Pew Research in 2018 polled a random sample of 1058 U S. teens (ages 13-17) about Internet use reported that they were online “almost constantly”-a fact of great interest to advertisers. Complete parts a through c below.
a) Explain the meaning of in the context of this situation. Choose the correct answer below.
A. The meaning of is that of the 1058 teens in the sample reported that they were online “almost constantly” "This is the researchers’ best estimate of , the proportion of the 1058 teens in the sample who said that.
B. The meaning of is that of the 1058 teens in the sample reported that they were online "almost constantly "This is the researchers’ best estimate of p, the proportion of all . teens who would say that.
C. The meaning of is that the researchers have confidence that of the 1058 teens in the sample reported that they were online “almost constantly”
D. The meaning of is that the researchers have confidence that of all US. teens would report that they were online “almost constantly”
b) Calculate the standard error of .

(Round to five decimal places as needed.)

Ask by Moran Gough. in the United States

Mar 28,2025

Question

Pew Research in 2018 polled a random sample of 1058 U S. teens (ages 13-17) about Internet use reported that they were online “almost constantly”-a fact of great interest to advertisers. Complete parts a through c below.
a) Explain the meaning of in the context of this situation. Choose the correct answer below.
A. The meaning of is that of the 1058 teens in the sample reported that they were online “almost constantly” "This is the researchers’ best estimate of , the proportion of the 1058 teens in the sample who said that.
B. The meaning of is that of the 1058 teens in the sample reported that they were online "almost constantly "This is the researchers’ best estimate of p, the proportion of all . teens who would say that.
C. The meaning of is that the researchers have confidence that of the 1058 teens in the sample reported that they were online “almost constantly”
D. The meaning of is that the researchers have confidence that of all US. teens would report that they were online “almost constantly”
b) Calculate the standard error of .

(Round to five decimal places as needed.)

Ask by Moran Gough. in the United States

Mar 28,2025

UpStudy AI · Accepted Answer

a) $$ \hat{p}=0.451 $$ means that $$45.1\%$$ of the 1058 teens in the sample reported that they were online "almost constantly." This sample result is used as the best estimate for $$ p $$, the true proportion of all U.S. teens who would report being online "almost constantly." Therefore, the best answer is

**B.** The meaning of $$ \hat{p}=0.451 $$ is that $$45.1\%$$ of the 1058 teens in the sample reported that they were online "almost constantly." This is the researchers' best estimate of $$ p $$, the proportion of all U.S. teens who would say that.

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b) The standard error of $$ \hat{p} $$ is calculated by

$$
\operatorname{SE}(\hat{p}) = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}.
$$

Substituting $$ \hat{p}=0.451 $$ and $$ n=1058 $$:

$$
\operatorname{SE}(\hat{p}) = \sqrt{\frac{0.451(1-0.451)}{1058}} = \sqrt{\frac{0.451 \times 0.549}{1058}}.
$$

Calculating the numerator:

$$
0.451 \times 0.549 \approx 0.247599.
$$

Then dividing by $$ 1058 $$:

$$
\frac{0.247599}{1058} \approx 0.0002339.
$$

Taking the square root:

$$
\sqrt{0.0002339} \approx 0.01530.
$$

Rounded to five decimal places, the standard error is

$$
\operatorname{SE}(\hat{p}) \approx 0.01530.
$$

a) $$ \hat{p}=0.451 $$ means that 45.1% of the 1058 teens in the sample said they were online "almost constantly." This is the best estimate for the proportion of all U.S. teens who would say the same. b) The standard error of $$ \hat{p} $$ is approximately 0.01530.

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