Suppose you have a bag of M&Ms with 19 M&Ms. Suppose 4 of them are red, 3 are green, and 12 are yellow.

(a) If one M&M is chosen at random from the bag, find the probability that it is yellow.

(b) If one M&M is chosen at random from the bag, and eaten, and then a second M&M is chosen at random from the bag, find the probability that they are both red.

Facebook has become a very popular website among senior citizens. A random sample of 65 senior Americans showed a sample average of 189 friends with a sample standard deviation of 25 friends. Estimate the number of Facebook friends senior Americans have in a 99% confidence interval.

(Do not use direct steps)

Researchers identified a number of new undergraduate students who said they suffered from “examination panic” and they felt they were not performing as well as they could on timed examinations. Researchers decided to conduct an experiment and randomly divided the students into three equal groups that would carry out a timed test as part of one of three treatment programs: one to undergo therapy sessions before the test day; the second to receive the tranquilizer just before the test; and the third to receive a placebo (a sugar tablet) just before the test.  When the results were collected, it was found that the distributions of scores were highly irregular, neither normal nor showing homogeneity of variance; therefore a one-way ANOVA was not appropriate.  Using the students data set, conduct a Kruskal-Wallis test. Show all the hypothesis testing steps. Write the results in APA format and include a copy of the SPSS output.

The assumptions for this test are:

1. All the samples are independent and randomly selected.

2. Each sample has at least 5 observations.

3. The k probability distributions are continuous.

4. The data is not normally distributed

Student Data.

a) If you have 4 cousins, what is the probability that 3 or more are male? (Assume male and female are equally likely).

b) In a normal distribution, what percent of scores are in T-score of 51 or higher?

c) If you roll two 6-sided dice, what percent of the time do both dice show numbers from 4 to 6?

d) In an elementary school, the correlation between age and height for all students in the school is _________ than the same correlation for only the fourth graders.

Fair Coin? In a series of 100 tosses of a token, the proportion of heads was found to be 0.61. However, the margin of error for the estimate on the proportion of heads in all tosses was too big. Suppose you want an estimate that is in error by no more than 0.04 at the 90% confidence level.

(a) What is the minimum number of tosses required to obtain this type of accuracy? Use the prior sample proportion in your calculation. You should toss the token at least ____ times.

(b) What is the minimum number of tosses required to obtain this type of accuracy when you assume no prior knowledge of the sample proportion? You should toss the token at least ____ times.

1. The ________________________ of two events A and B is the event that consists of all the elements contained in A and B.
2. If A and B are mutually exclusive then A∩B = _________ and P(A∩B) = ________.
3. If A and B are independent, P(A∩B) = ____________________ (finish the formula).

4.  The law of large numbers says that if an experiment is repeated again and again, the         relative frequency probability will get closer to the _____________________________

5.  If the P(A\B) = 0.6 and P(A∩B) = 0.3, find P(B).

6.  If you roll a single fair die and count the number of dots on top, what is the probability of getting a number of at most 3 on a single throw?

7.  You roll two fair dice, a blue one and a yellow one. Each part has single probability.

1. Find P(odd number on the blue die and even on the yellow die).

     b)  Find P(even on the blue die and greater than 1 on the yellow die).

8.  An urn contains 12 balls identical in every respect except color.  There are 6 red balls, 4 green balls, and 2 blue balls. Each part has single probability.

     a)  You draw two balls from the urn, but replace the first ball before drawing the second.  Find the probability that the first ball is red and the second is green.

     b)  Repeat part (a), but do not replace the first ball before drawing the second.

9.  A computer package sale comes with four different choices of printers and five choices of monitors.  If a store wants to display each package combination that is for sale, how many packages must be displayed?   

10.  You have 100 parts in a box and 25 of them are bad.  What is the probability that:

            a)         the first part you draw will be bad?

            b)         the first part will be good?

            c)         if you draw two parts, both will be good?

7. A hospital conducted a study of the waiting time in its emergency room. The hospital has a main campus and three satellite locations. Management has a business objective of reducing waiting time for emergency room cases that do not require immediate attention. To study this, a random sample of 15 emergency room cases that did not require immediate attention at each location were selected on a particular day, and the waiting time (measured from check-in to when the patient was called into the clinic area) were collected and stored in ER.

a. At the 0.05 level of significance, is there evidence of a difference in the mean waiting times in the four locations?

b. Does the result in (a) give you statistical permission to probe for individual differences between hospital locations?

For each of the following two-samples t-tests (problems 1-6): (a) Determine if a F test for the ratio of two variances is appropriate to calculate for the context. If it is appropriate, conduct the analysis and report the result. Include what statistical conclusion you should draw from the analysis (i.e., whether you should conduct a pooled-variance t-test or an unequal-variances t-test). (b) Identify the most appropriate t-test to conduct for the situation/data given. Don’t forget to consider if the context requires one/two-tail tests. (c) Provide a statistical and practical interpretation of your findings.

6. Target versus Walmart: Who had the lowest prices? To address your consumer thirst for knowledge you identify 20 items (all brand-name items) currently on your household shopping list. You visit both your Local Target and Walmart, price each item, organize, and then store these data in TargetWalmart. Is there evidence to support that prices are cheaper at Walmart? (Use a 0.05 level of significance)

For each of the following two-samples t-tests (problems 1-6): (a) Determine if a F test for the ratio of two variances is appropriate to calculate for the context. If it is appropriate, conduct the analysis and report the result. Include what statistical conclusion you should draw from the analysis (i.e., whether you should conduct a pooled-variance t-test or an unequal-variances t-test). (b) Identify the most appropriate t-test to conduct for the situation/data given. Don’t forget to consider if the context requires one/two-tail tests. (c) Provide a statistical and practical interpretation of your findings.

4. A problem with a cell phone that prevents a customer from receiving calls is upsetting both customers and the telecommunications company. The file Phone contains samples of 20 problems reported to two different offices of the telecommunication company and the time to clear these problems (in minutes) from the customers’ phones. Is there evidence that addressing this phone issue results in different mean waiting times at the two offices? (Use a 0.05 level of significance)

For each of the following two-samples t-tests (problems 1-6): (a) Determine if a F test for the ratio of two variances is appropriate to calculate for the context. If it is appropriate, conduct the analysis and report the result. Include what statistical conclusion you should draw from the analysis (i.e., whether you should conduct a pooled-variance t-test or an unequal-variances t-test). (b) Identify the most appropriate t-test to conduct for the situation/data given. Don’t forget to consider if the context requires one/two-tail tests. (c) Provide a statistical and practical interpretation of your findings.

2. An article appearing in The Exponent, an independent college newspaper published by the Student Publishing Foundation, reported that the average American college student spends one hour (60 minutes) on Facebook daily. But you wonder if there is a difference between males and females. You select a sample of 60 Facebook users (30 males, 30 females) at Baker University. The time spent on Facebook per day (in minutes) for these 60 users is stored in FacebookTime. Is there evidence of a difference in mean time spent on Facebook per day between males and females? (Use a 0.05 level of significance)

For each of the following two-samples t-tests (problems 1-6): (a) Determine if a F test for the ratio of two variances is appropriate to calculate for the context. If it is appropriate, conduct the analysis and report the result. Include what statistical conclusion you should draw from the analysis (i.e., whether you should conduct a pooled-variance t-test or an unequal-variances t-test). (b) Identify the most appropriate t-test to conduct for the situation/data given. Don’t forget to consider if the context requires one/two-tail tests. (c) Provide a statistical and practical interpretation of your findings.

1. A bank with a branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the 12-1pm lunch period. Management decided to first study the waiting time in the current process. The waiting time is defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window. Data are collected from a random sample of 15 customers and stored in Bank1. Suppose that another branch, located in a residential area, is also concerned with improving the process of serving customers in the 12-1pm lunch period. Data are collect from a random sample of 15 customers and stored in Bank2. Can we conclude the wait times are different at the two branches? (Use a 0.05 level of significance)

Bank 1

Bank 2

Let X be the sum of rolling 2 dice.

a) Plot the CDF and PMF of X.

b) Determine P(5 < X <=8 | x<=10)

c) Determine the median, mean and variance of X

d) Bonus: Compute the correlation between X and Y = the number on the first dice.

In a poll of 568 human resource​ professionals, 35.9​% said that body piercings and tattoos were big grooming red flags. Complete parts​ (a) through​ (d) below. ​a) Among the 568 human resource professionals who were​ surveyed, how many of them said that body piercings and tattoos were big grooming red​ flags? 204 ​(Round to the nearest integer as​ needed.) ​b) Construct a​ 99% confidence interval estimate of the proportion of all human resource professionals believing that body piercings and tattoos are big grooming red flags. . 307less than p less than 0.411 ​(Round to three decimal places as​ needed.) ​c) Repeat part​ (b) using a confidence level of​ 80%. nothingless than p less than nothing ​(Round to three decimal places as​ needed.)

An agent for a residential real estate company in a large city has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward that goal, the agent would like to use the size of an apartment, as defined by square footage to predict the monthly rental cost. The agent selects a sample of 25 apartments in a particular residential neighborhood and collects the following data:

Make a Normal Probability Plot and a Residual plot of the Residuals (Y axis) vs. Apartment Size (X axis). Based on these results, evaluate whether the assumptions of regression have been seriously violated.

Given the following discrete uniform probability distribution, find the expected value and standard deviation of the random variable. Round your final answer to three decimal places, if necessary.