Bob reported that the patients suffering from the “Mad Man Disease” who used his “magic dust” elixir properly resulted in an odds-ratio = .6 relative to controls who did not use his elixir, whose probability of suffering from the “Mad Man Disease” was only p = .3.

(a) Describe the meaning of the odds-ratio for elixir users in words.

(b) What was the probability of suffering from the “Mad Man Disease” for the elixir group?

Given the following numbers:   25 16 61 18 15 20 15 20 24 17 19 28, derive the mean, median, mode, variance, standard deviation, skewness, kurtosis, range, minimum, maximum, sum, and count. Interpret your results. What is the empirical rule for two standard deviations of the data?

please do this as simple as you can!

if you flip a fair coin 10 times what is the probability of
a) getting all tails?
b) getting all heads
c) getting atleast 1 tails

1.Time taken for oil change

It is known that the amount of time needed to change the oil on a car is normally distributed with a standard deviation of 5 minutes. The manager of a service shop recorded the amount of time (in minutes) to complete a random sample of 10 oil changes. They are listed below. 11 10 16 15 18 12 25 20 18 24

a. The sample average is: _______ minutes (up to 2 decimal points)

B.The sample standard deviation is: _______ minutes (up to 2 decimal points)

The following information applies to the next two questions:

Compute a 95% interval estimate of the population mean.

1. Lower Confidence Level ___ Minute (up to 2 decimal points)
2. Upper Confidence Level ___ Minutes (up to 2 decimal points)
3. Based on your answer above, if you take your car to this particular shop, your car will be serviced between  and minutes. You are  % certain about this.

4. Suppose that the manager feels that the range of values he obtained above are too wide to attract customers. What can he do to obtain a narrower range of values?

Use a 90% confidence interval

Take a random sample of 100 oil changes

Train his employees well so that the variability in time to change oil reduces

All the above

None of the above

5. A marketing researcher wants to estimate the mean amount spent ($) on Amazon.com by Amazon Prime member shoppers. A random sample of 100 Amazon Prime member shoppers who recently made a purchase on Amazon.com yielded a mean of $1,500 and a standard deviation of $200.

Construct a 90% Confidence Interval estimate for the mean spending for all Amazon Prime shoppers.

What is the Lower Confidence Level $______

What is the Upper Confidence Level $______

8. Based on the above calculation, which one of the following statements is correct

We are 90% confident that an Amazon Prime Member spends $1500

We are 90% confident that an Amazon Prime Member spends between $1467.10 and $1532.90

Both of the above statements are true

An Amazon Prime member spends between $1467.10 and $1532.90

9. The researcher is not happy with the estimate, and she wants tighter interval, i.e., a smaller level of error. If she wants the estimate to be within ±$25 with 90% confidence, what sample size does she need?

Sample size _____ (report the next whole number, 100.2 should be reported as 101)

10. The salaries of graduates from the MBA program of a Big Ten school are NOT normally distributed. In order to get a better understanding of the range of salaries made by the graduates, the marketing director compiles a five-year record of salaries offered to students at campus recruitment events. He randomly selects groups of 120 students graduating in Fall, Summer, and Spring for the past five years (i.e., 15 groups, each with 120 students).

According to the Central Limit Theorem, the salaries within any of these 15 groups will be distributed normally. True or False?

According to the Central Limit Theorem, the average salaries of these 15 groups will be distributed normally. True or False

6. A lawyer commutes daily from his suburban home to his midtown office. The average time for a one-way trip is 24 minutes, with a standard deviation of 3.8 minutes. Assume the distribution of the trip-length to be normally distributed. (a) If the office opens at 9:00am and he leaves his house at 8:40 am daily, what percentage of the time is he late for work? You must draw the distribution and indicate the relevant numbers etc. You must also give the answer as a number. (b) Find the length of time above which we find the longest 20% of the trips. You must draw the distribution and indicate the relevant numbers etc. You must also give the answer as a number. (c) During a period of 20 work days, on how many days should you expect the lawyer to be late for work? (d) What is the probability that he is late on at most 10 of those 20 days?

The state of California has a mean annual rainfall of 27.6 inches, whereas the state of New York has a mean annual rainfall of 48.7 inches. Assume the standard deviation for California is 7.4 inches and for New York is 3.1 inches. Find the probability that, for a sample of 45 years of rainfall for California, the mean annual rainfall is at least 29 inches.

Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $32 and the estimated standard deviation is about $7.

(a) Consider a random sample of n = 80 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution?

The sampling distribution of x is approximately normal with mean μ_x = 32 and standard error σ_x = $0.09. The sampling distribution of x is not normal.     The sampling distribution of x is approximately normal with mean μ_x = 32 and standard error σ_x = $7. The sampling distribution of x is approximately normal with mean μ_x = 32 and standard error σ_x = $0.78.

Is it necessary to make any assumption about the x distribution? Explain your answer.

It is necessary to assume that x has an approximately normal distribution. It is necessary to assume that x has a large distribution.     It is not necessary to make any assumption about the x distribution because μ is large. It is not necessary to make any assumption about the x distribution because n is large.

(b) What is the probability that x is between $30 and $34? (Round your answer to four decimal places.)

(c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $30 and $34? (Round your answer to four decimal places.)
(d) In part (b), we used x, the average amount spent, computed for 80 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen?

1. Listed below are the budgets​ (in millions of​ dollars) and the gross receipts​ (in millions of​ dollars) for randomly selected movies. .

Find the value of the linear correlation coefficient r.

2. For a sample of eight​ bears, researchers measured the distances around the​ bears' chests and weighed the bears. Calculator was used to find that the value of the linear correlation coefficient is

r equals=0.963

What proportion of the variation in weight can be explained by the linear relationship between weight and chest​ size?

a. What proportion of the variation in weight can be explained by the linear relationship between weight and chest​ size?

3. Assume that you have paired values consisting of heights​ (in inches) and weights​ (in lb) from 40 randomly selected men. The linear correlation coefficient r is

0.559.

Find the value of the coefficient of determination. What practical information does the coefficient of determination​provide?

4.

The data show the bug chirps per minute at different temperatures. Find the regression​ equation, letting the first variable be the independent​ (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of 0.05. What is wrong with this predicted​ value?

What is the regression​ equation?

5.

The data below shows height​ (in inches) and pulse rates​ (in beats per​ minute) of a random sample of women. .

Find the value of the linear correlation coefficient r.

r equals =

​(Round to three decimal places as​ needed.)

The state of California has a mean annual rainfall of 27.6 inches, whereas the state of New York has a mean annual rainfall of 44.5 inches. Assume the standard deviation for California is 6.3 inches and for New York is 8.2 inches. Find the probability that, for a sample of 40 years of rainfall for California, the mean annual rainfall is at least 29 inches.

Five people on the basement of a building get on an elevator that stops at seven floors. Assuming that each has an equal probability of going to any floor, find

(a) the probability that they all get off at different floors; (3 POINTS)

(b) the probability that two people get off at the same floor and all others get off at different floors. (4 POINTS)

Let’s consider a study that followed a randomly selected group of 100 State U students during a two-year period at the school. The study found that a linear relationship exists between the number of hours students spend engaging in social media each week and their cumulative gpa during the two-year period. The model for this relationship can be given by the equation

g?pa = −0.032 × (hours) + 2.944 (a) Interpret the slope of the line in the context of the data.

(b) The residual gpa for a particular student who spent 20 hours per week using social media was found to be 0.476. What was this student’s cumulative gpa during the two-year period?

(c) Would the correlation coefficient for the linear relationship be positive or negative? Explain.

(d) If another study found that the linear correlation coefficient between a student’s gpa and the number of hours spent at the library was r = 0.46, could you conclude that this relationship is stronger than the one between gpa and hours spent on social media? Explain.

Consider the following data collected from a sample of 12 American black bears:

(a) Sketch a scatterplot of the data. Treat length as the explanatory variable. Describe the association.

(b) Construct the equation for the line of best fit.

(c) Estimate the weight of a bear which measures 142.5 cm in length.

(d) What percent of the variation in the bears’ weights can be described by the differences in their lengths?