The SAT is the most widely used college admission exam. (Most community colleges do not require students to take this exam.) The mean SAT math score varies by state and by year, so the value of µ depends on the state and the year. But let’s assume that the shape and spread of the distribution of individual SAT math scores in each state is the same each year. More specifically, assume that individual SAT math scores consistently have a normal distribution with a standard deviation of 100. An educational researcher wants to estimate the mean SAT math score (μ) for his state this year. The researcher chooses a random sample of 635 exams in his state. The sample mean for the test is 486.

Find the 90% confidence interval to estimate the mean SAT math score in this state for this year.

(Note: The critical z-value to use, zc, is: 1.645.)

Your answer should be rounded to 3 decimal places.

art major x=86 x=80 s=4 theater major x=88 x=84 s=6 find the z score for each student b. based on the z score which student performed better within their class c. Find the coefficient of variation for both art and theater classes d. which class was more variable. 3. A landscaper wishes to use several different types of plants. The categories include color (red, yellow, and green), type (flowers and shrubs}, and height (tall, medium and short). how many different combinations can he/she use if she selects one color, one type and one height

4. In a recent study, the following data was obtained in response to the question, do not favor recycling in your neighborhood

No Yes No Opinion

Males 35 20 25

Female 15 25 20

If a person is picked at ramdom

a. what is the probability that the person is either male or has no opinion

b. male given they have no opinion

c. male with opinion

d. has no opinion given they are male

e. a female and a No

f. a No given they are female

g. either female or is a Yes

h. No opinion given they are female

What is a requirement of the data collections process to be able to use a “run” chart?

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 in 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 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 probabilities for various order quantities, an estimate of the profit potential, and to help make 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. Managerial Report 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.

*IF THERE IS ANYWAY YOU CAN SHOW HOW TO DO ON EXCEL. if not it is fine but would be greatly appreciated. :)

1. Listed below is the selling price for a share of PepsiCO Inc. at the close of each year.

Year             Price                            Year                Price

1990             12.9135                       2000                49.5625

1991             16.8250                       2001                48.6803

1992             20.6125                       2002                42.2211

1993             20.3024                       2003                46.6215

1994             18.3160                       2004                52.2019

1995             27.7538                       2005                59.8534

1996             29.0581                       2006                62.0002

1997             36.0155                       2007                77.5108

1998             40.6111                       2008                54.7719

1999             35.0230                       2009                60.8025

a. Plot the data.

b. Use EXCEL’s Data Analysis add-in to determine the least squares trend equation.

c. Discuss the regression equation and include both the coefficient of determination and the          

   correlation coefficient in the discussion. Make sure to test the coefficient to determine if  

   it is statistically significant at the .01 significance level.

d. Calculate the points for the years 1992 and 2004.

e. (i) Estimate the selling price in 2014.                                                                                                                       

(ii) Does this seem like a reasonable estimate based on historical data? Why or why not?

f. By how much has the stock price increased or decreased (per year) on average during the period?

Show ALL of your work and show it in a neat and orderly fashion.

is 1. f(x/θ) = 2x/θ^2 complete sufficient statistic

2. f(x/θ) =((logθ) θ^x  ) / (θ -1) complete sufficient statistic?

Please assist with the following:

The National Highway Traffic Safety Administration (NHTSA) conducted a survey to learn about how drivers throughout the United States are using seat belts (Associated Press, August 25, 2003). Sample data consistent with the NHTSA survey are as follows:

1. For the United States, what is the probability that a
2. The seat belt usage probability for a U.S. driver a year earlier was .75. NHTSA chief Dr. Jeffrey Runge had hoped for a .78 probability in 2003. Would he have been pleased with the 2003 survey results?
3. What is the probability of seat belt usage by region of the country? What region has the highest seat belt usage?
4. What proportion of the drivers in the sample came from each region of the country? What region had the most drivers selected? What region had the second most drivers selected?
5. Assuming the total number of drivers in each region is the same, do you see any reason why the

probability estimate in part (a) might be too high? Explain.

Starbucks wants to survey its employees regarding employee satisfaction in Chicago. It divides the city into 15 geographic regions and selects a simple random sample from each region. What kind of sample is this?

A researcher studies two groups of subjects. One group consists entirely of women, the other entirely of men. He measures and compares their resting heart rate, recorded in beats per minute.  Which of the following is true? Select one.

Suppose that you and two friends go to a​ restaurant, which last month filled approximately 77 % of the orders correctly. Complete parts​ (a) through​ (d) below.

a. What is the probability that all three orders will be filled​ correctly?

b. What is the probability that none of the three orders will be filled correctly?

c. What is the probability that at least two of the three orders will be filled correctly?

d. What are the mean and standard deviation of the binomial distribution used in a through c? Interpret these values

3. The estimated regression equation for a model involving two independent variables and 65 observations is:
   
   yhat = 55.17+1.1X₁ -0.153X₂
   
   Other statistics produced for analysis include: SSR = 12370.8, SST = 35963.0, S_b1 = 0.33, S_b2 = 0.20. (16 points)
   1. Interpret b₁ and b₂ in this estimated regression equation
   2. Predict y when X₁ = 65 and X₂ = 70.
   3. Compute R-square and Adjusted R-Square.
   4. Comment on the goodness of fit of the model.
   5. Compute MSR and MSE.
   6. Compute F and use it to test whether the overall model is significant using a p-value (α = 0.05).
   7. Perform a t test using the critical value approach for the significance of β₁. Use a level of significance of 0.05.
   8. Perform a t test using the critical value approach for the significance of β₂. Use a level of significance of 0.05.

Lake Vostok is Antarctica's largest and deepest subsurface lake. The mean depth of the lake is believed to be 344 meters. 25 random samples of the depth of this lake were obtained. Assume the underlying distribution is normal and σ = 30 meters. Please use 3 decimal places in all calculations.

b) Find the probability of the Type II error if the true mean depth of the lake is Pa = 328 meters; that is, find B(328). Assume that a = 0.01. Hint: If your numeric answer is wrong, please confirm that your hypotheses are correct before you run out tries.

One factor in rating a National Hockey League team is the mean weight of its players. A random sample of players from the Detroit Red Wings was obtained. The weight (in pounds) of each player was carefully measured, and the resulting data have a sample size of 18 with a sample mean of 208 pounds and a sample standard deviation of 11.1 pounds. You can assume that all of the assumptions are met.

a) What are the assumptions that are required to perform inference on this data?

b) Should you use a z distribution or a t distribution in this problem. Note that you will only get one try to get this question correct.

c) Please explain the correct answer.

d) Find the 95.9% confidence interval for the true mean weight of the players from the Detroit Red Wings.

i) If this would be a z distribution, what would be the critical value? Please use 4 decimal places.

ii) If this would be a t distribution, what would be the critical value? Please use 4 decimal places.

iii) If this would be a t distribution, what would be the degrees of freedom?

iv) The 95.9% confidence interval for the true mean weight of the players from the Detroit Red Wings is

e) Interpret your answer from the interval above (part d)

f) Please show all of the code for this part (part d) below

g) If the half-width of the interval needed to be at most 5.23 pounds, how many players would have to be randomly sampled from the team? Please use at least 4 decimal places in all numbers used (unless the number is exact). Note: This number might not be realistic. What is the new sample size?

h) Please show all of the code for this part (part g) below

The presidential election is coming. Five survey companies (A, B, C, D, and E) are doing survey to forecast whether or not the Republican candidate will win the election. Each company randomly selects a sample size between 1000 and 1500 people. All of these five companies interview people over the phone during Tuesday and Wednesday. The interviewee will be asked if he or she is 18 years old or above and U.S. citizen who are registered to vote. If yes, the interviewee will be further asked: will you vote for the Republican candidate? On Thursday morning, these five companies announce their survey sample and results at the same time on the newspapers. The results show that a% (from A), b% (from B), c% (from C), d% (from D), and e% (from E) will support the Republican candidate. The margin of error is plus/minus 3% for all results. Suppose that c > a > d > e > b. When you see these results from the newspapers, can you exactly identify which result(s) is (are) not reliable and not accurate? That is, can you identify which estimation interval(s) does (do) not include the true population proportion? If you can, explain why you can; if no, explain why you cannot and what information you need to identify. Discuss and explain your reasons. You must provide your statistical analysis and reasons.

Use the geometric probability distribution to solve the following problem.

On the leeward side of the island of Oahu, in a small village, about 72% of the residents are of Hawaiian ancestry. Let n = 1, 2, 3, … represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.

(a)

Write out a formula for the probability distribution of the random variable n. (Enter a mathematical expression.)
P(n) =

(b)

Compute the probabilities that n = 1, n = 2, and n = 3. (For each answer, enter a number. Round your answers to three decimal places.)
P(1) =
P(2) =
P(3) =

(c)

Compute the probability that n ≥ 4. Hint: P(n ≥ 4) = 1 − P(n = 1) − P(n = 2) − P(n = 3). (Enter a number. Round your answer to three decimal places.)

(d)

What is the expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry? Hint: Use μ for the geometric distribution and round. (Enter a number. Round your answer to the nearest whole number.)
residents

Use the data below to solve. The data gives the square footage and sales prices for several houses in Bellevue, Washington. Use this information to solve the following:

PLEASE SHOW YOUR WORK : )

1) You plan to build a 500 square foot addition to your home. How much do you think your home value will increase as a result?

2) What percentage of the variation in home value is explained by the variation in the house size?

3) A 3000 square foot home is listed for $500,000. Is this price out of line with typical sales in Bellevue? What might cause this discrepancy?

Square Footage   Value
2000   238139.3695
2200   259711.9508
2400   300953.668
3000   369965.7313
3200   340091.2955
3600   405425.021
2900   345131.0331