Question

The Pew Research Center conducts an annual Internet Project, which includes research related to social networking. The two‑way table shows the percent of cell phone owners who use a social networking site on their phone, broken down by age, and is based on data reported by Pew as of January 2014.

Use social networking on phone	Yes	No	Total
Age 18 – 29	228	112	340
Age 30 – 49	281	281	562
Age 50 – 64	106	481	587
Age 65+	21	408	429
Total	636	1282	1918

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(a) Regarding the Internet Project survey as approximately an SRS of Americans over the age of 18 , give a 99% confidence interval (a,b) for the proportion of Americans over the age of 18 who use a social networking site on their phone.

(Enter your answers rounded to four decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)

a:

b:

(b) Compare the conditional distributions of age for those who use and do not use a social networking site on their phone. Using the table as a reference, give the sample conditional probabilities as percents in the appropriate answer boxes.

Use social networking on phone	Yes	No
Age 18 – 29	A%	B%
Age 30 – 49	C%	D%
Age 50 – 64	E%	F%
Age 65+	G%	H%

(Enter your answers as percents rounded to two decimal places.)

A:

B:

C:

D:

E:

F:

G:

H:

What are the most important differences?

The table shows younger individuals (under age 50 ) are much less likely to use social networking on their phone than older individuals (age 50 and over).

The table shows younger individuals (under age 50 ) are much more likely to use social networking on their phone than older individuals (age 50 and over).

The table shows that individuals of all age categories are about equally likely to use social networking on their phone.

The table shows no discernible pattern relating age category to likelihood of social networking use on one's phone.

(c) Carry out the chi‑square test for the hypothesis of no difference between the age distribution of those who use and do not use a social networking site on their phone. What is the mean of the χ2 distribution used to test the null hypothesis?

(Enter your exact answer as a whole number.)

mean =

Calculate the test statistic.

(Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)

χ2=

What is the approximate ?P ‑value? Select the best explanation.

If the null hypothesis were true, the mean of the test statistics from many independent random samples would be 3 . Our observed test statistic is equal to 3 . The ?P ‑value is approximately zero.

If the null hypothesis were true, the mean of the test statistics from many independent random samples would be 3 . Our observed test statistic is much larger than 3 . The ?P ‑value is approximately zero.

If the null hypothesis were true, the mean of the test statistics from many independent random samples would be 5 . Our observed test statistic is much larger than 5 . The ?P ‑value is approximately zero.

If the null hypothesis were true, the mean of the test statistics from many independent random samples would be 3 . Our observed test statistic is much larger than 3 . The ?P ‑value is approximately 1 .

What conclusion do these values imply?

There is weak evidence of a relationship between age and phone use for social networking.

There is strong evidence of a relationship between age and phone use for social networking.

There is no evidence of a relationship between age and phone use for social networking.

The null hypothesis is true.

(d) Look at the terms of the chi‑square statistic and compare observed and expected counts in the cells that contribute the most to chi‑square. Based on this and your findings in part (b), complete the short comparison of the difference in age distribution of those who use and do not use a social networking site on their phone.

The cells that contribute most to the chi‑square statistic are the

cell and the "Age 65+ and Yes" cell. For the 18–29 group, we observe a much

number of Yes responses than expected if the null were true. For the Age 65+ group, we observe a much

number of Yes responses than expected if the null were true. It appears

individuals are much more likely to use social networking on their phone than

individuals.

Question Source: Moore, The Basic Practice Of Statistics, 8e|Publisher: W.H. Freeman

Answer 1

(c)

Mean of Distribution = Degrees of Freedom = (r -1) X (c -1) = (4 - 1) X (2 - 1) = 3

So,

mean = 3

H0: Null Hyothesis: Use social networking on phone and age are independent

HA: Null Hyothesis: Use social networking on phone and age are dependent.

Assuming H0, the expected frequencies are got as follows:

Use social networking on phone	Yes	No	Total
Age 18 - 29	636 X 340/1918 = 112.74	227.26	340
Age 30 - 49	186.36	375.64	562
Age 50 - 64	194.65	392.35	587
Age 65+	142.25	286.75	429
Total	636	1282	1918

From the above Table, Chi Square Table is got as follows:

O	E	(O - E)2/E
228	112.74	117.836
112	227.27	58.464
281	186.36	48.061
281	375.64	23.844
106	194.65	40.374
21	142.25	103.350
408	286.75	51.270
Total = =		463.224

So,

Answer is:

= 463.224