Historically, the number of cars arriving per hour at Lundberg’s Car

Wash is observed to be the following:

a. Set up a probability distribution table (including the lower end of

the probability range) for the car arrivals.

b. Simulate 25 hours of car arrivals. What is the average number of

arrivals per hour?

c. Repeat part b multiple times (by pressing F9). Over what range

does the average number of arrivals vary?

d. Now simulate 500 hours of car arrivals. What is the average

number of arrivals per hour?

e. Repeat part d multiple times (by pressing F9) Over what range

does the average number of arrivals vary?

f. Do your answers for part c and e differ? Why or why not?

Use the sample data and confidence level given below to complete parts​ (a) through​ (d).

In a study of cell phone use and brain hemispheric​ dominance, an Internet survey was​ e-mailed to 2510 subjects randomly selected from an online group involved with ears. 1092 surveys were returned. Construct a 95​% confidence interval for the proportion of returned surveys.

a) Find the best point estimate of the population proportion p.

___ (Round to three decimal places as​ needed.)

​b) Identify the value of the margin of error E.

___ ​(Round to three decimal places as​ needed.)

​c) Construct the confidence interval.

___ < p < ___​ (Round to three decimal places as​ needed.)

​d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.

A. There is a 95​% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

B. 95% of sample proportions will fall between the lower bound and the upper bound.

C. One has 95​% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

D. One has 95​% confidence that the sample proportion is equal to the population proportion.

The following table summarizes the results from a two-factor study with 3

levels of Factor A and 4 levels of Factor B using a separate sample of 5

participants in each treatment condition. Fill in the missing values. Make

sure to show your work.

Source

SS

df

MS

F

Between

treatments

650

Factor A

5

0

Factor B

AxB

interaction

120

Within treatments

2

5

Total

Explain the difference between continuous random variables and discrete random variables. please give examples!

A manufacturer wants to compare the number of defects on the day shift with the number on the evening shift. A sample of production from recent shifts showed the following defects:

Day Shift                     5          8          7          6          9          7

Evening Shift              8          10        7          11        9          12            14        9

The objective is to determine whether the mean number of defects on the night shift is greater than the mean number on the day shift at the 95% confidence level.

1. State the null and alternate hypotheses.
2. What is the level of significance?
3. What is the test statistic?
4. What is the decision rule?
5. Use the Excel Data Analysis pack to analyze the problem. Include the output with your answer. (Note: You may calculate by hand if you prefer).
6. What is your conclusion? Explain.
7. Does the decision change at the 99% confidence level?

Why do we naturally tend to trust some strangers more than others? One group of researchers decided to study the relationship between eye color and trustworthiness. In their experiment the researchers took photographs of 80 students (20 males with brown eyes, 20 males with blue eyes, 20 females with brown eyes, and 20 females with blue eyes), each seated in front of a white background looking directly at the camera with a neutral expression. These photos were cropped so the eyes were horizontal and at the same height in the photo and so the neckline was visible. They then recruited 105 participants to judge the trustworthiness of each student photo. This was done using a 10-point scale, where 1 meant very untrustworthy and 10 very trustworthy. The 80 scores from each participant were then converted to z-scores, and the average z-score of each photo (across all 105 participants) was used for the analysis. Here is a summary of the results.

Eye color n x s

Brown 40 0.55 1.68

Blue 40 −0.37 1.54

Can we conclude from these data that brown-eyed students appear more trustworthy compared to their blue-eyed counterparts? Test the hypothesis that the average scores for the two groups are the same.

State the null and alternative hypotheses.

H0: μBrown = μBlue Ha: μBrown > μBlue

H0: μBrown = μBlue Ha: μBrown < μBlue

H0: μBrown ≠ μBlue Ha: μBrown > μBlue

H0: μBrown = μBlue Ha: μBrown ≠ μBlue

H0: μBrown ≠ μBlue

Ha: μBrown < μBlue

Report the test statistic, the degrees of freedom, and the P-value. (Round your test statistic to three decimal places, your degrees of freedom to the nearest whole number, and your P-value to four decimal places.)

t =

df =

P-value =

State your conclusion. (Use α = 0.05.)

We reject H0 and conclude that brown-eyed people seem more trustworthy according to this experiment.

We do not reject H0 and can not conclude that brown-eyed people seem more trustworthy according to this experiment.

Testing ONE mean versus a claim (z or t)
Testing TWO means head to head (t)

1. What if we want to test MORE than TWO means?
2. What are the null hypotheses for each?  
3. How do the null hypotheses change for ANOVA?

Salaries of 39 college graduates who took a statistics course in college have a​ mean, x overbar​, of $ 68 comma 900. Assuming a standard​ deviation, sigma​, of ​$19 comma 972​, construct a 99​% confidence interval for estimating the population mean mu.

An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use . Factor A is method of loading and unloading; Factor B is the type of ride.

Set up the ANOVA table (to whole number, but p-value to 2 decimals and F value to 1 decimal, if necessary).

The following table compares the completion percentage and interception percentage of 5 NFL quarterbacks. Completion Percentage 57 59 61 65 65 Interception Percentage 4.8 4.7 4.5 3.1 1.1 Table

Step 4 of 5 : Construct the 98% confidence interval for the slope. Round your answers to three decimal places.

The Diabetes Control and Complications Trial followed diabetes patients diagnosed with retinopathy before joining the study. They were randomly assigned to one of two treatments and monitored for 6 years. The study found that 121 of the 344 patients assigned to the conventional treatment showed a sustained progression of their original retinopathy. In contrast, only 62 of the 376 patients assigned to the intensive treatment had sustained retinopathy progression.

Find a point estimate of the difference between the proportion of conventional treatment patients with sustained retinopathy progression and the proportion of intensive treatment patients with sustained retinopathy progression. (Use 3 decimal places)

X and Y are the future lifetimes of two machines. The joint PDF of the two random variables is f(x, y) = 12(x+y+1)^-5, x>), y>0. Calculate E(X|Y = 2).

2) Male company employees aged 21 to 26 are found to drive an average of 19484 km a year. The annual mileage is normally distributed with a standard deviation of 6812 km. The company has decided to levy a user fee on those employees who are in the top 30%. Find the yearly mileage total of those who will be charged a user fee.

3) If α = 0.06, standard deviation is s = 3.15, sample mean is x= 12.7, and n = 500, find the confidence interval for the population mean.