Data from the Bureau of Labor Statistics’ Consumer Expenditure Survey (CE) show that annual expenditures for cellular phone services per consumer unit increased from $237 in 2001 to $634 in 2007. Let the standard deviation of annual cellular expenditure be $52 in 2001 and $207 in 2007.

For the following 2 groups, do a power analysis to determine the statistical power at the p=0.05 and p=0.01 levels. For the power analysis, seek power for a difference in means of 2.79. Repeat the statistical analysis using 95% and 99% confidence intervals.

[11.540 8.203 8.214 13.165 11.451 13.015 11.060 10.488 8.849 8.271]

[4.708 8.013 9.886 7.026 6.051 5.546 7.914 9.951 9.880 7.381]

The mean number of minutes for app engagement by a table user is 7.5 minutes. Suppose the standard deviation is 1.25 minutes. Take a sample of 80.

a. What are the mean and standard deviation for the sample mean number of app engagement by a tablet user?

b. Find the 90th percentile for the sample mean time for app engagement for a tablet user. Interpret this value in a complete sentence.

c. Find the probability that the sample mean is between 7 and 7.75 minutes.

d. What are the mean and standard deviation for the sums?

e. Find the 90th percentile for the sum of the sample. Interpret this value in a complete sentence.

f. Find the probability that the sum of the sample is at least 10 hours.

The wedding date for a couple is quickly approaching, and the wedding planner must provide the caterer an estimate of how many people will attend the reception so that the appropriate quantity of food is prepared for the buffet. The following table contains information on the number of RSVP guests for the 150 invitations. Unfortunately, the number of guests does not always correspond to the number of RSVPed guests.

Based on her experience, the wedding planner knows it is extremely rare for guests to attend a wedding if they notified that they will not be attending. Therefore, the wedding planner will assume that no one from these 55 invitations will attend. The wedding planner estimates that the each of the 20 guests planning to come solo has a 75% chance of attending alone, a 20% chance of not attending, and a 5% chance of bringing a companion. For each of the 65 RSVPs who plan to bring a companion, there is a 90% chance that she or he will attend with a companion, a 5% chance of attending solo, and a 5% chance of not attending at all. For the 10 people who have not responded, the wedding planner assumes that there is an 80% chance that each will not attend, a 15% chance each will attend alone, and a 5% chance each will attend with a companion.

1. Assist the wedding planner by constructing a spreadsheet simulation model to determine the expected number of guests who will attend the reception. Round your answer to 2 decimal places.
   
   guests
   
2. To be accommodating hosts, the couple has instructed the wedding planner to use the Monte Carlo simulation model to determine X, the minimum number of guests for which the caterer should prepare the meal, so that there is at least a 90% chance that the actual attendance is less than or equal to X. What is the best estimate for the value of X? Round your answer to the nearest whole number.
   
   guests

Using the normal approximation, find the approximate probability of at most 16 successes of 40. You may need to consult your z table or the shiny app

Create a model and use Excel Solver to answer the following: A computer company manufactures two types of computers. Each type of computer will require assembly time, inspection time, and storage space. The amounts of each of these resources that can be devoted to the production of the computers is limited. The manager wants to determine the quantity of each computer to produce to maximize the profit generated by sales of these computers.

In order to develop a suitable model of the problem, the manager has met with design and manufacturing personnel. As a result of those meetings, the manager has obtained the following information:

The manager has also acquired information on the availability of resources. These daily amounts are:

The manager also met with the firm's marketing manager and learned that demand for the microcomputers was such that whatever combination of these two types of computers is produced, all the output can be sold.

a. What is the mix of computers that the company should produce if they want to maximize profits?

b. What is the optimal value for profit using the mix from part a.?

c. If type 2 computer became twice as profitable (i.e. profit rose from $75 each to $150 each), would the solution change? If so, what is the new solution (please state the mix and the new profit amount)?

Consider the following results for two samples randomly taken from two populations.

Sample A Sample B

Sample Size 31 35

Sample Mean 106 102

Sample Standard Deviation 8 7

Test the hypothesis Ho=sigma1-sigma2=0 vs Ha=sigma1-sigma2 do not equal 0 at 5% level of significance. Show all six steps using p-value approach.

Find the mean of this probability distribution. Round your answer to one decimal place.

2

Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places

3

2.36 Is it worth it?: Andy is always looking for ways to make money fast. Lately, he has been trying to make money by gambling. Here is the game he is considering playing: The game costs $2 to play. He draws a card from a deck. If he gets a number card (2-10), he wins nothing. For any face card ( jack, queen or king), he wins $3. For any ace, he wins $5, and he wins an extra $20 if he draws the ace of clubs. Round answers to 2 decimal places.


a) Andy's expected profit per game is: $


b) Would you recommend this game to Andy as a good way to make money? Explain.

• Yes, Andy could be lucky and might earn money in the long-run playing this game
• No, we expect Andy to lose money each time he plays this game

4

2.38 Baggage fees: An airline charges the following baggage fees: $25 for the first bag and an extra $35 for the second. Suppose 54% of passengers have no checked luggage, 34% have only one piece of checked luggage and 12% have two pieces. We suppose a negligible portion of people check more than two bags.


a) The average baggage-related revenue per passenger is: $ (please round to the nearest cent)
b) The standard deviation of baggage-related revenue is: $ (please round to the nearest cent)
c) About how much revenue should the airline expect for a flight of 120 passengers? $ (please round to the nearest dollar)

5

For a group of four 70-year old men, the probability distribution for the number xx who live through the next year is as given in the table below.

Verify that the table is indeed a probability distribution. Then find the mean of the distribution.
mean =
Report answer accurate to 1 decimal place.

6

Consider the discrete random variable XX given in the table below. Calculate the mean, variance, and standard deviation of XX.

μμ =
σ2σ2 =
σσ =


What is the expected value of XX?

7

A bag contains 4 gold marbles, 9 silver marbles, and 24 black marbles. The rules of the game are as follows: You randomly select one marble from the bag. If it is gold, you win $4, if it is silver, you win $3. If it costs $1 to play, what is your expected profit or loss if you play this game?

$

8

The PTO is selling raffle tickets to raise money for classroom supplies. A raffle ticket costs $3. There is 1 winning ticket out of the 180 tickets sold. The winner gets a prize worth $76. Round your answers to the nearest cent.

What is the expected value (to you) of one raffle ticket? $

I need help with this

thanks

Suppose that for a dataset the mean is known. Using the 25 random samples, we computed the sample variance as s^2=0.001.
a) Does the data support the claim that the true standard deviation is less than 0.05? (use alpha = 0.05 and alternative hypothesis sigma^2 < 0.0025)
b) Compute a two-sided 95% confidence interval for the true variance of the data.

Roads A, B, and C are the only way to escape from a certain provincial prison. Prison records show that, of the prisoners who tried to escape, 9 % used road A, 14 % used road B, the remainder used road C. The records also indicate that 85 % of those who tried to escape using road A were captured. 13 % of those using road B were captured, and 58 % of those using road C were captured. Use four decimals in your answers (a) What is the probability that a prisoner escaping from this provincial prison is not captured? (b) What is the probability that a captured prisoner used road A in their escape attempt? (c) What is the probability that a prisoner who didn't get captured has used road C?

Suppose x has a distribution with μ = 30 and σ = 28. (a) If a random sample of size n = 49 is drawn, find μx, σ x and P(30 ≤ x ≤ 32). (Round σx to two decimal places and the probability to four decimal places.) μx = σ x =   P(30 ≤ x ≤ 32) = (b) If a random sample of size n = 67 is drawn, find μx, σ x and P(30 ≤ x ≤ 32). (Round σ x to two decimal places and the probability to four decimal places.) μx = σ x = P(30 ≤ x ≤ 32) = (c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).) The standard deviation of part (b) is part (a) because of the sample size. Therefore, the distribution about μx is.

The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about ten. Suppose that 16 individuals are randomly chosen.

(a) For the group of 16, find the probability that the average percent of fat calories consumed is more than thirty-five (Round to 3 decimal places)

(b) Find the first quartile for the percent of fat calories.

(c) Find the first quartile for the average percent of fat calories.

The following data on price ($) and the overall score for 6 stereo headphones that were tested by Consumer Reports were as follows.

a. Does the t test indicate a significant relationship between price and the overall score?

The test t-Conclusion at α = .05

t =  (to 2 decimal places.)

p-value is - Select your answer -less than .02between .02 and .05between .05 and .1between .1 and .2greater than .2Item 2

What is your conclusion? Use α = .05.
- Select your answer -There is a significant relationship between price and overall scoreThere is no significant relationship between price and overall scoreItem 3 .

b. Test for a significant relationship using the F test.
p-value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .1greater than .1Item 4

What is your conclusion? Use α = .05.

Because p-value is - Select your answer -greater than or equal toless than or equal toequal toItem 5 .05, we - Select your answer -acceptrejectItem 6 H₀: β₁ is - Select your answer -greater than or equal to zeroless than or equal to zeroequal to zeroItem 7 .

c. Show the ANOVA table for these data. Round your answers to three decimal places, if necessary.

In August 2003, 56% of all employed adults in the United States reported that basic mathematical skills were critical or very important to their job. A researcher believes that this proportion has increased, so a random sample of 480 employed adults was taken and 297 of them felt that basic mathematical skills are critical or very important to their job.

Be sure to check if the conditions are met, and show how you checked them - show ALL work.

1a) Is there sufficient evidence to conclude that the percentage of all employed adults who feel basic mathematical skills are critical or very important to their job has increased? Use a significance level of α =0.05.

whats your conclusion?

1b) Find a 90% confidence interval for the proportion of all employed adults in the United States who feel that basic mathematical skills are critical or very important to their job. State your answer in words:

1c) How large of a sample would be needed in order to have a margin of error E=3% and a confidence level of 98%? sample size n=?

A researcher wishes to estimate the proportion of adults who have high speed internet access. What size sample should be obtained if she wishes the estimate to be within .03 with 99% confidence if a) she uses a previous estimate of .58? b) she does not use any prior estimate?