Pollsters at Quinnipiac University surveyed 751 likely New York voters and found out that 368 of 751 are going to vote for Candidate A rather than Candidate B.

1. At the 95 percent confidence level, can a winner be predicted?
2. What is the margin of error?
3. What is the probability of error?
4. What sample size is necessary in order to change the margin of error to 2 percent while leaving the probability of error the same?

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of 534 judges, it was found that 288 were introverts.

(a) Let p represent the proportion of all judges who are introverts. Find a point estimate for p. (Round your answer to four decimal places.)

(b) Find a 99% confidence interval for p. (Round your answers to two decimal places.)

lower limit ?

upper limit ?

The general fund budget (in billions of dollars) for a U.S. state for 1988 (period 1) to 2011 (period 24) follows.

Develop a linear trend equation for this time series to forecast the budget (in billions of dollars). (Round your numerical values to three decimal places.)

T_t =

(c) What is the forecast (in billions of dollars) for period 25? (Round your answer to two decimal places.)

$  billion

A certain company produces and sells frozen pizzas to public schools throughout the eastern United States. Using a very aggressive marketing strategy, they have been able to increase their annual revenue by approximately $10 million over the past 10 years. But increased competition has slowed their growth rate in the past few years. The annual revenue, in millions of dollars, for the previous 10 years is shown.

Using Minitab or Excel, develop a quadratic trend equation that can be used to forecast revenue (in millions of dollars). (Round your numerical values to three decimal places.)

T_t =

(c) Using the trend equation developed in part (b), forecast revenue (in millions of dollars) in year 11. (Round your answer to two decimal places.)

$  million

Consider the following time series data.

Develop the three-week moving average forecasts for this time series. (Round your answers to two decimal places.)

Compute MSE. (Round your answer to two decimal places.)

MSE =

What is the forecast for week 7?

Use α = 0.2 to compute the exponential smoothing forecasts for the time series.

Compute MSE. (Round your answer to two decimal places.)

MSE =

What is the forecast for week 7? (Round your answer to two decimal places.)

Use a smoothing constant of α = 0.4 to compute the exponential smoothing forecasts.

Consider arranging the letters of FABULOUS.

(a). How many different arrangements are there?

(b). How many different arrangements have the A appearing anywhere before the S (such as in FABULOUS)?

(c). How many different arrangements have the first U appearing anywhere before the S (such as in FABULOUS)?

(d). How many different arrangements have all four vowels appear consecutively (such as FAUOUBLS)?

I am stuck with b , c and d

A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:

y = β₀ + β₁x + ε where

• y = traffic flow in vehicles per hour
• x = vehicle speed in miles per hour.

The following data were collected during rush hour for six highways leading out of the city.

In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation.

ŷ = b₀ + b₁x + b₂x²

(a) Develop an estimated regression equation for the data of the form ŷ = b₀ + b₁x + b₂x² (Round b₀ to the nearest integer and b₁ to two decimal places and b₂ to three decimal places.)

ŷ =

Find the value of the test statistic. (Round your answer to two decimal places.)

Base on the model predict the traffic flow in vehicles per hour at a speed of 38 miles per hour. (Round your answer to two decimal places.)

vehicles per hour

A study of emergency service facilities investigated the relationship between the number of facilities and the average distance traveled to provide the emergency service. The following table gives the data collected.

Develop an estimated regression equation for the data corresponding to a second-order model with one predictor variable. (Round your numerical values to four decimal places.)

1. Data on students in liberal arts colleges in the U.S. was collected, and the average cost per student was recorded for each school. The following five-number summary was calculated for this data set: minimum= $17,554; first quartile = $23,115; median = $26,668; third quartile = $45,879; maximum=$102,262.

WHEN TYPING CORRECT NUMERICAL ANSWER TYPE: 12,345 NOT 12345 or $12345 or $12,345

a. Calculate the Upper Fence

__________________

b. Using the definition of outlier discussed in your textbook, is the maximum an outlier (Yes/No)?

__________________

c. Calculate the Lower Fence

___________________

d. Using the definition of outlier discussed in your textbook, is the maximum an outlier (Yes/No)?

___________________

2.

Suppose an algebra professor found that the correlation (r) between study time (in hours) and exam score (out of 100) is +.80, and the regression line was found to be ExamScore = 20 + 4*HoursStudied. He arrived at this equation through years of collecting data on his students.

What is the explanatory variable?

What is the response variable?

Is there a positive relationship, a negative relationship or no relationship?

Is the relationship strong or weak?

What is the slope (type number):

What is the intercept (type number):

Predict the exam score for a student who studies 10 hours. (type number)

3.

The quantitative reasoning GRE scores are known to approximately have a Normal distribution with a mean of μ = 151 points and a standard deviation of σ = 8 points.  

FORMAT FOR PARTS 1-3: lowerbound, upperbound. using numbers as example:  5,10

1.  Use the Empirical Rule to specify the ranges into which 68% of test takers fall.

2. Use the Empirical Rule to specify the ranges into which 95% of test takers fall.

3. Use the Empirical Rule to specify the ranges into which 99.7% of test takers fall .

FOR ANSWERS 4-5 type number ONLY: for example if 10% just type 10

4.  What percentage of test takers score lower than 159?

5. What percentage of test takers scored between 135 and 151?

A patient is tested for cancer. This type of cancer occurs in 5% of the population. The patient has undergone testing that is 90% accurate and the results came back positive. What is the probability that the patient actually has cancer? (Conditional probability)

Please solve using a TI-84 plus.

Conclusions. In Exercises 9-12, refer to the exercise identified. Make subjective estimates to decide whether results are significantly low or significantly high, then state a conclusion about the original claim. For example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).

(reference) #8 Pulse rates Claim: the standard deviation of pulse rates of adult males is more than 11 bpm. for the random sample of 153 adult males in data set 1 "body data" in appendix b, the pulse rates have a standard deviation of 11.3 bpm

#12 ( question) Exercise 8 “Pulse Rates”

Annual income: The mean annual income for people in a certain city (in thousands of dollars) is 41, with a standard
deviation of 35. A pollster draws a sample of 91 people to interview.

Part 1 of 5
(a) What is the probability that the sample mean income is less than 37? Round the answer to at least four decimal places.
The probability that the sample mean income is less than 37 is?

Part 2 of 5
(b) What is the probability that the sample mean income is between 40 and 45? Round the answer to at least four decimal places.
The probability that the sample mean income is between 40 and 45 is?

Part 3 of 5
(c) Find the 30th percentile of the sample mean. Round the answer to at least one decimal place.
The 30th percentile of the sample mean is?

Part 4 of 5
(d) Would it be unusual for the sample mean to be less than 33? Round the answer to at least four decimal places
It (is/isnt)unusual because the probability of the sample mean being less than 33 is?

Part 5 of 5
(e) Do you think it would be unusual for an individual to have an income of less than 33? Explain. Assume the variable is normally distributed. Round the answer to at least four decimal places.
(yes/no), because the probability that an individual has an income less than 33 is?

The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed and indicate the parameter(s) being tested.

a.) ?0: ?1 = ?2 ?? ?1: ?1 > ?2
  
b.) ?0: ? = 8.6 ?? ?1: ? > 8.6

At a fashion retailer, there are multiple cashiers providing checkout service to customers simultaneously. On average, customers arrive at the checkout area every 6 minutes. The standard deviation of the inter-arrival time is 6 minutes. The average checkout time for each customer is 12 minutes, with its standard deviation equal to 12 minutes. Suppose that customers form a single line. What is the minimum number of cashiers required, in order to guarantee an average customer waiting time below 5 minutes?

Much of Trail Ridge Road in Rocky Mountain National Park is over 12,000 feet high. Although it is a beautiful drive in summer months, in winter the road is closed because of severe weather conditions. Sustained gale-force winds (over 32 miles per hour and often over 90 miles per hour) occur on the average of 0.7 times every 56 hours at a Trail Ridge Road weather station.

(a) Let r = frequency with which gale-force winds occur in a given time interval. Explain why the Poisson probability distribution would be a good choice for the random variable r.

1) Frequency of gale-force winds is a common occurrence. It is reasonable to assume the events are independent.

2) Frequency of gale-force winds is a rare occurrence. It is reasonable to assume the events are dependent.  

3) Frequency of gale-force winds is a common occurrence. It is reasonable to assume the events are dependent.

4) Frequency of gale-force winds is a rare occurrence. It is reasonable to assume the events are independent.

(b) For an interval of 106 hours, what are the probabilities that r = 2, 3, and 4? What is the probability that r < 2? (Use 2 decimal places for λ. Use 4 decimal places for your answers.)

(c) For an interval of 173 hours, what are the probabilities that r = 3, 4, and 5? What is the probability that r < 3? (Use 2 decimal places for λ. Use 4 decimal places for your answers.)

Brokerage Satisfaction with Trade Price Satisfaction with Speed of Execution Overall Satisfaction with Electronic Trades

a. Develop an estimated regression equation using trade price and speed of execution to predict overall satisfaction with the broker. What is the coefficient of determination?

b. Develop an estimated regression equation using trade price and speed of execution to predict overall satisfaction with the broker. What is the SSR?

c. Develop an estimated regression equation using trade price and speed of execution to predict overall satisfaction with the broker. Can you conclude that there is a relationship between satisfaction with speed of execution and overall satisfaction with the electronic trade (can you reject the hypothesis that the parameter is = 0)? Group of answer choices

Problem 2.

You pay 5$ /round (nonrefundable) to play the game of rolling a pair of fair dice.

If you roll an even sum, you lose, no pay off. If you roll an odd sum, that's your win (say, roll of 7 pays you 7$).

Discrete random variable X represents the winnings.

• For example, the lowest value of X is x=0 when you roll an even sum.
• For example, x=3 only when you roll {1,2} or {2,1}. You win 1+2=3$ (odd sum). AndP ( x = 3 ) = P ( { 1 , 2 } ) + P ( { 2 , 1 } ) = 1 / 36 + 1 / 36 = 1 / 18.

a) Find all possible values of X with their probabilities. Make the table as in Problem 1, a) for the probability distribution of X. Above, we calculated just one row of the table:

Dice related probabilities are discussed in 5.1, page 252, Example 5.

b) Find the expected value of X and interpret it.

Expected value is discussed in 6.1, page 320 (as mean), 321 and Examples 5,6,7.

c) Does it make mathematical sense to play the game? Remember, you have to pay 5$/game to play, what is your net gain/loss per game in the long run?

d) What price a (instead of 5$) would make the game fair? It is called the fair price as you break even in the long run: μ ( X ) − a = 0.