Question

Let's look at college students. The following table gives us data to examine the relation between age and full-time or part-time status. The numbers in the table are expressed as thousands of college students.

College students by age and status
	Status
Age	Full-time	Part-time
15-19	3392	394
20-24	5240	1110
25-34	1717	1732
35 and over	756	2058

(a) What is the estimate of the number of full-time college students aged 15 to 19?
thousands of college students

(b) Give the joint distribution of age and status for this table. (Round your answers to four decimal places.)

Age	Full-time	Part-time
15-19
20-24
25-34
35 and over

(c) What is the marginal distribution of age? (Round your answers to four decimal places.)

15-19
20-24
25-34
35 and over

Display the results graphically.

(d) What is the marginal distribution of status? (Round your answers to four decimal places.)

full-time
part-time

Display the results graphically.

6.

–/1.25 POINTSMBASICSTAT7 25.E.006.MY NOTESASK YOUR TEACHERThe popularity of computer, video, online, and virtual reality games has raised concerns about their ability to negatively impact youth. The data in this exercise are based on a recent survey of 14- to 18-year-olds in Connecticut high schools. Here are the grade distributions of boys who have and have not played video games.

	Grade average
	A's and B's	C's	D's and F's
Played games	735	449	193
Never played games	205	144	80

The null hypothesis "no relationship" says that in the population of all 14- to 18- year-old boys in Connecticut, the proportions who have each grade average are the same for those who play and don't play video games.(a) Find the expected cell counts if this hypothesis is true, and display them in a two-way table. Check that the row and column totals agree with the totals for the observed counts. (Round your answers to two decimal places.)

	A's and B's	C's	D's and F's
Played games
Never played games

(b) Are there any large deviations between the observed counts and the expected counts?

Yes, the observed and expected counts for played games and never played games in the A's and B's column are off by more than 15.Yes, the observed and expected counts for played games and never played games in the C's column are off by more than 15.     Yes, the observed and expected counts for played games and never played games in the D's and F's column are off by more than 30.No, the observed and expected counts for played games and never played games in any column are off by more than 20.

7.

–/1.25 POINTSMBASICSTAT7 25.E.002.

Answer 1

The given data here is:
(We would be looking at the first 4 parts here )

Age	Full Time	Part Time
15-19	3392	394	3786
20-24	5240	1110	6350
25-34	1717	1732	3449
35 and over	756	2058	2814
	11105	5294	16399

a) The estimate of the number of full-time college students aged 15 to 19: ( can be directly seen from the above table)

= 3392

Therefore 3392 is the required estimate here.

b) The joint distribution probabilities here are computed as:

Age	Full Time	Part Time
15-19	0.2068	0.0240
20-24	0.3195	0.0677
25-34	0.1047	0.1056
35 and over	0.0461	0.1255

c) The marginal distribution of Age here is obtained as:

Age	P(Age)
15-19	0.2309
20-24	0.3872
25-34	0.2103
35 and over	0.1716

This is computed by getting the proportion of Frequency for Age category from the total Frequency. This is graphed as:

d) For status, a similar probability distribution is obtained as:

Status	P(Status)
Full Time	0.67717544
Part Time	0.32282456