1. A previous study gave (0.74, 0.88) as a confidence interval for p. Find the minimum sample size required to ensure that your estimate
(
ˆ
p
)
will be within 0.09 of p with 98% confidence.
IMPORTANT: Use a critical value that you found with your calculator (not from a table), and round it to 3 places after the decimal point before you plug it into a formula and perform your calculations. Do not round-off any other intermediate results.
n =
2. (a) For a confidence level of 88%, find the critical value
z
α
/
2
. Round your answer to 2 places after the decimal point.
z
α
/
2
=
(b) For a confidence level of 99% and a sample size of 12, find the critical value
t
α
/
2
. Round your answer to 3 places after the decimal point.
t
α
/
2
=
3. Suppose your boss wants you to obtain a sample to estimate a population mean. Based on previous analyses, you estimate that 14 is the approximate value of the population standard deviation. You would like to be 98% confident that your estimate is within 29 of the true population mean. What is the minimum sample size required?
IMPORTANT: Use a critical value that you found with your calculator (not from a table), and round it to 3 places after the decimal point before you plug it into a formula and perform your calculations. Do not round-off any other intermediate results.
n =
4. A marketing survey involves product recognition in New York and California. Of 883 New Yorkers surveyed, 247 knew of the product while 225 of 575 Californians knew of the product. Construct a 98% confidence interval for the difference between the two population proportions, p1 - p2 (where p1 is the proportion of New Yorkers who knew of the product, and p2 is the proportion of Californians who knew of the product).
Give your answers as decimals, rounded to 3 places after the decimal point (if necessary).
98% confidence interval for p1 - p2: (
,
)
5. Independent samples from two different populations that are both approximately normally distributed yield the following data:
¯
x
1
=
187.8
,
¯
x
2
=
186
,
s
1
=
2.6
,
s
2
=
1.2
,
n
1
=
35
,
n
2
=
26
.
Construct a 95% confidence interval for the difference of the population means,
μ
1
−
μ
2
.
Round your answers to 3 places after the decimal point, if necessary. If it is not appropriate to construct a confidence interval in this situation, then enter "0" in both answer boxes below.
95% confidence interval: (
,
)
6. Independent random samples from two different populations that are approximately normally distributed yield the following data. Although they are unknown, the two population standard deviations are assumed to be equal to each other.
¯
x
1
=
72.7
,
¯
x
2
=
71.6
,
s
1
=
3.3
,
s
2
=
5.1
,
n
1
=
22
,
n
2
=
19
.
Construct a 98% confidence interval for the difference of the population means,
μ
1
−
μ
2
.
Round your answers to 3 places after the decimal point, if necessary. If it is not appropriate to construct a confidence interval in this situation, then enter "0" in both answer boxes below.
98% confidence interval: (
,
)
7. The two data sets in the table below are dependent random samples. The population of
(
x
−
y
)
differences is approximately normally distributed.
x 59 64 52 57 60 56 65
y 38 38 31 33 29 25 25
For all three parts below, round your answers to 3 places after the decimal point, if necessary
(a) Find the value of
¯
d
.
¯
d
=
(b) Find the value of sd.
sd =
(c) Construct a 95% confidence interval for the mean difference. If it is not appropriate to construct a confidence interval in this situation, then enter "0" in both answer boxes below.
95% confidence interval: (
,
)
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