Recall again that Rind & Bordia (1996) investigated whether or not drawing a happy face
on customers’ checks increased the amount of tips received by a waitress at an upscale
restaurant on a university campus. During the lunch hour a waitress drew a happy,
smiling face on the checks of a random half of her customers. The remaining half of the
customers received a check with no drawing (18 points).
The tip percentages for the control group (no happy face) are as follows:
45% 39% 36% 34% 34% 33% 31% 31% 30% 30% 28%
28% 28% 27% 27% 25% 23% 22% 21% 21% 20% 18%
8%
The tip percentages for the experimental group (happy face) are as follows:
72% 65% 47% 44% 41% 40% 34% 33% 33% 30% 29%
28% 27% 27% 25% 24% 24% 23% 22% 21% 21% 17%

This time, you are to perform a “hypothesis test” using the tip data, answering each of
the questions below. For short-answer questions, be brief. However, you must give
enough detail to justify your answers. Single-sentence responses will generally not
suffice, but do not exceed a paragraph for any given answer.

l. Using the formula discussed in class, calculate Cohen’s d effect size measure.
Provide a brief interpretation of the statistic. Note: simply saying that the
effect is “small”, “medium”, or “large” will not suffice.

Take 3 dice and throw these dice 30 times. Let X be the sum of the number of dots on upper faces of the dice.

Obtain probability distribution of X. Also find mean and variance.

E. Martz tells us that chi-square analysis can be used for more than just practical applications:

Chi-square analysis compares the counts of two categorical variables to tell you if a relationship exists between the variables or not. You can apply chi-square analysis to answer important questions about factors in everyday life, and even about events like elections... or Halloween. If you are a character in a slasher film, is there a connection between your gender and your dying in some horrible manner?

As explained in the above passage, you can use chi-square analysis to compare a wide range of topics.

To complete the Discussion activity, please do the following:

Answer each question fully. Use a minimum of 250 words for a complete discussion post. While it is not required in this discussion, feel free to bring in outside resources to support your answers. Outside resources include materials outside of the textbook, such as a website.

• Propose a life event or situation and two categorical variables for it. Complete a chi-square analysis of this event or situation and these variables, and share your results.
• Do you agree with your findings? Why or why not?
• What other factors, if any, should be considered?
• In your peer responses, explain whether you agree with other’s posts on their chi-square analyses. Why or why not? Fully explain your answers.

Jobs and productivity! How do retail stores rate? One way to answer this question is to examine annual profits per employee. The following data give annual profits per employee (in units of 1 thousand dollars per employee) for companies in retail sales. Assume σ ≈ 4.0 thousand dollars.

3.7 6.7 3.6 8.5 7.5 5.9 8.7 6.4 2.6 2.9 8.1 −1.9 11.9 8.2 6.4 4.7 5.5 4.8 3.0 4.3 −6.0 1.5 2.9 4.8 −1.7 9.4 5.5 5.8 4.7 6.2 15.0 4.1 3.7 5.1 4.2

(a) Use a calculator or appropriate computer software to find x for the preceding data. (Round your answer to two decimal places.) thousand dollars per employee

(b) Let us say that the preceding data are representative of the entire sector of retail sales companies. Find an 80% confidence interval for μ, the average annual profit per employee for retail sales. (Round your answers to two decimal places.) lower limit -- thousand dollars upper limit -- thousand dollars

(c) Let us say that you are the manager of a retail store with a large number of employees. Suppose the annual profits are less than 3 thousand dollars per employee. Do you think this might be low compared with other retail stores? Explain by referring to the confidence interval you computed in part

(b). Yes. This confidence interval suggests that the profits per employee are less than those of other retail stores. No. This confidence interval suggests that the profits per employee do not differ from those of other retail stores. Correct: Your answer is correct.

(d) Suppose the annual profits are more than 6.5 thousand dollars per employee. As store manager, would you feel somewhat better? Explain by referring to the confidence interval you computed in part (b). Yes. This confidence interval suggests that the profits per employee are greater than those of other retail stores. No. This confidence interval suggests that the profits per employee do not differ from those of other retail stores.

(e) Find an 95% confidence interval for μ, the average annual profit per employee for retail sales. (Round your answers to two decimal places.) lower limit 3.75 Incorrect: Your answer is incorrect. thousand dollars upper limit 6.41 Incorrect: Your answer is incorrect. thousand dollars

USA Today reported that approximately 25% of all state prison inmates released on parole become repeat offenders while on parole. Suppose the parole board is examining five prisoners up for parole. Let x = number of prisoners out of five on parole who become repeat offenders.

x 0, 1, 2, 3, 4, 5

P(x) 0.212, 0.374, 0.224, 0.158, 0.031, 0.001

(a) Find the probability that one or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.)

How does this number relate to the probability that none of the parolees will be repeat offenders?

These probabilities are not related to each other.

This is five times the probability of no repeat offenders.

This is the complement of the probability of no repeat offenders.

These probabilities are the same.

This is twice the probability of no repeat offenders.

(b) Find the probability that two or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.)

(c) Find the probability that four or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.)

(d) Compute μ, the expected number of repeat offenders out of five. (Round your answer to three decimal places.) μ = prisoners

(e) Compute σ, the standard deviation of the number of repeat offenders out of five. (Round your answer to two decimal places.) σ = prisoners

A classroom contains 9 students. A student committee of 3 (president, vice-president, and treasurer) must be selected. Harry Potter will serve only as president and only if either of his friends Ron Weasley or Hermione Granger serve as vice president; otherwise he leaves the group. The others (including Ron and Hermione) have no such restrictions. What is the probability that Ron or Hermione become the president of this group?

The answer is not 0.25

John Calipari, head basketball coach for the 2012 national champion University of Kentucky Wildcats, is the highest paid coach in college basketball, with an annual salary of $5.4 million. The following sample shows the head basketball coach's salary for a sample of 10 schools playing NCAA Division I basketball. Salary data are in millions of dollars.

a. Use the sample mean for the 10 schools to estimate the population mean annual salary for head basketball coaches at colleges and universities playing NCAA Division I basketball.

b. Use the data to estimate the population standard deviation for the annual salary for head basketball coaches.

c. What is the 95% confidence interval for the population variance?

d. What is the 95% confidence interval for the population standard deviation?

e. What is the 95% confidence interval for the population mean?

#1) Consider the following table summarizing the speed limit of a certain road and the number of accidents occurring on that road in January

a) Find the slope of the regression line predicting the number of accidents from the posted speed limit. Round to 3 decimal places.

b) Find the intercept of the regression line predicting the number of accidents from the posted speed limit. Round to 3 decimal places.

c) Predict the number of reported accidents for a posted speed limit of 43mph. Round to the nearest whole number.

#2) Consider the following:

a) What is slope of the regression line predicting Y from X, rounded to 2 decimal places?

b) What is the intercept of the regression line predicting Y from X, rounded to 2 decimal places?

c) What is the correlation between X and Y, rounded to 2 decimal places?

The next day, Valentines Day, February 14th, the owner tries to improve her sales technique pushing for orders of higher amounts. Again she attempts to write down a number of random sale amounts as the day goes on. As she is so busy she manages to record only n=14 sale prices among all flower sales that day. She calculated the average sale price of the 14 sales as 97.71 euro and calculated that they varied with a standard deviation of 15.73 euro.

Estimate the value of the population mean, µ, the true mean sale amount of all sales on February 14, by calculating a 95% confidence interval. Fill in the blanks in the following:

An estimate of the population mean is:____________

The standard error is .:__________

The distribution is (examples: normal / t12 / chisquare4 / F5,6). _________________

For a 95% confidence interval the distributional cut-off is (3 dec places). ________________

It is quite likely that the true mean sale amount of all sales on February 14 is between ______________and __________ , with 95% confidence.

Three randomly selected households are surveyed. The numbers of people in the households are 1​, 2​, and 12. Assume that samples of size n=2 are randomly selected with replacement from the population of 1​, 2​, and 12. Listed below are the nine different samples. Complete parts​ (a) through​ (c). 1​,1   1​,2   1​,12   2​,1   2​,2   2​,12   12​,1   12​,2   12​,12 a. Find the median of each of the nine​ samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution of the distinct median values. Sample Median __(1,2,1.5),__(3.1.5,2),__(4,3,2),__(6.5,13,8),__(7,12.5,14),__(18,12,,24Probability __,__,__,__,__,__ (Type integers or fractions. Use ascending order of the sample​ medians.)

Assume that 74% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below, rounded to four decimal places:

a. There are some lefties (≥ 1) among the 5 people.

b. There are exactly 3 lefties in the group.

c. There are at least 4 lefties in the group.

d. There are no more than 2 lefties in the group.

e. How many lefties do you expect?

f. With what standard deviation?

(a) Explain how an undesirable outcome relates to output variables. (b) Provide a thorough example (in detail in the form of a paragraph) of how a particular risk reduction strategy of your choosing can act to reduce the chances of undesirable outcomes?

6) For the following problems, identify the hypotheses, define Type I and Type II errors, and discuss the consequences of each error. (When you set up the hypotheses, consider which is the hypothesis you are ”trying to prove”, and that is your alternative. The null hypothesis is then the status quo.)

a. The FDA judges the safety of new drugs. When faced with a new drug, there are two possible decisions: approve the drug or disapprove the drug.

b. You are faced with two investments. One is very risky, but potential returns are high, while the other one is safe but the potential is quite limited. Pick one.

c. You are an airline pilot. You smell smoke in the cockpit, and the nearest airport is less than 5 minutes away. Should you land the plane immediately?

For many florists, the days leading up to Valentine's Day are among the busiest of the year. An owner of a florist wanted to estimate the average sale amount for all sales made on the day before Valentine's Day, February 13th. When she had time she wrote down the sale price of a transaction of fresh flowers on a sheet of paper. By 3pm she had collected n=41 sale prices of all flower sales that were made day. The variable of interest is the total euro amount of each purchase. During her quick tea-break she calculated the average sale price of the 41 sales as 76.45 euro and found that they varied with a standard deviation of 22.41 euro.

Estimate the value of the population mean, µ, the true mean sale amount of all sales on February 13, by calculating a 95% confidence interval. Fill in the blanks in the following:

An estimate of the population mean is _________
.
The standard error is __________
.
The distribution is ____________ (examples: normal / t12 / chisquare4 / F5,6).

For a 95% confidence interval the distributional cut-off is __________

It is quite likely that the true mean sale amount of all sales on February 13 is between ___________ and ____________ ,with 95% confidence.