STAT 200

Question 1. If you perform Hypothesis Testing with alpha level of 0.01

What is the probability that true null hypothesis will be accepted?

Question 2. True or False: It is easier to reject the null hypothesis if the researcher uses a smaller alpha (α) level.

Question 3. When a new drug is created, the pharmaceutical company must subject it to testing before receiving the necessary permission from the Food and Drug Administration (FDA) to market the drug. Suppose the null hypothesis is “the drug is safe.” What is the Type I Error? Check the correct answer:

a) To conclude the drug is unsafe when in, fact, it is safe.

b) To conclude the drug is safe when, in fact, it is unsafe.

Student	N	x̅		Student	N	x̅
Acopan	40	18.1		Harris	41	18.1
Ambol	42	18.2		Jacobs	43	18.2
Anderson	44	18.3		Johnson	45	18.3
Attai	46	18.4		Kurata	47	18.4
Broseker	48	18.5		Mendoza	49	18.5
Buchheit	50	18.6		Monyei	51	18.6
Bullock	52	18.7		Munshi	53	18.7
Caywood	54	18.8		Pickering	55	18.8
Cox	56	18.1		Rager	57	18.1
Eickhoff	58	18.2		Ritchey	59	18.2
Fox	32	18.3		Rosen	33	18.3
Gray	34	18.4		Sekamwa	35	18.4
Hampton	36	18.5		Turner	37	18.5

Problem 4. A survey was done to see if the mean age when people start smoking is at least 19. Ho: mean starting age 19 Ha: mean starting age < 19 The sample of N smokers was shown the mean x̅ (see your numbers in the table). Distribution is normal and population standard deviation is known, σ = 1.5. Complete the Hypothesis Testing and make decision if your sample data support the claim at the significance level 5%?

(This is Left-Tailed test).

Student	N	x̅		Student	N	x̅
Acopan	30	0.95		Harris	43
Ambol	31			Jacobs	44
Anderson	32			Johnson	45
Attai	33			Kurata	46
Broseker	34			Mendoza	47
Buchheit	35			Monyei	48
Bullock	36			Munshi	49
Caywood	37			Pickering	50
Cox-Martinez	38			Rager	51
Eickhoff	39			Ritchey	52
Fox	40			Rosen	53
Gray	41			Sekamwa	54
Hampton	42			Turner	55

Problem 5. The cost of a daily newspaper varies

from city to city. However, the standard deviation of price remains 20¢ (population standard deviation σ=0.20). A study was done to test the claim that the average cost of a daily newspaper is $1.00 (Ho: μ=1). Sample of N newspapers were checked and the average price was found as x̅ (sample mean). Take N and x̅ from the table. Complete the Hypothesis Testing at the significance level 1% and make the decision if your sample data support the claim that the average cost of a daily newspaper is $1.00 (this is Two-Tailed test).

Problem 6. Hypothesis Testing

1) Give an example of Type I and Type II Errors. 2) What is the difference between Left-Tailed and Right-Tailed Tests? 3) How do we use p-value in Hypothesis Testing?

7. What is the probability of rolling a pair of dice and a) obtaining a total score of 8? b) obtaining a total score of 10 or more?

8. A box contains four black pieces of cloth, two striped pieces, and six dotted

pieces. A piece is selected randomly and did not placed back in the box. Then, a second piece is selected randomly. What is the probability that:

a) both pieces are dotted?

b) the first piece is black and the second piece is dotted?

c) one piece is black and one piece is striped?

9. In the shown Venn Diagram

N

N(total) = 500 is total number of students N(A) = 200 is a number of students who take Statistics

N(B) = 100 is a number of students who take Calculus

N(AՈB) = 50 is a number of students who take both courses, Statistics and Calculus.

Based of the given data find the probability that students a) take Statistics, but do not take Calculus. b) do not take Statistics or Calculus (Remember, probability should be less than 1).

10. A fair coin is flipped 9 times. What is the probability of getting exactly 4 heads?

Use formula or Table for Binomial distribution.

11. In a spinning wheel casino game you pay $5 and can win $1, $3, $5, $20 or lose your bet.

Data below shows how many times appears every option if you play 40 times.

Lose – 22 times

$1 win – 3 times $3 win – 4 times $5 win – 5 times $20 win – 6 times

Complete table for Discrete Probability Distribution in this case

X, $ you get from each game	0	1	3	5	20
P(x)

and calculate expected value E(x).

E(x) =

12. Calculate a) Permutations P(10,3). b) Combinations C(10,3)

13. For this problem you should use Appendix Table for Binomial Distribution. A fair coin tossed 7 times. Find the probability of getting a) Exactly 3 Heads. b) Less than 3 Heads (3 is not included).

14. Find the area under the standard normal distribution curve a) to the left of z = 0.55 b) to the right of z = 1.47 (use Appendix Table for Normal distribution).

15. Assuming an average life expectancy has Normal Distribution with a mean μ = 80 and the standard deviation σ = 10, find the probability that a person life expectancy will be between 69 and 82? (Tip: convert 69 and 82 to z1, z2 and use Appendix Table for Normal Distribution to find probability that z will be between z1 and z2).

16. Study conducted with groups of N=10 children each (sample size), to evaluate how long it takes to learn foreign language on a basic communication level. It was found that it takes them in average ͞x =20 days (sample average) with a sample standard deviation of s=5 days.

Construct a 90% confidence interval for the population mean for the time needed for children to learn basics of foreign language.

(Population standard deviation is not known. For Margin of Error use t-value from attached Appendix Table for t-Distribution)

A

B

A

B