For a data set obtained from a sample, n=79 and x¯=46.55. It is known that σ=3.8.

a. What is the point estimate of μ?

The point estimate is___ .

b. Make a 95% confidence interval for μ.

Round your answers to two decimal places.

(_____,______)

c. What is the margin of error of estimate for part b?

Round your answer to three decimal places.

E=___

Out of a sample of 460 students, 295 indicated that they preferred chocolate ice cream to vanilla ice cream.

a. Estimate the value of the population proportion of those who preferred chocolate ice cream. (Round the final answer to 3 decimal places.)

Estimated population proportion           

b. Compute the standard error of the proportion. (Round the final answer to 4 decimal places.)

Standard error of the proportion           

c. Determine a 90% confidence interval for the population proportion of those who preferred chocolate ice cream. (Round the final answers to 3 decimal places.)

Confidence interval for the population proportion is between      and    .

d. Interpret your findings.    

If 460 such intervals were determined, the population  (Click to select)  mean or proportion  would be included in about ______ intervals.

The owner of a local car dealership has just received a call from a regional distributor stating that a $5000 bonus will be awarded if the owner's dealership sells at least 10 new cars next Saturday. On an average Saturday, this dealership has 75 potential customers look at new cars, but there is no way to determine exactly how many customers will come this particular Saturday. The owner is fairly certain that the number would not be less than 40, but also thinks it would be unrealistic to expect more than 120 (which is the largest number of customers to ever show up in 1 day). The owner determined that, on average, about one out of ten customers who look at cars at the dealership actually purchase a car - or, a .10 probability (or 10% chance) exists that any given customer will buy a new car.

a. Create a spreadsheet model for the number of cars the dealership might sell next Saturday

b. What is the probability that the dealership will earn the $5000 bonus?

c. If you were this dealer, what is the maximum amount of money you would be willing to spend on sales incentives to try to earn this bonus?

Please show how you got each answer

Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand is $200. Her best guess is that she can sell 1000 cups per week at $.80 per cup. The variable cost of producing a cup of lemonade is $.30?

a) given her other assumptions, what level of sales volume will enable Julie to break even using goal seek function

b) given her other assumptions, discuss how a change in sales and variable cost jointly affect profit using the two-way data table

The following table shows ceremonial ranking and type of pottery sherd for a random sample of 434 sherds at an archaeological location.

Use a chi-square test to determine if ceremonial ranking and pottery type are independent at the 0.05 level of significance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: Ceremonial ranking and pottery type are not independent.
H₁: Ceremonial ranking and pottery type are independent.H₀: Ceremonial ranking and pottery type are independent.
H₁: Ceremonial ranking and pottery type are not independent.     H₀: Ceremonial ranking and pottery type are not independent.
H₁: Ceremonial ranking and pottery type are not independent.H₀: Ceremonial ranking and pottery type are independent.
H₁: Ceremonial ranking and pottery type are independent.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)


Are all the expected frequencies greater than 5?

YesNo     

What sampling distribution will you use?

Student's tuniform     chi-squarebinomialnormal

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

p-value > 0.1000.050 < p-value < 0.100     0.025 < p-value < 0.0500.010 < p-value < 0.0250.005 < p-value < 0.010p-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis.     Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is sufficient evidence to conclude that ceremonial ranking and pottery type are not independent.At the 5% level of significance, there is insufficient evidence to conclude that ceremonial ranking and pottery type are not independent.    

Two plots at Rothamsted Experimental Station were studied for production of wheat straw. For a random sample of years, the annual wheat straw production (in pounds) from one plot was as follows.

Use a calculator to verify that, for this plot, the sample variance is s² ≈ 0.370.

Another random sample of years for a second plot gave the following annual wheat production (in pounds).

Use a calculator to verify that the sample variance for this plot is s² ≈ 0.854.

Test the claim that there is a difference (either way) in the population variance of wheat straw production for these two plots. Use a 5% level of signifcance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: σ₁² = σ₂²; H₁: σ₁² > σ₂²H_o: σ₁² > σ₂²; H₁: σ₁² = σ₂²     H_o: σ₂² = σ₁²; H₁: σ₂² > σ₁²H_o: σ₁² = σ₂²; H₁: σ₁² ≠ σ₂²

(b) Find the value of the sample F statistic. (Use 2 decimal places.)


What are the degrees of freedom?

What assumptions are you making about the original distribution?

The populations follow independent chi-square distributions. We have random samples from each population.The populations follow dependent normal distributions. We have random samples from each population.     The populations follow independent normal distributions. We have random samples from each population.The populations follow independent normal distributions.

(c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)

p-value > 0.2000.100 < p-value < 0.200     0.050 < p-value < 0.1000.020 < p-value < 0.0500.002 < p-value < 0.020p-value < 0.002

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.     At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.Reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.     Reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.Fail to reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.

5.         Ben, a graduate student, wants to write his thesis on the impact of hours of study on    exam performance. His goal is to demonstrate scientifically that when he scored very          high on a recent exam it was not just the result of luck, but rather it was due to the many             hours of study he put in. He conjectured that as he studied more, he was able to do more             practice problems, and completing more practice problems helped him to score higher on the exam. He acknowledged however that his IQ may have had an effect on the relationship between the number of hours of study and his score on the exam. He thinks a           student with a very high IQ may not have to put in many hours to get a higher score on an     exam.

            a. What is the problem statement

            b. Identify and label all the variables. Then draw a theoretical (or conceptual) framework                     for the problem.

            c. From the theoretical framework, identify three research hypotheses and formulate a                 null hypothesis (H_o) and an alternative hypothesis (H_A) for each one.

A teacher wanted to estimate the proportion of students who take notes in her class. She used data from a random sample of size n = 76 and found that 45 of them took notes. The 97% confidence interval for the proportion of student that take notes is:

Please Use R studio and show all the steps to answer this question

NY Marathon 2013 the table below shows the winning times (in minutes) for men and women in the new york city marathon between 1978 and 2013. (the race was not run in 2012 because of superstorm sandy.) assuming that performances in the big apple resemble performances elsewhere, we can think of these data as a sample of performance in marathon competitions. Create a 90% confidence interval for the mean difference in winning times for male and female marathon competitors.

A regional planner employed by a public university is studying the demographics of nine counties in the eastern region of an Atlantic seaboard state. She has gathered the following data:

County

a) Is there a linear relationship between the median income and median age? (Round your answer to 3 decimal places.)

The correlation of income and Median age is _______

B) Use regression analysis to determine the relationship between median income and median age. (Round your answers to 2 decimal places.)

Income=__________+_________Median Age

C.)Interpret the value of the slope in a simple regression equation. (Round your answers to 2 decimal places.)

For each year (increase/decrease) in age, the income increases ____________ on average.

D.)Include the aspect that the county is "coastal" or not in a multiple linear regression analysis using a "dummy" variable. (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)

Income=_________+___________Median Age+__________Coastal

E.)Test each of the individual coefficients to see if they are significant. (Negative amounts should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 2 decimal places.)

A set of reliability testing data for a special equipment was obtained and the ordered ages at failure (hours) were: 8.3, 13, 16.9, 20.1, 23.8, 26.5, 29.8, 33.2, 36.5, 41, 45.1, 51.7, 61.3. Assume that these times to failure are normally distributed. Estimate the equipment reliability and hazard function at age 25 hours.

3. Fun size M&Ms candies contain between 15 and 18 candies and uniformly distributed among bags. Sup- pose a sample of 30 bags is chosen from a large Costco size bag of Fun Size M&Ms.

a) What is the population mean and standard deviation? Hint: bag size is given to us as uniformly distributed

b) What is the probability that the mean number of candies in 30 bags is less than 15 candies?

c) What is the probability that the mean number of candies in 30 bags is more than 18 candies?

A company is concerned about the quality of production in its four plants. To test the quality, managers take measurements of valve openings (the dependent variable) by one machine operator (the independent variable) in each plant. The results are stacked in columns by operator 1 through 4 below.

6.33       6.26     6.44    6.29

6.26       6.36     6.38    6.23

6.31       6.23     6.58    6.19

6.29       6.27     6.54    6.21

6.4         6.19     6.56

               6.5       6.34

               6.19     6.58

               6.22

Please provide the five step hypothesis testing process using a 5% level of significance, conduct a post-hoc test if required, and provide the Minitab output for the ANOVA and post-hoc test.

To conduct this test in Minitab, please use the following process:

Stack the data in columns as given above. To begin a one-way ANOVA with Stacked Data, select Stat from the menu bar. Select ANOVA from the pulldown menu. Select One-Way. In the slot Response, list the column containing the observations. In the slot Factor, list the column containing the group identifiers. For multiple comparisons, select Comparisons and make your selection from the dialog box that appears. The multiple comparison options are Tukey’s, Fisher’s, Dunnett’s, or Hsu’s MCB tests. In the multiple comparison dialog box, you can insert the family error rate in the box on the right as a whole number.

A game works as follows: each player rolls one dice (let's call it ''n''). After both players have made the first roll, they have the choice to leave or not. If a player exits, he automatically looses; if not, he rolls a second time (let's call this second roll "m'') and receives n^m points . The player with the most points wins, in case of a tie no one wins.
a) Give the fundamental space of the two throws.
b) Give the fundamental space of the number of points obtained.
c) Show that a player should automatically withdraw if n = 1.
e) Let n₁ and n₂ be the value of n of the first and second player (respectively). Knowing that n₁ = 2 and n₂ = 3, what is the probability that the first player wins?
d) Knowing that the first player will pull out automatically if n₁ = 1, half the time if n₁ < n₂ and never otherwise, what is the probability that the first player will win?
probability of the first player pulling out?

There is 2 players in the game.

chap 2

A)

Here is a set of sample data

Identify the 5 number summary (min, Q1, median, Q3, max)
, , , ,

B)

The five number summary of a dataset was found to be:

46, 51, 55, 59, 70

An observation is considered an outlier if it is below:

An observation is considered an outlier if it is above:

C)

Here is a set of data.

Identify the 5 number summary (min, Q1, median, Q3, max)