Question

INSTRECTION:

-show sufficient work to support your answes. if you have to make any assumptions, state them clearly.

-all confidence interval and hypothesis test results need to be expressed in sentenses that would make senense.

-round your answers to 4 decimal place.

7. (7 points) We play a game in which you draw one card from a standard deck of cards. If you drawa card with a value of 5 or less, I will pay you $60. If not, you pay me $23. (Aces are considered the highest card in the deck.) Write down the probability distribution that goes with this proposition. (Use positive values for amounts that you win and negative values for amounts that you pay.) a. Find the expected value for this distribution. b. Find the standard deviation for this distribution. C. d. If you played this game 50 times, how much would you expect to win or lose? (4 points) A study on the effects of television-viewing on children reports that child ren watcha mean of 4.0 hours of television per night. Linda believes that the mean number of hours children in her neighborhood watch television per night is greater than 4.0 hours. She performs a hypothesis test. 8. a. Write the null and alternative hypotheses for Linda's test. b. Linda rejects the null hypothesis. Assume that in reality, children in her neighborhood watch a mean of 3.9 hours of television per night. Did Linda make an error? If so, was it a Type I or Type II error?

Answer 1

7a) The standard deck of cards contain 4 suits , each suits contains Ace, King , Queen , Jack, 10,9,8,7,6,5,4,3,2 from high to low value

There are 4*4=16 cards of value 5 or low (2,3,4,5)

and 52-16 = 36 card greater than 5

Let X be the value of drawn card , Y be the money won

X	Y	P(Y)
5 or less	60	16/52=0.3077
Greater than 5	-23	36/52=0.6923

2.

E(Y) =

yP()

= 60*0.3077 +(-23)*0.6023

= 2.54

Expected value =2.54

3.

Variance = Σy?P(g) - ΣyP(y)))

= 60^2*0.3077+(0.23)^2*0.6023 -2.54^2

= 1467.5

Standard deviation =

Variance

= 38.31

4. expected win for single game $2.54

Since the value is positive , we consider its a win

For 50 games , expected value of win = 50*$2.54

=$126.96