Fifteen six-sided dice are placed in a cup. The cup is shaken and turned over on a table, and the number of 1s is recorded. Use R commands to find the probabilities and histogram for the number of possible 1s. Please show the way I should set this up in R.

1. R has many build-in dataset. The data mtcars is one of them. The following R code read-in data and save the data to input.

                  input <- mtcars[,c("am","cyl","hp","wt")]

             Write a few line of R code to conduct a regression analysis with am as the response variable, and

             cyl, hp, wt as explanation variables.

Consider the following hypotheses:

H₀: p ≥ 0.52

H_A: p < 0.52

Which of the following sample information enables us to reject the null hypothesis at α = 0.01 and at α = 0.10? (You may find it useful to reference the appropriate table: z table or t table) (Round all intermediate calculations to at least 4 decimal places.)

The following data represent x = boat sales and y = boat trailer sales from 1995 through 2000.

1. Determine the Y intercept of the least-squares regression line. (Specify your answer to 2nd decimal point)

2.Determine the slope of the least-squares regression line. (Specify your answer to 3rd decimal point)

3. Based on Q1 and Q2, estimate, for a year during which 500,000 boats are sold, the number of boat trailers that would be sold.

The probability that a voter chosen at random is in the 18 to 20 years old age range is ___. (Round to three decimal places as​ needed.)

The probability is ____.

Write the null and alternative hypotheses for each situation described below, and indicate whether each test would be left-tailed, right-tailed, or two-tailed. Make sure that you use the correct population parameter. To submit the assignment, you may just type your answers in the text box. (You don't have to worry about typing subscripts or Greek letters on this assignment unless you want to. For example, for , you could type H0: mu = 30.)

1. A cereal manufacturer claims that, for a particular brand of cereal, the average amount of cereal in a box is 20 ounces. A consumer advocate believes that the boxes are underfilled.

2. In the past, it was reported that 30% of American adults were obese. A health researcher believes that the proportion is now different from that.

3. A homeowner claims that the average monthly water bill is $80.00. A potential buyer believes that the average bill is higher than that.

Determine the critical value. Remember:

• When estimating the mean, if the population standard deviation (σ) is known, use z.
• When estimating the proportion, use z.
  • Find z using = -norm.s.inv((1-confidence level)/2)

• When estimating the mean, if the population standard deviation (σ, sigma) is unknown--meaning that you have a sample standard deviation (s)--use t.
  • Find t using =t.inv.2t(1-confidence level, n-1)

Group of answer choices

Estimating the mean at 95% confidence, n=25, s=4.5

      [ Choose ]            2.576            1.645            3.17            1.96            2.586            1.76            2.06      

Estimating the mean at 95% confidence, n=15, sigma=4.5

      [ Choose ]            2.576            1.645            3.17            1.96            2.586            1.76            2.06      

Estimating the proportion at 95% confidence, n=500, pbar=.24

      [ Choose ]            2.576            1.645            3.17            1.96            2.586            1.76            2.06      

Estimating the mean at 90% confidence, n=15, s=300

      [ Choose ]            2.576            1.645            3.17            1.96            2.586            1.76            2.06      

Estimating the proportion at 90% confidence, n=100, pbar=.3

      [ Choose ]            2.576            1.645            3.17            1.96            2.586            1.76            2.06      

Estimating the mean at 99% confidence, n=11, s=0.77

      [ Choose ]            2.576            1.645            3.17            1.96            2.586            1.76            2.06      

Estimating the mean at 99% confidence, n=11, sigma=0.77

      [ Choose ]            2.576            1.645            3.17            1.96            2.586            1.76            2.06      

Estimating the mean at 99% confidence, n=500, s=0.77

      [ Choose ]            2.576            1.645            3.17            1.96            2.586            1.76            2.06      

The ballistic coefficient is a measure of body’s ability to overcome air resistance in flight. That parameter is inversely proportional to the deceleration of a flying body and is very important for bullets. The ballistic coefficient was measured for the bullets of two versions of 9 mm Makarov cartridges, PM and PMM (which is a later and modified version). Sample bullets are chosen randomly.

Use α=0.025.

Find a 95% two-sided confidence interval for the mean difference in the ballistic coefficient.

Round your answers to three decimal places (e.g. 98.765).

______ ≤μ1-μ2≤ ______

In a test of

Upper H 0H0​:

muμequals=100

against

Upper H Subscript aHa​:

muμnot equals≠​100,

the sample data yielded the test statistic

z equals 1.87z=1.87.

Find the

Upper PP​-value

for the test.

P equals=???

​(Round to four decimal places as​ needed.)

The average ticket price for a Spring Training baseball game is $31.46, with a standard deviation of $8.46. In a random sample of 40 Spring Training tickets, find the probability that the mean ticket price exceeds $34. (Round your answer to three decimal places)

The Wind Mountain excavation site in New Mexico is an important archaeological location of the ancient Native American Anasazi culture. The following data represent depths (in cm) below surface grade at which significant artifacts were discovered at this site (Reference: A.I. Woosley and A.J. McIntyre, Mimbres Mogollon Archaeology, University of New Mexico Press).

For this problem, use seven classes.

(a) Find the class width.


(b) Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. (Give relative frequencies to 4 decimal places.) Show Your Work!!

A pediatrician randomly selected 50 six-month-old boys from her practice's database and recorded an average weight of 15.6 pounds with a standard deviation of 0.45 pounds. She also recorded an average length of 25.7 inches with a standard deviation of 0.27 inches.

(a) Find a 95% confidence interval for the average weight (in pounds) of all six-month-old boys. (Round your answers to two decimal places.)_____ lb to______ lb

(b) Find a 99% confidence interval for the average length (in inches) of all six-month-old boys. (Round your answers to two decimal places.) in ____ to ______in

(c) What do you have to assume about the pediatrician's database in order to make inferences about all six-month-old boys?

1. The pediatrician's database must contain all measurements from the entire population of six-month old boys.

2. The pediatrician's database must be updated daily.

3. The pediatrician's database must produce intervals that contain the respective sample means.

4. The pediatrician's database must be kept secure using state of the art security software.

5. The pediatrician's database must be representative of the entire population of six-month old boys.

There are 27 tickets in the lottery, of which 5 tickets win and 3 give the right to draw the next ticket. Calculate the probability of winning by purchasing one lottery ticket.

The average February temperature in Indiana is normally distributed with a mean of 28.89 degree and a variance of 26.16 degree (X~N(28.89,26.16)). The average February 2017 temperature is 42.85 degree. What is the probability that the average February temperature is greater than 42.85 degree?

Consider the following hypotheses:

H₀: p ≥ 0.45

H_A: p < 0.45

What is the pvalue for A,B,C,and D?