10.67 The Pew Research Center conducted a poll in January 2014 ofonline adults who use social networking sites. According to this poll,89% of the 18-29 year olds and 82% of the 30-49 year olds who areonline use social networking sites (www.pewinternet.org). Supposethat this survey included 562 online adults in the 18-29 age group and624 in the 30-49 age group.andbe the proportion of all online adults in thea. LetP2P1age groups 18-29 and 30-49, respectively, who use socialnetworking sites. Construct a 95% confidence interval forP1 P2b. Using a 1% significance level, can you conclude that pi isdifferent from p2? Use both the critical-value and the p-valueapproaches

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Asked Nov 7, 2019
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10.67 The Pew Research Center conducted a poll in January 2014 of
online adults who use social networking sites. According to this poll,
89% of the 18-29 year olds and 82% of the 30-49 year olds who are
online use social networking sites (www.pewinternet.org). Suppose
that this survey included 562 online adults in the 18-29 age group and
624 in the 30-49 age group.
and
be the proportion of all online adults in the
a. Let
P2
P1
age groups 18-29 and 30-49, respectively, who use social
networking sites. Construct a 95% confidence interval for
P1 P2
b. Using a 1% significance level, can you conclude that pi is
different from p2? Use both the critical-value and the p-value
approaches
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10.67 The Pew Research Center conducted a poll in January 2014 of online adults who use social networking sites. According to this poll, 89% of the 18-29 year olds and 82% of the 30-49 year olds who are online use social networking sites (www.pewinternet.org). Suppose that this survey included 562 online adults in the 18-29 age group and 624 in the 30-49 age group. and be the proportion of all online adults in the a. Let P2 P1 age groups 18-29 and 30-49, respectively, who use social networking sites. Construct a 95% confidence interval for P1 P2 b. Using a 1% significance level, can you conclude that pi is different from p2? Use both the critical-value and the p-value approaches

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Expert Answer

Step 1

Solution:

a.Obtain the critical value at 95% confidence level:

From the given information, the proportion of olds between 18 and 29 years is 0.89 and proportion of olds between 30 and 49 years is 0.82.

The sample size of persons between 18 and 29 is 562 and sample size of persons between 30 and 49 years is 624.

The level of significance=(1–0.95)/2=0.025.

The required confidence level from left tail normal table=0.95+0.025=0.9750.

Procedure for finding the z-value is listed below:

  1. From the table of standard normal distribution, locate the probability value of 0.9750.
  2. Move left until the first column is reached. Note the value as 1.9
  3. Move upward until the top row is reached. Note the value as 0.06.
  4. The intersection of the row and column values gives the area to the two tail of z.

The critical value Z=1.96.

Step 2

The 95% confidence interval for p1 – p2 is calculated below:

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р(1-в) . Р. (1-Р.) CI (P)7a п п, 0.89(1-0.89) 0.82(1-0.82) (0.89-0.82)1.96, 562 624 -0.07 0.04 (0.03,0.11)

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Step 3

b.

The hypotheses are stated below:

Null hypothesis:

Ho=p1 = p2

Alternative Hypothesis:

Ha=p1 ≠ p2

The statistic value is obtained below:

...
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пр+пр. р п +n, 562x0.89 624x0.82 562 624 0.8532 (B-P) Z = 1 |P(1-Р) 1 п п, (0.89-0.82) 1 1 0.8532(1-0.8532 562 624 0.07 0.0206 -3.40

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