1. An experiment was done to determine if a pair of dice is “fair”, that is, the probability that each number on each die is the same. Tom tosses the dice 50 times and determines that the mean sum of the sample is 6.6, with a standard deviation of 1. 133. According to the mechanics of tossing two dice, the mean should be 7. Determine if this is a fair dice at the .05 level of significance. Also determine the p-value.

1. Determine if a t or a z hypothesis test should be used.
2. Is this a one-tail or a two-tail hypothesis test?
3. Find H0 and H1.
4. Use both the Classical Approach and the P-Value Approach to determine whether to reject or fail to reject the null hypothesis.
5. Interpret the conclusion.

Katie has 5 marbles in her book bag 3 Yellow (Y1, Y2, Y3) and 2 black marbles (B1 and B2). She is doing an experiment for her class where she picks one marble at a time randomly from her book bag. Katie stops picking marbles when she selects a black marble.

1. show the possible outcomes in a tree diagram

2. what are the possible values of the discrete random variable (x) that represent the total number of yellow marbles that can be picked before a black marble can be picked. Make probability distribution for each value and all components that are needed for each value.

When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 10%. Let X = the number of defective boards in a random sample of size n = 20, so X ~ Bin(20, 0.1). (Round your probabilities to three decimal places.)

(a) Determine P(X ≤ 2).

b. Determine P(X ≥ 5).

c. Determine P(1 ≤ X ≤ 4).

d. What is the probability that none of the 20 boards is defective?

e. Calculate the expected value and standard deviation of X. (Round your standard deviation to two decimal places.)

Fiction Cruiseline offers three ways to exercise on their cruise ships. 73 of the 86 passengers participated in at least one method of exercise. 36 people went rock climbing, 44 people went ice skating, and 19 went to the fitness center. 14 people went rock climbing and ice skating, 11 people went rock climbing and to the fitness center, and 9 people went ice skating and to the fitness center. Draw a Venn Diagram for the three sets if necessary. Include how you found the number of ALL three activities.

Calculate the probability for:

A randomly selected passenger did not go ice skating, given they did at least two activities

1.A researcher collects a sample of 30 individuals who have a mean age of 34.6, a median age of 41.5, and a modal age of 44. Make one observation regarding the nature of the distribution of data that the researcher collected.  What would be the best measure of central tendency to use in describing a distribution of this form?  Whydid you choose the measure of central tendency that you did?

2.A statistician computes a 95% confidence interval for the number of prior arrests of those convicted of violent crimes. The interval ranged from 1.6 to 3.6 prior arrests.  Given these data, what is the probability that the population mean is greater than 3.6 prior arrests?  Why?

a)A university planner wants to determine the proportion of spring semester students who will attend summer school. Suppose the university would like a 0.90 probability that the sample proportion is within 0.281 or less of the population proportion.What is the smallest sample size to meet the required precision? (There is no estimation for the sample proportion.)  (Enter an integer number.)

b)A university planner wants to determine the proportion of fall semester students who will attend summer school. She surveys 30 current students discovering that 20 will return for summer school.At 90% confidence, compute the margin of error for the estimation of this proportion.

c)For the t distribution with 14 degrees of freedom, calculate P(T < 2.624)!

A study of 90 workers following a new pre-work stretching exercise program was conducted. One of the variables measured over the 4-week study was the increase in number of minutes worked in an hour. A previous program had produced an average increase of µ = 2 mins per hour. The company wants to evaluate whether the new program had increased µ in comparison
with the previous program. The study data yielded x̅= 2.17 and s = 1.05.

a. At the 5 percent level of significance, compare the new program to the previous one.

b. What is the probability of making a Type II error if the actual value of µ is 2.1 min per
hour?

The manufacturer of a new line of ink-jet printers would like to include as part of its advertising the number of pages a user can expect from a print cartridge. The results from a sample of 14 cartridges can be found here

a. what is the point estimate of the population mean and standard deviation?

b. develop a 90% interval for the population mean

c. if the point estimate of the population mean and standard deviation are accurate, what is the probability that another sample of 14 cartridges will last an average of more than 1650 pages?

please show your work

Question 3 [25]
OK furniture store submit weekly records the number of customer contacts contacted per week. A sample of 50 weekly reports showed a sample mean of 25 customer contacts per week. The sample standard deviation was 5.2. (Show all your works)
a) Compute the Margin of error at 0.05 significant level
[6]
b) Provide a 95% confidence interval for the population mean.
[4]
c) Compute the Margin of error at 0.01 significant level
[6]
d) Provide a 99% confidence interval for the population mean.
[4]
e) With a 0.99 probability, what size of sample should be taken if the desired margin of error is 1.5