Identify the sample and sample statistic - For 186 randomly selected babies, the average (mean) of their births weights is 3,103 grams (based on data from “Cognitive Outcomes of Preschool Children with Prenatal Cocaine Exposure.” By Singer et al., Journal of the American Association, Vol. 291, No 20).

A) Sample-preschool children, statistic birth weights

B) Sample-186 babies, statistic 3,103 grams

C) Sample 186 babies, statistic Cocaine Exposure

What are the absolute and relative errors? – The bakery menu claims that there are 12 doughnuts in a bag, but the baker always puts 13 doughnuts (the true value) in each bag.

A) Absolute 1 donut, relative 7.7%

B) Absolute -1 donut, relative -7.7%

C) No answer text provided.

What are the absolute and relative errors? –The official distance for a marathon is 26 miles 385 yards or 26.21875 miles, but the organizers of a marathon map a course that is actually 26.34567 in length.

A)Absolute 26.21875 miles, relative .12692 miles

B) Absolute .12692 miles , Relative 0.5%

C) Absolute 26.34567 miles, Relative 12.6%

Using the Standard Normal Table. What is the probability a z-score is between -1.82 and -0.68?

In other words, what is P( -1.82 < z < -0.68)?

Find V(X) of the geometric distribution (Hint for the problem: Use the interchange derivative and summation, Find E(X^2), and then use the formula V(X) = E(X^2) - E(X)^2). Please show all work and all steps.

1. Suppose in a survey of n = 2000 students, 1200 responded that they prefer small classes and 800 responded that they prefer large classes. Let p denote the fraction of all students who preferred small classes at the time of the survey, and X ̄ be the fraction of survey respondents who preferred small classes. (Hint: X is distributed as a Bernoulli random variable) (a) Show that E(X ̄) = p and Var(X ̄) = p(1 − p)/n. (b) Use the survey result to estimate p, and calculate the standard error of your estimator. (Hint: Notice that this is the same as estimating the sample mean)

For the following sample, display the data using a frequency distribution table and then using a histogram . Assume the data is continuous and measured on a ratio scale.

23 21 18 17 17 15 20 3 4 28

16 15 15 15 27 2 3 15 16 16

a) How would you describe the shape of the distribution?

b) Which is the most appropriate measure of central tendency?

c) Calculate the most appropriate measure of central tendency.

A random sample was selected to determine whether the gas fuel cost different between east side (consider as 1) and west side (consider as 2). Given α=0.05. The data are summarized below:

East Side West Side Difference

Average 2.90/gal                                       2.99/gal                                       -0.09/gal

Count 12                                                     12 12

Standard deviation 0.81                                                  0.95                                          0.38

(d) Is there sufficient evidence to indicate that the gas fuel cost different between east side and west side?

Group of answer choices

Yes

No

Taylor reads that 65% of men do not wassh their hands after going to the resteroom. He camps put in a restroom and randomly observes 40 men. Of these 40 men, 30 do not wash their hands. Is this a significantly different percentage at the 1% level of significance?

Consider the time series given by y_t = a₁y_t-1 + a₂y_t-2 + ε_t. Where ε_t is independent white noise and y_t is stationary.

A.    Compute the mean of y_t. E(y_t)

B.   Compute the variance of y_t. E[y_t − E(y_t)]²

C.    Compute the first three autocovariances for y_t. (E[(y_t −E(y_t))(y_t−i −E(y_t−i))] i=1,2,3).

2. A professor was curious as to whether the students in a very large class she was teaching, who turned in their tests first, scored differently from the class mean on the test. The μ on the test was 75 with σ = 10; the scores were approximately normally distributed. The mean score for the first 20 tests was 78. Did the students turning in their tests first score significantly different from the larger mean at the .05 level?

   a) Use the four steps of hypothesis testing b) Illustrate the distributions involved

   c) Calculate the 95% confidence interval (*even if ns result)

You have torn a tendon and are facing surgery to repair it. The surgeon explains the risks to you: infection occurs in 4% of such operations, the repair fails in 14%, and both infection and failure occur together in 2%. What percent of these operations succeed and are free from infection?

The scores 30 students earned on the Calculus I final exam are listed in the data set below (in percentage).

examscores=c(95,68,65,50,82, 85,91,83,70,67, 68,65,52,39,48, 75,65,70,68,65, 69,71,68,73,78, 80,51,65,64,87)

Include your R commands and output for each part of the problem.

a) Create a stem and leaf plot for this data.

b) Comment on at least three features of the distribution using statistical terminology.

c) One of the data values is 39%. Would that value be considered unusual? Show work to justify your answer.

d) One of the data values is 39%. Would that value be considered an outlier? Show work to justify your answer.

Recall the researcher who investigated the relationship between hours of sleep and reaction times in the Week 4 Application. As a follow up to that study, the researcher wants to conduct a correlation to investigate further if there is a relationship between hours of sleep and reaction time. For this experiment, participants are allowed to sleep as much as they would like (that is, they are not assigned to sleep any specific number of hours). When 20 participants come to their appointment time, they report to the researcher how many hours of sleep they had the previous night. The researcher then tests their reaction times.

data:

The risk of developing iron deficiency is especially high during pregnancy. Consider the following data on transferrin receptor concentration (mg/L) for a sample of women with laboratory evidence of overt iron-deficiency anemia. Please answer each question below showing all calculations by hand.

11.2, 10.5, 7.6, 11.3, 10.4, 9.7, 20.8, 9.4, 19.5, 9.4, 8.3

(a) What is the median transferrin receptor concentration for these 11 women?

(b) What is the mean transferrin receptor concentration for these 11 women?

(c) Do you regard the mean or the median as more representative of the center of the data? Explain your choice.

(d) What are the variance and standard deviation for transferrin receptor concentrations of these 11 women?

What is differences between a parameter and a random variable in statistics?

I want clear explanation !!