Download Practice Quiz #6

1) A survey of college graduates asked , “how old were you when you earned your
bachelor’s degree?” The results of 35 respondents revealed a sample mean of 24.1 years
with sample standard deviation 3.2 years.
a) Construct a 90% confidence interval for the population mean age at which
college graduates first get married.
b) Interpret your confidence interval in the context of the question.
2) A random sample of 1100 “teenagers” (ages 12 to 17) were asked whether they played
games online; 775 said that they did.
a) Construct a 95% confidence interval for the proportion of all teenagers who
play games online.
b) Interpret the confidence interval in the context of the problem.
c) How large should the sample be in order to have a margin of error of 1% with
95% confidence.
3) A random sample of 900 college students were asked if the college they are currently
attending was their first choice. Only 19% of them said yes. Construct and interpret a
99% confidence interval for the proportion of all college students who are currently
attending their school of first choice.
4) A random sample of 55 retired people in the United States was asked how many
different jobs they held their working adult life (from the time they left school until the
time they retired). The average was 8.3 jobs with standard deviation 4.9 jobs. Construct
and interpret a 95% confidence for the average number of jobs held by all retirees during
their working adult life.
1) A survey of college graduates asked , “how old were you when you earned your
bachelor’s degree?” The results of 35 respondents revealed a sample mean of 24.1 years
with sample standard deviation 3.2.
µ = average age at which all college graduates earn their bachelor’s degree
n = 35, df = 34, 𝑥̅ = 24.1, s = 3.2
a) Construct a 90% confidence interval for the population mean age at which
college graduates earn their bachelor’s degree.
t* = 1.69
3.2
24.1 ± 1.691 (
) = 24.1 ± 0.915 = (23.185,25.015)
√35
[make sure you are using t* and not z*!!]
b) Interpret your confidence interval in the context of the question.
I am 90% confident that the average age at which all college graduates earn their
bachelor’s degree is between 23.185 and 25.015 years old.
2) A random sample of 1100 “teenagers” (ages 12 to 17) were asked whether they played
games online; 775 said that they did.
a) Construct a 95% confidence interval for the proportion of all teenagers who
play games online.
775
𝑝̂ = 1100 = 0.70455, 𝑞̂ = 1 − 0.70455 = 0.29545, n = 1100, z* = 1.960
0.70455 × 0.29545
0.70455 ± 1.960√
= 0.70455 ± 0.02696
1100
= (0.67759,0.73151)
b) Interpret the confidence interval in the context of the problem.
I am 95% confident that the proportion of all teenagers who play games online is
between 0.67758 and 0.73151.
c) How large should the sample be in order to have a margin of error of 1% with
95% confidence.
1.9602 × 0.70455 × 0.29545
𝑛=
= 7997
(. 01)2
3) A random sample of 900 college students were asked if the college they are currently
attending was their first choice. Only 19% of them said yes. Construct and interpret a
99% confidence interval for the proportion of all college students who are currently
attending their school of first choice.
𝑝̂ = 0.19, 𝑞̂ = 1 − 0.19 = 0.81, n = 900, z* = 2.576
171
Note: 19% of 900 = 171, so if you use the calculator, 𝑝̂ = 900 = 0.19
0.19 ± 2.576√
0.19 × 0.81
= 0.19 ± 0.03369 = (0.15631,0.22369)
900
I am 99% confident that the proportion of all college students who are currently attending
their school of first choice is between 15.6% and 22.4%
4) A random sample of 55 retired people in the United States was asked how many
different jobs they held their working adult life (from the time they left school until the
time they retired). The average was 8.3 jobs with standard deviation 4.9 jobs. Construct
and interpret a 95% confidence for the average number of jobs held by all retirees during
their working adult life.
µ = average number of jobs held by all retirees during their working adult life
n = 55, df = 54, 𝑥̅ = 8.3, s = 4.9
t* = 2.005
4.9
8.3 ± 2.005 (
) = 8.3 ± 1.3247 = (6.9753,9.6247)
√55
[make sure you are using t* and not z*!!]
I am 95% confident that the average number of jobs held by all retirees during their
working adult life is between 6.98 jobs and 9.62 jobs.