1. It is believed that the population proportion of adults in the US who own dogs is 0.65. I surveyed people leaving the veterinarians office and found that 96 out of 150 owned a dog. Test this hypothesis at the .05 significance level. Assume a random sample.

2. Randomly surveyed 10 employees at work for their average on how many times they use the rest room per shift. the results were as follows 2,2,3,1,0,4,1,1,0,5

the mean for this is 1.9 times per shift.

test the hypothesis at a .5 significance level.

3.  In the company there are 845 employees who use laptops within the organization. In our office downtown in the city, there are 75 employees who use laptops, walking around in our downtown office there are 55 mac users and 20 dell users. Test this hypothesis with this random sample.

The following table represents the percentage of voters, by age, who favor increasing the minimum wage in a particular city.

Ages 18 - 29 30 - 39 40 - 49 50 - 59 60 and up Percentage 70% 30% 35% 15% 20%

a) Would a pie chart be appropriate for this data? Explain why or why not.

b) Would a Pareto chart be appropriate for this data? Explain why or why not.

QUESTION SEVEN a) A cigarette manufacturing firm distributes two brands of cigarettes. Two random samples are selected and it is found that 56 of 200 smokers prefer brand Α and that 29 of 150 smokers prefer brandΒ . Can we conclude at the 0.05 level of significance that the percentage of smokers who prefer brand Α exceeds that of brand Β by more than 10%?

b) An auditor claims that 10% of invoices for a certain company are incorrect. To test this claim a random sample of 200 invoices are checked and 24 are found to be incorrect. Test at the 1% significant level to see if the auditor’s claim is supported by the sample evidence.

c) The personnel department of a company developed an aptitude test for screening potential employees. The person who devised the test asserted that the mean mark attained would be 100. The following results were obtained with a random sample of applicants:

x = 96,   s= 5.2,   n=13

Test this hypothesis against the alternative that the mean mark is less than 100, at the 1% significance level.

According to recent studies, 57.6% of American citizens are overweight. Suppose that 17% of those who are overweight are children. If American citizen is randomly selected, determine the following probabilities:

a) Selected citizen is overweight and a child

b) Selected citizen is not a child given that he/she is overweight

c) Selected citizen is not a child and is not overweight

The City Council wants to gather input from residents about the recreational opportunities in the city. Categorize each technique as simple random sample, stratified sample, systematic sample, cluster sample, or convenience sample.

a) Get an alphabetical list of all residents and question every 250th resident on the list.

b) Have 10 volunteers go downtown on Saturday afternoon and question people that they see. The volunteers may quit when they have questioned 25 people.

c) Get an alphabetical list of all residents and use a random number to get a sample of 3000 residents to question.

d) Divide the town into 25 distinct geographical neighborhoods then randomly choose 50 residents in each neighborhood to question.

e) Divide the town into 25 distinct geographical neighborhoods then randomly choose 10 of the neighborhoods. Question all the residents in the chosen neighborhoods

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond).

For the past several years, we have the following data

x: 17,0,20,35,37,33,26,−15,−24,−22

y: 20,−10,8,18,19,11,18,−8,−5,−4

(a) Compute ∑x, ∑x2, ∑y, ∑y2

(b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x and for y.

(c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. Use the intervals to compare the two funds.

(d) Compute the coefficient of variation for each fund. Use the coefficients of variation to compare the two funds. If s represents risks and image from custom entry tool represents expected return, then image from custom entry tool can be thought of as a measure of risk per unit of expected return. In this case, why is a smaller CV better? Explain.

how does the logistic regression work to further the ability of the results

In the SPSS system exactly what is the variable measure for abany?

How productive are U.S. workers? One way to answer this question is to study annual profits per employee. A random sample of companies in computers (I), aerospace (II), heavy equipment (III), and broadcasting (IV) gave the following data regarding annual profits per employee (units in thousands of dollars).

Shall we reject or not reject the claim that there is no difference in population mean annual profits per employee in each of the four types of companies? Use a 5% level of significance.

(b) Find SS_TOT, SS_BET, and SS_W and check that SS_TOT = SS_BET + SS_W. (Use 3 decimal places.)

Find d.f._BET, d.f._W, MS_BET, and MS_W. (Use 3 decimal places for MS_BET, and MS_W.)

Find the value of the sample F statistic. (Use 3 decimal places.)


What are the degrees of freedom?
(numerator)=
(denominator)=

(f) Make a summary table for your ANOVA test.

We are creating a new card game with a new deck. Unlike the normal deck that has 13 ranks (Ace through King) and 4 Suits (hearts, diamonds, spades, and clubs), our deck will be made up of the following.

Each card will have:
i) One rank from 1 to 16.
ii) One of 5 different suits.

Hence, there are 80 cards in the deck with 16 ranks for each of the 5 different suits, and none of the cards will be face cards! So, a card rank 11 would just have an 11 on it. Hence, there is no discussion of "royal" anything since there won't be any cards that are "royalty" like King or Queen, and no face cards!

The game is played by dealing each player 5 cards from the deck. Our goal is to determine which hands would beat other hands using probability. Obviously the hands that are harder to get (i.e. are more rare) should beat hands that are easier to get.

e) How many different ways are there to get exactly 3 of a kind (i.e. 3 cards with the same rank)?
The number of ways of getting exactly 3 of a kind is
DO NOT USE ANY COMMAS

What is the probability of being dealt exactly 3 of a kind?
Round your answer to 7 decimal places.

f) How many different ways are there to get exactly 4 of a kind (i.e. 4 cards with the same rank)?
The number of ways of getting exactly 4 of a kind is
DO NOT USE ANY COMMAS

What is the probability of being dealt exactly 4 of a kind?
Round your answer to 7 decimal places.

g) How many different ways are there to get a full house (i.e. 3 of a kind and a pair, but not all 5 cards the same rank)?
The number of ways of getting a full house is
DO NOT USE ANY COMMAS

What is the probability of being dealt a full house?
Round your answer to 7 decimal places.


h) How many different ways are there to get a straight flush (cards go in consecutive order like 4, 5, 6, 7, 8 and all have the same suit. Also, we are assuming there is no wrapping, so you cannot have the ranks be 14, 15, 16, 1, 2)?
The number of ways of getting a straight flush is
DO NOT USE ANY COMMAS

What is the probability of being dealt a straight flush?
Round your answer to 7 decimal places.


i) How many different ways are there to get a flush (all cards have the same suit, but they don't form a straight)?
Hint: Find all flush hands and then just subtract the number of straight flushes from your calculation above.
The number of ways of getting a flush that is not a straight flush is
DO NOT USE ANY COMMAS

What is the probability of being dealt a flush that is not a straight flush?
Round your answer to 7 decimal places.


j) How many different ways are there to get a straight that is not a straight flush (again, a straight flush has cards that go in consecutive order like 4, 5, 6, 7, 8 and all have the same suit. Also, we are assuming there is no wrapping, so you cannot have the ranks be 14, 15, 16, 1, 2)?
Hint: Find all possible straights and then just subtract the number of straight flushes from your calculation above.
The number of ways of getting a straight that is not a straight flush is
DO NOT USE ANY COMMAS

What is the probability of being dealt a straight that is not a straight flush?
Round your answer to 7 decimal places.

Specialty Toys, Inc. sells a variety of new and innovative children’s toys. Management learned that the preholiday season is the best time to introduce a new toy, because many families use this time to look for new ideas for December holiday gifts. When Specialty discovers a new toy with good market potential, it chooses an October market entry date. In order to get toys into its stores by October, Specialty places one-time orders with its manufacturers in June or July of each year. Demand for children’s toys can be highly volatile. If a new toy catches on, a sense of shortage in the marketplace often increases the demand to high levels and large profits can be realized. However, new toys can also flop, leaving Specialty stuck with high levels of inventory that must be sold at reduced prices. The most important question the company faces is deciding how many units of a new toy should be purchased to meet anticipated sales demand. If too few are purchased, sales will be lost; if too many are purchased, profits will be reduced because of low prices realized in clearance sales. For the coming season, Specialty plans to introduce a new product called Weather Teddy. This variation of a talking teddy bear is made by a company in Taiwan. When a child presses Teddy’s hand, the bear begins to talk. A built-in barometer selects one of five responses that predict the weather conditions. The responses range from “It looks to be a very nice day! Have fun” to “I think it may rain today. Don’t forget your umbrella.” Tests with the product show that, even though it is not a perfect weather predictor, its predictions are surprisingly good. Several of Specialty’s managers claimed Teddy gave predictions of the weather that were as good as those of many local television weather forecasters. As with other products, Specialty faces the decision of how many Weather Teddy units to order for the coming holiday season. Members of the management team suggested order quantities of 15,000, 18,000, 24,000, or 28,000 units. The wide range of order quantities suggested indicates considerable disagreement concerning the market potential. The product management team asks you for an analysis of the stock-out proba- bilities for various order quantities, an estimate of the profit potential, and help with mak- ing an order quantity recommendation. Specialty expects to sell Weather Teddy for $24 based on a cost of $16 per unit. If inventory remains after the holiday season, Specialty will sell all surplus inventory for $5 per unit. After reviewing the sales history of similar products, Specialty’s senior sales forecaster predicted an expected demand of 20,000 units with a .95 probability that demand would be between 10,000 units and 30,000 units.

Prepare a managerial report that addresses the following issues and recommends an order quantity for the Weather Teddy product.

1. Use the sales forecaster’s prediction to describe a normal probability distribution that can be used to approximate the demand distribution. Sketch the distribution and show its mean and standard deviation.

2. Compute the probability of a stock-out for the order quantities suggested by members of the management team.

3. Compute the projected profit for the order quantities suggested by the management team under three scenarios: worst case in which sales = 10,000 units, most likely case in which sales = 20,000 units, and best case in which sales = 30,000 units.

4. One of Specialty’s managers felt that the profit potential was so great that the order quantity should have a 70% chance of meeting demand and only a 30% chance of any stock-outs. What quantity would be ordered under this policy, and what is the projected profit under the three sales scenarios?

5. Provide your own recommendation for an order quantity and note the associated profit projections. Provide a rationale for your recommendation.

1. (Binomial) The probability that a patient recovers from a delicate heart operation is 0.85. Of the next 7 patients, what is the probability that

   1. (a) exactly 5 survive?

   2. (b) between 3 and 6 survive (inclusive)?

   3. (c) What is the probability that 4 or more patients will NOT recover from the heart operation?

According to a Yale program on climate change communication survey, 71% of Americans think global warming is happening.†

(a)

For a sample of 16 Americans, what is the probability that at least 13 believe global warming is occurring? Use the binomial distribution probability function discussed in Section 5.5 to answer this question. (Round your answer to four decimal places.)

(b)

For a sample of 140 Americans, what is the probability that at least 90 believe global warming is occurring? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

(c)

As the number of trials in a binomial distribution application becomes large, what is the advantage of using the normal approximation of the binomial distribution to compute probabilities?

As the number of trials becomes large, the normal approximation simplifies the calculations required to obtain the desired probability.As the number of trials becomes large, the normal approximation gives a more accurate answer than the binomial probability function.   

(d)

When the number of trials for a binomial distribution application becomes large, would developers of statistical software packages prefer to use the binomial distribution probability function shown in Section 5.5 or the normal approximation of the binomial distribution discussed in Section 6.3? Explain.

Please answer the following:

1. United Dairies, Inc., supplies milk to several independent grocers throughout Dade County, Florida. Managers at United Dairies want to develop a forecast of the number of half gallons of milk sold per week. Sales data for the past 12 weeks are:

.

1. Show the exponential smoothing forecasts using α = 0.1.
   1. Applying the MSE measure of forecast accuracy, would you prefer a smoothing constant of α=0.1 or α= 0.2 for the United Dairies sales time series?
   2. Are the results the same if you apply MAE as the measure of accuracy?
   3. What are the results if MAPE is used?

2.    Use exponential smoothing with a α = 0.4 to develop a forecast of demand for week 13. What is the resulting MSE?