1.In a single throw of two coins, find the probability of getting

a) both tails,

b) at least 1 tail,

c) at the most 1 tail.

2.In a lottery, there are 10 prizes and 20 blanks. A ticket is chosen at random. What is the probability of getting a prize?

3.A single 6-sided die is rolled. What is the probability of rolling a 2 or a 5?

4.A single card is chosen at random from a standard deck of 52 playing cards. What is the probability of choosing a king or a club?

5.In a math class of 30 students, 17 are boys and 13 are girls. On a unit test, 4 boys and 5 girls made an A grade. If a student is chosen at random from the class, what is the probability of choosing a girl or an A student?

6.In constructing a confidence interval,

(a) If I increase the level of confidence, I will ____________the width of the interval.

(b) If I increase the sample size n, I will ____________the width of the interval.

(c) If (somehow) I increase the standard deviation, I will __________the width of the

Interval (try speculate here).

**use confidence interval applet.

7.To see if there is a significant difference in grades given in English 100 and Religion 103, 20 students who had taken both courses the first semester of their freshman year were randomly selected and their grades were recorded.

a) State the null and alternative hypotheses.

b) For each student in the sample, the difference in grade is taken by subtracting the religion grade from the English one. The average of these differences is 0.17 with standard deviation 0.32.

Determine the P-value associated with this sample mean under the null hypothesis (p =0.05). Based on this result, can we reject H0?

c) Change the P-value to 1% level. Can we still reject H0?

** use statistical significance applet.

8.Using the **one variable statistical calculator applet, check and build histogram for each of the 9 datasets. *do not need to show all histogram - only check&view.

a)Which dataset showed a normal distribution.

b)State the mean and standard deviation of that dataset.

9.Using the same dataset as in Q8 above, and taking the mean and standard deviation you found in Q8, answer the following questions using **normal density curve applet(it is ok to give approximate numbers)

i.What proportion (percentage) of the data (area under the curve) is below the raw score of 80?

ii.What proportion (percentage) of the data (area under the curve) is above the raw score of 140?

iii.What proportion (percentage) of the data (area under the curve) is between the raw score of 110 and 120?

10.By using the same data/statistics from Q7 above, and using **statistical power applet, find the power of the given test using a 2 tail confidence interval:

a)P=0.05, (letting u=0.17, std dev = 0.32, N=20)

b)P=0.01, (letting u=0.17, std dev = 0.32, N=20)

c)What can you say happen to power of the test, when we decrease p? State a possible reason why.