1. Suppose we would like to determine if the typical amount spent per customer for dinner at a new restaurant in town is more than $20.00.  A sample of 49 customers over a three-week period was randomly selected and the average amount spent was $22.60.  Assume that the standard deviation is known to be $2.50.

•Using a 95% confidence level of significance, would we conclude the typical amount spent per customer is more than $20.00?

•Discuss your interpretation of your findings.

2. Suppose an editor of a publishing company claims that the mean time to write a textbook is at most 15 months.  A sample of 16 textbook authors is randomly selected and it is found that the mean time taken by them to write a textbook was 12.5.  Assume also that the standard deviation is known to be 3.6 months.

•Assuming the time to write a textbook is normally distributed and using a 95% confidence level of significance, would you conclude the editor’s claim is true?  

•Discuss your interpretation of your findings.

**Please show all work**

Use the population of ages {56, 49, 58, 46} of the four U.S. presidents (Lincoln, Garfield, McKinley, Kennedy) when they were assassinated in office. Assume that random samples of size n = 2 are selected with replacement.

1. List the 16 different samples. For example, the samples for age 56 would be

56, 56

56, 49

56, 58

56, 46.

2. After listing all 16 samples, find the mean of each sample, then construct a table representing the sampling distribution of the sample mean. In the table, combine values of the sample mean that are the same.

3. Compare the mean of the population {56, 49, 58, 46} to the mean of the sampling distribution of the sample mean.

4. Do the sample means target the value of the population mean? In general, do sample means make good estimators of population means? Why or why not?

Are sexually active teenagers any better informed about AIDS and other potential health problems related to sex than teenagers who are sexually inactive? A 15-item test of general knowledge about sex and health was administered to random samples of teens who are sexually inactive, teens who are sexually active but with only a single partner, and teens who are sexually active with more than one partner. Is there any significant difference in the test scores? Inactive:10,12,8,10,8,5 active one partner: 11,11,6,5,15,10 active more than one partner 12,12,10,4,3,15

Please show computations without software.

The lifespan of an electrical component has an exponential distribution with parameter lambda = 0.013. Suppose we have an iid sample of size 100 of these components

Some hints: P(X < c) for an exponential(lambda) can be found via pexp(c,lambda) E[X] = 1/lambda and Var[X] = 1/lambda^2

Round all answers to 4 decimals

Using the exact probability distribution, what is the probability that a single component will be within 15.38 units of the population mean?

Using Chebyshev's inequality, what is a lower bound on the probability that the sample mean will be within 15.38 units of the population mean?

Using the CLT, what is an approximation to the probability that the sample mean will be within 15.38 units of the population mean?

The president of Doerman Distributors, Inc., believes that 30% of the firm's orders come from first-time customers. A random sample of 100 orders will be used to estimate the proportion of first-time customers.

(a)

Assume that the president is correct and

p = 0.30.

What is the sampling distribution of

p

for n = 100? (Round your answer for

σ_p

to four decimal places.)

σ_p

=

E(p)

=

Since np =  and n(1 − p) =  , approximating the sampling distribution with a normal distribution  ---Select--- is is not appropriate in this case.

(b)

What is the probability that the sample proportion

p

will be between 0.20 and 0.40? (Round your answer to four decimal places.)

(c)

What is the probability that the sample proportion will be between 0.25 and 0.35? (Round your answer to four decimal places.)

Let a bowl contain 15 chips of the same size and shape. Only one of those chips is red. Continue to draw chips from the bowl, one at a time at random and without replacement, until the red chip is drawn. Show your work.

a) Find the probability mass function of X, the number of trials needed to draw the red chip.

b) Compute the mean and variance of X.

c) Determine P(X <= 10).

Suppose that the weights of airline passenger bags are normally distributed with a mean of 48.01 pounds and a standard deviation of 3.6 pounds.

a) What is the probability that the weight of a bag will be greater than the maximum allowable weight of 50 pounds? Give your answer to four decimal places.

b) Assume the weights of individual bags are independent. What is the expected number of bags out of a sample of 11 that weigh greater than 50 lbs? Give your answer to four decimal places.

c) Assuming the weights of individual bags are independent, what is the probability that 4 or fewer bags weigh greater than 50 pounds in a sample of size 11? Give your answer to four decimal places.

​A.  Is the reaction to the new phone associated with the sex of the​ customer? How strong is the​ association?

Since V = ? (What does V equal?) fill in blank, there is blank association between the two variables?

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

​B. How should the company use the information from this study when marketing its new​ product? answer choices below A-D

A.

Assuming that the reactions of the women sampled are representative of all​ women, the company should market toward women first since they had few unfavorable reactions.

B.

The company should market toward men first because more men participated in the survey.

C.

The company should market toward men first since they had a higher percentage of favorable reactions.

D.

Assuming that the reactions of the women sampled are representative of all​ women, the company should market toward women first since they had a higher percentage of favorable reactions.

​C. Can you think of an underlying lurking variable that might complicate the relationship shown​ here? Justify your answer.? Answer choices below A-D

A.

There are no lurking variables because the sex of the customer is the only variable that is associated with the reactions to the new phone.

B.

Variables such as the average age of the participants or the median income of the town where the mall is located are possible lurking variable because​ people's opinions may be related to the age or wealth.

C.

Variables such as the proportion that carry a​ phone, the time of​ day, or the day of the week are possible lurking variables because these may be associated with the sex of the customer and also with the reactions to the new phone.

D.

The mall where the data was gathered is the only significant lurking variable because it may have different types of customers than other malls.

A) A poker hand consists of five cards randomly dealt from a standard deck of 52 cards. The order of the cards does not matter. Determine the following probabilities for a 5-card poker hand. Write your answers in percent form, rounded to 4 decimal places. Determine the probability that exactly 3 of these cards are Aces. Answer: % Determine the probability that all five of these cards are Spades. Answer: % Determine the probability that exactly 3 of these cards are face cards. Answer: % Determine the probability of selecting exactly 2 Aces and exactly 2 Kings Answer: % Determine the probability of selecting exactly 1 Jack. Answer: %

B) Lacy draws a diamond from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card and gets a heart. Are these events independent? Input Yes or No: Determine the probability of drawing a diamond and then a heart without replacement. Write your answer in decimal form, rounded to four decimal places as needed. Answer = Linda draws a diamond from a standard deck of 52 cards. She returns the diamond to the deck, then draws a second card. Her second card is a heart. Are these events independent? Input Yes or No: Determine the probability of drawing a diamond and then a heart with replacement. Write your answer in decimal form, rounded to four decimal places as needed.

C)A 3-digit PIN number is selected. What it the probability that there are no repeated digits? The probability that no numbers are repeated is . Write your answer in decimal form, rounded to the nearest thousandth.

D)In a lottery daily game, a player picks four numbers from 0 to 9 (without repetition). How many different choices does the player have 1) If order matters? 2) If order does not matter?

Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 1.3 and a mean diameter of 208 inches.

If 60 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would be greater than 208.1 inches? Round your answer to four decimal places.

PLEASE DO NOT ANSWER UNLESS YOU ARE CONFIDENT YOUR ANSWER IS CORRECT.

Assume that the population proportion is 0.59. Compute the standard error of the proportion,

σ_p,

for sample sizes of 100, 200, 500, and 1,000. (Round your answers to four decimal places.)

For a sample size of 100For a sample size of 200For a sample size of 500For a sample size of 1000

What can you say about the size of the standard error of the proportion as the sample size is increased?

σ_p

increases as n increases.

σ_p

decreases as n increases.    

σ_p

approaches p as n increases.

σ_p

approaches

p

as n increases.

A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2 for a sample of N=11N=11 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test statistics to assess the significance of the regression model and partial slopes. Use a significance level α=0.05α=0.05.

R2=R2=
F=F=
P-value for overall model =

t1=t1=
for b1b1, P-value =
t2=t2=
for b2b2, P-value =

What is your conclusion for the overall regression model (also called the omnibus test)?

• The overall regression model is statistically significant at α=0.05α=0.05.
• The overall regression model is not statistically significant at α=0.05α=0.05.

Which of the regression coefficients are statistically different from zero?

• neither regression coefficient is statistically significant
• the slope for the first variable b1b1 is the only statistically significant coefficient
• the slope for the second variable b2b2 is the only statistically significant coefficient
• both regression coefficients are statistically significant

uppose the following data are product weights for the same items produced on two different production lines.

Test for a difference between the product weights for the two lines. Use α = 0.05.

State the null and alternative hypotheses.

H₀: Median for line 1 − Median for line 2 < 0
H_a: Median for line 1 − Median for line 2 = 0H₀: Median for line 1 − Median for line 2 ≤ 0
H_a: Median for line 1 − Median for line 2 > 0     H₀: The two populations of product weights are not identical.
H_a: The two populations of product weights are identical.H₀: Median for line 1 − Median for line 2 ≥ 0
H_a: Median for line 1 − Median for line 2 < 0H₀: The two populations of product weights are identical.
H_a: The two populations of product weights are not identical.

Find the value of the test statistic.

W =

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.Reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.     Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.Reject H₀. There is sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.

The restaurant owner Lobster Jack wants to find out what the peak demand periods are, during the hours of operation, in order to be better prepared to serve his customers. He thinks that, on average, 60% of the daily customers come between 6:00pm and 8:59pm (equally distributed in that time) and the remaining 40% of customers come at other times during the operating hours (again equally distributed). He wants to verify if that is true or not, so he asked his staff to write down during one week the number of customers that come into the restaurant at a given hour each day. His staff gave him the following data:

Help the manager figure out if his instincts are correct or not. Use a Chi-Squared test to see if the observed distribution is similar to the expected. Use the average demand for a given time as your observed value.

Part 1:

What is the p-value of your Chi-Square test?

Parts 2:

The owner now wants you to help him analyze his sales data. The restaurant is famous for its Lobo lobster roll. You were given some information based on which you deduced that the demand for the lobster roll was normally distributed with a mean of 220 and standard deviation of 50. You also know that the lobster supplier can provide lobster at a rate that mimics a uniform distribution between 170 and 300. One Lobster is used per roll and the lobsters need to be fresh (i.e. the restaurant can only use the lobsters that are delivered that day).

You decide to run 200 simulations of 1000 days each.

1. Calculate the expected sales of Lobster roll per day based on your simulation results. I solved

201

2. Use the expected sales from each of your 200 simulations to create a confidence interval for the average expected sales. What is the 95% confidence interval, L (Your confidence interval is mean +/- L), for this estimate?

The controller of Tri Con Global Systems Inc. has developed a new costing system that traces the cost of activities to products. The new system is able to measure post-manufacturing activities, such as selling, promotional, and distribution activities, and allocate these activities to products in a manner that provides a more complete view of the company's product costs. This system produces better strategic information about the relative profitability of product lines. In the course of implementing the new costing system, the controller realized that the company's current period GAAP net income would increase significantly if the new product cost information were used for inventory valuation on the financial statements. The controller has been under intense pressure to improve the company's net income, and this would be an easy and effective way for her to help meet the company's short-term net income goals. As a result, she has decided to use the new costing system to determine GAAP net income. Instructions: Answer the questions below using 150 words or more for both questions. After this, make sure to reply to one of your peer's responses using 50 words or more. Pencil Why does the company's net income increase when the new costing system is applied? Pencil Is the controller acting ethically by using the new costing system for GAAP net income? Explain your answer.