024 » Module VI Quiz

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Question #1
In a random sample of 300 women, 49% favored stricter gun control legislation. In a random sample of 200 men, 28% favored stricter gun control legislation. Construct a 98% confidence interval for the difference between the population proportions Þ1-Þ2
A.   0.099 < Þ1−Þ2 < 0.321
B.   0.122 < Þ1−Þ2 < 0.298
C.   0.126 < Þ1−Þ2 < 0.294
D.   0.110 < Þ1−Þ2 < 0.310
Question #2
A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. Construct the 95% confidence interval for the true proportion of all voters in the state who favor approval.
A.   0.435 < p < 0.508
B.   0.471 < p < 0.472
C.   0.438 < p < 0.505
D.   0.444 < p < 0.500
Question #3
When 319 college students are randomly selected and surveyed, it is found that 120 own a car. Find a 99% confidence interval for the true proportion of all college students who own a car.
A.   0.332 < p < 0.421
B.   0.323 < p < 0.429
C.   0.306 < p < 0.446
D.   0.313 < p < 0.439
Question #4
The amounts (in ounces) of juice in eight randomly selected juice bottles are: 15.2 15.5 15.9 15.5 15.0 15.7 15.0 15.7 Construct a 98% confidence interval for the mean amount of juice in all such bottles.
A.   15.77 oz < μ < 15.10 oz
B.   15.08 oz < μ < 15.80 oz
C.   15.87 oz < μ < 15.00 oz
D.   15.16 oz < μ < 15.72 oz
Question #5
The principal randomly selected six students to take an aptitude test. Their scores were: 76.5 85.2 77.9 83.6 71.9 88.6 Determine a 90% confidence interval for the mean score for all students.
A.   85.84 < μ < 75.39
B.   75.48 < μ < 85.75
C.   76.42 < μ < 84.81
D.   85.74 < μ < 75.49
Question #6
A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 225 milligrams with s = 15.7 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.
A.   215.1 mg < μ < 234.9 mg
B.   215.0 mg < μ < 235.0 mg
C.   214.9 mg < μ < 235.1 mg
D.   216.9 mg < μ < 233.1 mg
Question #7
A savings and loan association needs information concerning the checking account balances of its local customers. A random sample of 14 accounts was checked and yielded a mean balance of $664.14 and a standard deviation of $297.29. Find a 98% confidence interval for the true mean checking account balance for local customers.
A.   $492.52 < μ < $835.76
B.   $493.71 < μ < $834.57
C.   $453.59 < μ < $874.69
D.   $455.65 < μ < $872.63
Question #8
x1= 22, n1= 38 and x2= 31, n2= 52; Construct a 90% confidence interval for the difference between population proportions Þ1−Þ2.
A.   -0.190 < Þ1−Þ2 < 0.156
B.   0.785 < Þ1−Þ2 < 0.373
C.   0.406 < Þ1−Þ2 < 0.752
D.   0.373 < Þ1−Þ2 < 0.785
Question #9
Two types of flares are tested and their burning times are recorded. The summary statistics are given below. Brand X n1=35 x̄1=19.4 min s1 = 1.4 min Brand Y n2=40 X̅2=15.1 min s2 = 0.8 min Construct a 95% confidence interval for the differences between the mean burning time of the brand X flare and the mean burning time of the brand Y flare.
A.   3.2 min <µx−µγ< 5.4 min
B.   3.6 min < µx−µγ < 5.0 min
C.   3.5 min < µx−µγ< 5.1 min
D.   3.8 min < µx−µγ< 4.8 min
Question #10
Independent samples from two different populations yield the following data. x̄1= 236, x̄2= 905, s1=88, s2=13. The sample size is 381 for both samples. Find the 85% confidence interval for µ1−µ2.
A.   -676 < µ1−µ2 < -662
B.   -670 < µ1−µ2 < -668
C.   -677 <µ1−µ2 < -661
D.   -683 < µ1−µ2 < -655
Question #11
A marketing survey involves product recognition in New York and California. Of 558 New Yorkers surveyed, 193 knew the product while 196 out of 614 Californians knew the product. Construct a 99% confidence interval for the difference between the two population proportions.
A.   0.0247 < P1− P 2 < 0.0286
B.   -0.0177 < P1− P 2 < 0.1243
C.   -0.0034 < P1− P 2 < 0.0566
D.   -0.0443 P1− P 2 < 0.0976
Question #12
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n = 51, x = 27;
A.   0.392 < p < 0.666
B.   0.413 < p < 0.645
C.   0.391 < p < 0.667
D.   0.414 < p < 0.644

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