An exhibitor at an arts and crafts fair sells only 2 types of products – jams and marinades. When a customer enters the exhibitor’s booth, the exhibitor believes that there is a probability of .40 that the customer would purchase jam. If the customer purchases jam, there a probability of .30 that the customer would also purchase marinade. If the customer does not purchase jam, there is a probability of .5 that the customer would purchase marinade

1. Complete the following probability tree by filling in the blanks with either the appropriate probabilities (to 2 decimal places) or symbols if appropriate. The blanks at the end of each possible outcome is to be filled in with what that outcome represents (e.g., JM would represent the outcome that the customer purchased jam and marinade) The blanks under the column X are to be filled in with the number of types of products purchased (e.g. if the customer purchased 1 of the 2 types of produced you would fill in the number 1 under the column X) Note: If you don’t want to use superscripts, you can use ‘ instead. For example, J^C can be typed as J’.

   Outcome          Prob.         X

                                                                                            M              JM              _______       2

                                                                                       _____

                                                                     J

                                                                                       _____

                                      ­.40                                                                          M^C

                                                                                                        _______         _______      ___

                  _____                             

                                                                                                           M        _______         _______     ___

                                               J^C                _____

                                                                                         _____

                                                                                                                      M^C

_______         _______      ___                 

2. Complete the following statements by inserting the appropriate probabilities (to 4 decimal places if necessay) in the spaces provided.

1. The probability that a customer would purchase either jam or marinade (or both) is _______

2. The probability that a customer would purchase both jam and marinade is ________

3. The probability that the customer purchased jam knowing that if he/she purchased marinade is

_______

A furniture supplier, Acme Chairs, Inc., manufactures a Basic office chair and a Deluxe office chair. Each Basic chair costs $25.00 to manufacture, and each Deluxe office chair costs $40.00 to manufacture. Acme Chairs wishes to determine the optimal production quantities per day for each chair model in order to minimize overall total cost.

The production of each chair requires three types of materials: Wood, Primer, and Paint. The amount of material available per day to manufacture the chairs is as follows:

30 units of wood.

600 oz. of primer.

750 oz. of paint.

Each chair requires the materials as shown below:

A. State the Objective function mathematically.

B State the constraints mathematically.

C. Instead, create an Excel Model for this Example.(please give step by step excel instructions)

Use Solver to determine the optimized solution. (Do not solve the problem graphically)

Prior to the 1999-2000 season in the NBA, the league made several rule changes designed to increase scoring. The average number of points scored per game in the previous season had been 183.2. Let μ denote the mean number of points per game in the 1999-2000 NBA season.

a. If the rule change had no effect on scoring, what value would μ have? Is this the null or alternative hypothesis?

b. If the rule change had the desired effect on scoring, what would be true about the value of μ? Is this a null or alternate hypothesis?

c. Based on your answers to part a and b clearly sate H_oand H_a using the proper notation.

A used car salesperson claims that the probability of he selling a used car to an individual looking to purchase a used car is 70% and this probability does not vary from individual to individual. Suppose 5 individuals come to speak to this salesperson one day. If his belief is correct,

1. The probability (to 4 decimal places) that he will sell a car to the first individual he speaks to is ______

2. The probability (to 4 decimal places) that he will not sell a car to any of these 5 individuals is ______

3. The probability (to 4 decimal places) that he will sell a car to exactly 2 individuals is _______

4. The expected number (to 2 decimal places) of individuals he will sell a car to is ­­________

5. The standard deviation (to 4 decimal places) in the number of individuals to whom he will sell a car is

________

6. If the salesperson pays the dealership who allows him to sell cars $1000 per day for the privilege of working at the dealership, and, if he earns $2000 for each car he sells, the expected income per day is

________

In a certain​ area, 34​% of people own a dog. Complete parts a and b below.

a. Find the probability that exactly 8 out of 20 randomly selected people in the area own a dog.

​(Type an integer or decimal rounded to three decimal places as​ needed.)

b. In a random sample of 20 people from this​ area, find the probability that

8 or fewer own a dog. _________

​(Type an integer or decimal rounded to three decimal places as​ needed.)

The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 220 customers on the number of hours cars are parked and the amount they are charged. Number of Hours Frequency Amount Charged 1 15 $ 2 2 36 6 3 53 9 4 40 13 5 20 14 6 11 16 7 9 18 8 36 22 220 Click here for the Excel Data File a-1. Convert the information on the number of hours parked to a probability distribution. (Round your answers to 3 decimal places.)

b-1. Find the mean and the standard deviation of the number of hours parked. (Do not round the intermediate calculations. Round your final answers to 3 decimal places.)

b-2. How long is a typical customer parked? (Do not round the intermediate calculations. Round your final answer to 3 decimal places.)

c-1 Find the mean and the standard deviation of the amount charged. (Do not round the intermediate calculations. Round your final answers to 3 decimal places.)

The linear model below explores a potential association between property damage and wind speed based on observational data from 94 hurricanes that hit the United States between 1950 and 2012. The variables are

Damage: property damage in millions of U.S. dollars (adjusted for inflation to 2014) for each hurricane

Landfall.Windspeed: Maximum sustained windspeed in miles per hour measured along U.S. coast for each hurricane

* Assume that the sample data satisfies all assumptions for linear regression.

Level of significance = 0.05.   

> summary(model)

Call:

lm(formula = Damage ~ Landfall.Windspeed)

Residuals:

   Min 1Q Median 3Q Max

-9294 -4782 -1996 -531 90478

Coefficients:

          Estimate Std. Error t value Pr(>|t|)

(Intercept) -10041.78 6064.29 -1.656 0.1012

Landfall.Windspeed 142.07 56.65 2.508 0.0139 *

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 12280 on 92 degrees of freedom

Multiple R-squared: [ A ], Adjusted R-squared: 0.05381

F-statistic: 6.289 on 1 and 92 DF, p-value: 0.01391

(a) Write the equation for the linear model using the variables Damages and Landfall Windspeed, taking the results of the t-tests into account.

(b) A hurricane is defined as a storm with wind speeds greater than 74 miles per hour. Interpret the value of the intercept in connection to the real-life context of this model (two or three sentences). Hint: Is the intercept truly meaningful, given the definition of a hurricane?

(c) The value of Pearson’s correlation coefficient for Damages and Landfall.Windspeed is 0.2529438. Calculate and interpret the value of R2 , denoted [A] in the table, in relation to the predictor and response variables.

(d) The range of observed maximum wind speeds in the sample data is 75 – 190 miles per hour. Is it appropriate to use the linear model to predict the cost of damage for a hurricane with a maximum wind speed of 150 miles per hour? Why or why not? If so, estimate the typical value of damages (specifying units).

(e) Would it be appropriate to use the linear model to predict the cost of damage for a hurricane with a maximum wind speed of 225 miles per hour? Why or why not? If so, estimate the typical value of damages (specifying units).

A poll was taken this year asking college students if they considered themselves overweight. A similar poll was taken 5 years ago. Five years ago, a sample of 270 students showed that 120 considered themselves overweight. This year a poll of 300 students showed that 140 considered themselves overweight. At a 5% level of significance, test to see if there is any difference in the proportion of college students who consider themselves overweight between the two polls. What is your conclusion? Show all work and please make legible

A random sample of surgical procedures was selected each month for 30 consecutive months, and the number of procedures with post-operative complications was recorded. The data are listed in the accompanying table.

1. What type of control chart is the most appropriate to analyze the process?
2. Compute the critical boundaries for the control chart.
3. Interpret the chart. Does the process appear to be in control? Explain.

The null hypothesis for an ANOVA analysis comparing four treatment means is rejected. The four sample means are = 10,    = 12, = 15, = 18. The sample size for each treatment is the same. If ( - ) is significantly different from zero, then ________.

A one-sample z-test for a population mean is to be performed. Let z 0 denote the observed value of the test statistic, z. Assume that a two-tailed test is being performed. True or false: If z0 is negative, the P-value is twice the area under the standard normal curve to the right of z0. 2) A) True B) False

Test a hypothesis using variables in the data set for which ANOVA is the appropriate test (do NOT use the variables assigned for the final project).

Data:

Gender abuse

female 7.00   

female .00

female 7.00

male 7.00

male .00

male 7.00

female 7.00

female 7.00

female .00

female .00

1. State the null and research hypotheses in statistical terms, including the appropriate notation.
2. Explain why ANOVA is the appropriate test. In your explanation, describe the formula (13.1) for the statistic and what it means.
3. Explain why you should not use several t tests for this hypothesis, and how you would address the problem that would result from doing so.
4. Using SPSS, compute an ANOVA to test the hypothesis. Attach the SPSS output with your assignment. [2 point]
5. Summarize the results of the ANOVA. Also include the correct notation. Are the results of the test significant, i.e., likely in the population? Why or why not? Should you reject or retain the null hypothesis?
6. If the result was significant, perform the appropriate test to find out which pairs of groups significantly differ. Attach the SPSS output with your assignment. Describe the significant pairwise differences between groups. If the result was not significant, indicate some of the non-significant pairwise differences.

(a) complete the table to show the cumulative frequency

(b) using the scale of 1 cm to represent $5 on the horizontal axis and 1cm to represent 5 students on the vertical axis, draw the cumulative frequency graph for the data.

(marks will be awarded for axis appropriately labelled, points correctly plotted and a smooth curve carefully drawn)

(c) use your graph to estimate (i) the median amount of money spent (ii)the probability that a student chosen at random spent less than $23 during the week.

show on your graph, using broken lines, how these estimates were determined.

1. If the coefficient of determination is 25%, the correlation between two continuous variables is

a) -5

b) 5

c) -.25

d) .25

e) a or b

f) none of the above

2. To assess the correlation between height and weight, one should use

a) spearman correlation

b) regression equation

c. pearson correlation

d) point biserial correlation

3. For a computed r = -0.547, given a dataset of n = 16, alpha = .05, and two-tailed significance, one should fail to reject the null hypothesis.

a) yes

b) no

Four unbiased coins, a quarter (25 cent coin), a dime (10 cents coin) and two different nickles (5 cent coins, one minted before year 2000 and other after Year 2000) are tossed simultaneously. If a head shows up on any coin, you are paid the amount on the coin but for tail, you are paid no money for that coin. Find the probability that upon a single simultaneous toss of all four coins, you are paid a total of 35 cents or more