Question

5.70 The ideal number of children. “What do you think is the ideal number of children for a family to have?” A Gallup Poll asked this question of 1020 randomly chosen adults. Slightly less than half (48%) thought that a total of two children was ideal. 20 Suppose that p = 0.48 is exactly true for the population of all adults. Gallup announced a margin of error of ±4 percentage points for this poll. What is the probability that the sample proportion for an SRS of size n = 1020 falls between 0.44 and 0.52? You see that it is likely, but not certain, that polls like this give results that are correct within their margin of error. We say more about margins of error in

Answer #1

n = 1020

p = 0.48

= 0.48

= sqrt(p(1 - p)/n)

= sqrt(0.48 * (1 - 0.48)/1020)

= 0.0156

P(0.44 < < 0.52)

= P((0.44 - )/ < ( - )/ < (0.52 - )/)

= P((0.44 - 0.48)/0.0156 < Z < (0.52 - 0.48)/0.0156)

= P(-2.56 < Z < 2.56)

= P(Z < 2.56) - P(Z < -2.56)

= 0.9948 - 0.0052

= 0.9896

"What do you think is the ideal number of children for a family
to have?" A poll asked this question of 1010 randomly chosen
adults. Slightly less than half (48%) thought that a total of two
children was ideal. Suppose that p = 0.48 is
exactly true for the population of all adults. The polling company
announced a margin of error of ±4 percentage points for this poll.
What is the probability that the sample proportion p̂ for
an SRS...

"What do you think is the ideal number of children for a family
to have?" A poll asked this question of 1070 randomly chosen
adults. Slightly less than half (48%) thought that a total of two
children was ideal. Suppose that
p = 0.48
is exactly true for the population of all adults. The polling
company announced a margin of error of
±4 percentage
points for this poll. What is the probability that the sample
proportion p̂ for an SRS...

"What do you think is the ideal number of children for a family
to have?" A poll asked this question of 1011 randomly chosen
adults. Almost half (49%) thought two children was ideal. Suppose
that p = 0.49 is exactly true for the population of all
adults. The polling company announced a margin of error of ±3
percentage points for this poll. What is the probability that the
sample proportion p̂ for an SRS of size n = 1011
falls...

"What do you think is the ideal number of children for a family
to have?" A Gallup Poll asked this question of 1016 randomly chosen
adults. Almost half (49%) thought two children was ideal.† We are
supposing that the proportion of all adults who think that two
children is ideal is p = 0.49.
What is the probability that a sample proportion p̂ falls
between 0.46 and 0.52 (that is, within ±3 percentage points of the
true p) if the...

"What do you think is the ideal number of children for a family
to have?" A Gallup Poll asked this question of 1016 randomly chosen
adults. Almost half (49%) thought two children was ideal.† We are
supposing that the proportion of all adults who think that two
children is ideal is p = 0.49.
What is the probability that a sample proportion p̂ falls
between 0.46 and 0.52 (that is, within ±3 percentage points of the
true p) if the...

"What do you think is the ideal number of children for a family
to have?" A Gallup Poll asked this question of 1016 randomly chosen
adults. Almost half (49%) thought two children was ideal.† We are
supposing that the proportion of all adults who think that two
children is ideal is p = 0.49.
What is the probability that a sample proportion p̂ falls
between 0.46 and 0.52 (that is, within ±3 percentage points of the
true p) if the...

1. A Gallup poll asked 1200 randomly chosen
adults what they think the ideal number of children for a family
is. Of this sample, 53% stated that they thought 2 children is the
ideal number. Construct and interpret a 95% confidence interval for
the proportion of all US adults that think 2 children is the ideal
number.
2. There were 2430 Major League Baseball games
played in 2009, and the home team won the game in 53% of the games....

return to the gallop poll setting of exercise 5.70 we are
supposing that the proportion of all adults who think that having
two children is ideal is p=0.48. what is the probability that a
sample proportion p falls between .44 and .52. within +-4
percentage points of the true p if the sample is an SRS of size
n=300? of size n=5000. general statement about the effect of larger
samples in a sample survey?

In 2002 General Social Survey asked, "what do you think is the
ideal number of children for a family to have?" The 30 females who
responded had a mean of 3.08 and a standard deviation of 1.91.
a) Are the conditions met by his data to calculate a 90%
confidence interval for the population mean? Explain
b) Regardless of what your answer to part (a) is, compute a 90%
interval for the population mean.
c) How many females should be...

A survey asked the question "What do you think is the ideal
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from 0 to 6. The 411 males who responded had a mean of 3.18, and
standard deviation of 1.6, where the 343 females had a median of
2, a mean of 3.27 and a standard deviation of 1.69. The 95%
confidence interval for the female population...

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