Question

Show all your work in detail to receive full
credit.

Assume that the samples are independent and that they have been
randomly selected.

1) In a random sample of 500 people aged 20-24, 22% were smokers.
In a random sample of 450 people aged

25-29, 14% were smokers.

Construct a 95% confidence interval for the difference
between the population

proportions p1 - p2.

(a) Find the best point estimate for p1 - p2 .

(b) Find the critical values by first sketching the normal
distribution curve and identifying the indicated area on

the graph.

(c) Find the margin of error. Be sure to set up the equation.

(d) Construct the confidence interval

Answer #1

1. In a random sample of 58 people aged 20-24, 22.7% were
smokers. In a random sample of 110 people aged 25-29, 29.5% were
smokers. Calculate the margin of error for a 95% confidence
interval that can be used to estimate the difference between the
population proportions p1 − p2 of the smokers
in these age groups.
Show your answer in decimal form, rounded to three
decimal places.
2. Confidence interval for the difference between
population proportions.
(Assume that the...

In a random sample of 500 people aged 20-24, 22% were smokers.
In a random sample of 450 people aged 25-29, 14% were smokers.
Construct a 95% confidence interval for the difference between the
proportions of 20-24 year olds and 25-29 year olds who are smokers.
Also, find the margin of error. What is the Parameter of interest?
What is the underlying Distribution?

) The table shows the number of smokers in a random sample of
500 adults aged 20-24 and the number of smokers in a random sample
of 450 adults aged 25-29. Assume that you plan to use a
significance level of α = 0.10 to test the claim that p1 ≠ p2. Find
the critical value(s) for this hypothesis test. Do the data provide
sufficient evidence that the proportion of smokers in the 20 -24
age group is different from...

(Assume that the samples are randomly selected and
independent.)
Sample statistics: x 1 = 36, n 1 = 64 and x 2 = 47, n 2
= 71;
Construct a 95% confidence interval for the difference
between population proportions p1 – p2
Select one:
0.368 < p1 – p2 < 0.757
-0.263 < p1 – p2 < 0.064
-0.294 < p1 – p2 < 0.757
0.399 < p1 – p2 < 0.726
2.
Two independent samples are randomly selected and...

Assume that the population of paired differences is
normally distributed.
3) A test of writing ability is given to a random sample of
students before and after they completed a formal
writing course. The results are given below. Construct a 99%
confidence interval for the mean difference
between the before and after scores.
Before 70 80 92 99 93 97 76 63 68 71 74
After 69 79 90 96 91 95 75 64 62 64 76
(a) Find the...

Independent random samples of
n1 = 700
and
n2 = 590
observations were selected from binomial populations 1 and 2,
and
x1 = 337
and
x2 = 375
successes were observed.
(a) Find a 90% confidence interval for the difference
(p1 − p2) in the two
population proportions. (Round your answers to three decimal
places.)

Independent random samples of
n1 = 600
and
n2 = 440
observations were selected from binomial populations 1 and 2,
and
x1 = 334
and
x2 = 378
successes were observed.
(a) Find a 90% confidence interval for the difference
(p1 − p2) in the two
population proportions. (Round your answers to three decimal
places.)
to
(b) What assumptions must you make for the confidence interval to
be valid? (Select all that apply.)
independent samples
random samples
nq̂ > 5...

Two different simple random samples are drawn from two different
populations. The first sample consists of 20 people with 10 having
a common attribute. The second sample consists of 2200 people with
1595 of them having the same common attribute. Compare the results
from a hypothesis test of p1 = p2 (with a 0.01 significance
level) and a 99% confidence interval estimate of p1 - p2.
1. Identify the test statistic ____ (round to 2 decimal
places)
2. Identify the...

Two different simple random samples are drawn from two different
populations. The first sample consists of 30 people with 15 having
a common attribute. The second sample consists of 1900 people with
1379 of them having the same common attribute. Compare the results
from a hypothesis test of p1=p2 (with a 0.01 significance level)
and a 99% confidence interval estimate of p1−p2.
Find hypothesis, test statistic, critical value, p value, and
95% CL.

5. In a random sample of 500 people in their 30's, 22% were
smokers. In a random sample of 450 people in their 20's, 14% were
smokers. The 95% confidence interval for the difference between the
population proportions P20's - P30's. turned out to be:
-0.128 < p1 - p2 < -0.032. What does this imply?
There is not a significant difference between the smoking habits
of people in their 20's and people in their 30's, but the sample
showed...

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