1. When people turn to for news is different for various age groups. A study indicated where different age groups primarily get their news:

Age Group

Media Under 36 36-50 50+

TV 180 221 260

Radio 75 97 109

Local newspaper 52 79 107

Internet 95 83 76

Is there enough evidence to conclude a relationship between age group and the media people primarily get their news? Make sure you performance a complete hypothesis test and interpret in the way we did in class.

2.A survey of 50 students at ABC college about the number of extracurricular activities resulted in the data shown:

Number of Activities # of students

0 8

1 20

2 12

3 6

4 3

5 1

(a)Let A be the event that a student participates in at least 1 activity. Find P(A).

(b)Let B be the event that a student participates in 3 or more activities. Find P(B).

3.Data on the 30 largest stock and balanced funds provided 1-year and 5-year percentage returns for the period ending March 31, 2000 (The Wall Street Journal, April 10, 2000). Suppose we consider a 1-year return in excess of 50% to be high and a 5-year return in excess of 300% to be high. Nine of the funds had 1-year returns in excess of 50%, seven of the funds had 5-year returns in excess of 300%, and five of the funds had both 1-year returns in excess of 50% and 5-year returns in excess of 300%.

(a)What is the chance of high 1-year return, and what is the chance of a high 5-year return?

(b)What is the chance of both a high 1-year return and a high 5-year return?

(c)What is the chance of neither a high 1-year return nor a high 5-year return?

4. "Since 1950, the January Barometer has predicted the annual course of the stock market with amazing accuracy" (1998 Stock Trader's Almanac). Over the 48 years from 1950 through 1997, the stock market has been up in January 31 times; it has been up for the year 36 times; and it has been up for the year and up for January 29 times.

(a)Find the chance the stock market will be up in January.

(b)Find the chance the stock market will be up for the year.

(c)What is the chance the stock market will be up for the year given it is up in January?

(d)Do the chances suggest that the stock market's "January performance" and its "annual performance" are independent events? Explain with calculation.

5.With the past ten years of observations, there are only three possible amounts of return of a certain stock after one year if invests $1000, as below:

Return (in thousands $) Probability

-4 0.25

6 0.65

15 0.1

(a)Find the expected return of this stock after one year if you invest $1000 now.

(b)There is a service charge of 10% of the amount of return if it is a positive return, find the expected return of this stock after one year if you invest $1000 now.