Take 5 cards from a 52 card deck without replacement.

a) Use the multiplication principle reason out the number of ways to get 1 pair

and 3 other non-paired cards

               (Hint: Fill in the number of ways to choose: 1 card type, 1 matching card,

1 card that doesn’t match, 1 card that doesn’t match any of the previous 3, 1 card that doesn’t match any of the previous.

b) How many ways can you draw out a set of 5 cards?

               c) What’s the probability of exactly one pair?

               d) How many times would you expect to exactly one pair in 50 trials?

               e) Run 50 trails (shuffle each time if you’re using a real deck of cards)

                              How many times did you get exactly one pair?

                              Is this consistent with what’d you expect from part (d)?

A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. Assume that the distributions follow the normal probability distribution and the population standard deviations are equal. The information is summarized below. Statistic Men Women Sample mean 23.81 21.97 Sample standard deviation 5.67 4.61 Sample size 32 36 At the 0.01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month?

State the decision rule for 0.01 significance level: H0: μMen= μWomen H1: μMen ≠ μWomen. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)

Compute the value of the test statistic. (Round your answer to 3 decimal places.)

What is your decision regarding the null hypothesis?

What is the p-value? (Round your answer to 3 decimal places.)

A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. Assume that the distributions follow the normal probability distribution and the population standard deviations are equal but unknown. The information is summarized below,

At the 0.05 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month? Please answer questions a to d. Please show all steps of derivation.

a. Write down the null hypothesis and the alternative hypothesis. (You can verbally describe if you do not know how to type in equations)  

b. State the decision rule for 0.05 significance level.

c. Compute the value of the test statistic.

d. What is your decision regarding the null hypothesis? What is your conclusion?

Isle Royale, an island in Lake Superior, has provided an important study site of wolves and their prey. Of special interest is the study of the number of moose killed by wolves. In the period from 1958 to 1974, there were 296 moose deaths identified as wolf kills. The age distribution of the kills is as follows.

(a) For each age group, compute the probability that a moose in that age group is killed by a wolf. (Round your answers to three decimal places.)

(b) Consider all ages in a class equal to the class midpoint. Find the expected age of a moose killed by a wolf and the standard deviation of the ages. (Round your answers to two decimal places.)

A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. Assume that the distributions follow the normal probability distribution and the population standard deviations are equal. The information is summarized below.

At the 0.01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month?

1. State the decision rule for 0.01 significance level: H₀: μ_Men= μ_Women   H₁: μ_Men ≠ μ_Women. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)

2. Compute the value of the test statistic. (Round your answer to 3 decimal places.)

3. What is your decision regarding the null hypothesis?

4. What is the p-value? (Round your answer to 3 decimal places.)​​​​​​​

1) You are studying staghorn sculpin within wetland creeks, and you use baited minnow traps separated by 10 meters. After an hour, you pull all your minnow traps up and count the number of sculpins found in each minnow trap. You organize the data in a frequency table seen below:

A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. Assume that the distributions follow the normal probability distribution and the population standard deviations are equal. The information is summarized below.

At the 0.01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month?

a. State the decision rule for 0.01 significance level: H₀: μ_Men= μ_Women   H₁: μ_Men ≠ μ_Women. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)

b. Compute the value of the test statistic. (Round your answer to 3 decimal places.)

c. What is your decision regarding the null hypothesis?

d. What is the p-value? (Round your answer to 3 decimal places.)

10) The number of patients admitted per day to a large hospital's ICU follows a skewed right distribution with a mean of 20 and a standard deviation of 8. Suppose a sample of 100 days was collected over the past year and the average number of patients admitted per day was calculated.

a) Which of the following statements about the sampling distribution of the sample mean is correct?

-It is a skewed right distribution with a mean of 20 and a standard deviation of .8.

-It is approximately normally distributed with a mean of 20 and a standard deviation of .8.

-It is approximately normally distributed with a mean of 20 and a standard deviation of 8.

-It is a skewed right distribution with a mean of 20 and a standard deviation of 8.

b) Does the Central Limit Theorem apply to this problem?

-Yes, since np and nq are both at least 15

-No

-Yes, since n is at least 30.

c) What is the probability that the mean in the sample exceeded 24 days?

-Approximately 1

-.1915

-Approximately 0

-.3085

Isle Royale, an island in Lake Superior, has provided an important study site of wolves and their prey. Of special interest is the study of the number of moose killed by wolves. In the period from 1958 to 1974, there were 296 moose deaths identified as wolf kills. The age distribution of the kills is as follows.

(a) For each age group, compute the probability that a moose in that age group is killed by a wolf. (Round your answers to three decimal places.)

(b) Consider all ages in a class equal to the class midpoint. Find the expected age of a moose killed by a wolf and the standard deviation of the ages. (Round your answers to two decimal places.)

Prompt:

A friend tells you he only needs a 25% on the final exam to pass his statistics class, and since the exams are always multiple choice with four possible answers he can randomly guess at the answers and still get 25%. Use what you have learned about the binomial distribution to answer the following questions.

Response parameters:

What do you think about your friend’s idea?

Why?

What do you think his chances of getting at least 25% on the exam are?

Do the number of questions on the exam make a difference? If it does, should your friend hope for a 20 question exam or a 100 question exam.

(Tip: it may help if you create a table of Binary probabilities with p = 0.25 and n = number of questions on the exam. Also, don’t confuse the probability of getting exactly 25% of the questions correct and getting at least 25% of the questions correct)