Each of the distributions below could be used to model the time spent studying for an exam. Take one random sample of size 25 from each of the distributions below. Then, take 1,000 resamples (i.e., sample with replacement) of size 25 from your sample. In each case (a,b,c), plot the empirical distribution of the sample mean, estimate the mean of the sample mean, and estimate the standard deviation of the sample mean. Compare the results to the theoretical results.

a. N(5, 1.52)

b. Unif(0,10)

c. Gamma(5,1)

1.

Counting the number of people who have been exposed to the Zika virus is an example of which of the following?

Continuous data

Discrete data

Quantitative data

Binary data

unanswered

2.Which type of bait catches the largest fish? A study was conducted using 3 different baits (worms, corn, and plastic lures), and the average weight of the fish caught was measured. What is the independent variable?

The type of bait

The weight of the fish

Corn

None of the above

3.

Which type of bait catches the largest fish? A study was conducted using 3 different baits (worms, corn, and plastic lures), and the average weight of the fish caught was measured. What type of variable is the dependent variable?

Continuous

Discrete

Qualitative

Binary

unanswered

4.

A study was conducted to determine if rats gain weight after experiencing different levels of exercise. Researchers used 24 rats, for three different levels of exercise, plus a control group. Rats were randomly assigned to each group until there were six rats per group. How many replications are there?

3

4

6

24

unanswered

5.

Which of the following are true when using the stratified sampling method? (Choose all that apply)

All subjects have and equally likely chance of being selected

Subjects are selected from each strata

Strata are usually created by convenience

All subjects are measured in the selected strata

unanswered

We flip a fair coin 20 times. Find the probability that we obtain between 8 and 17 heads, inclusively. Show work and please explain to someone that hardly understands statistics!

Use 6.89 days as a planning value for the population standard deviation. Assuming 95% confidence, what sample size would be required to obtain a margin of error of 1.5 days (round up to the next whole number)? Assuming 90% confidence, what sample size would be required to obtain a margin of error of 2 days (round up to the next whole number)?

a) For 30 randomly selected Rolling Stones concerts, the mean gross earnings is 2.79 million dollars. Assuming a population standard deviation gross earnings of 0.47 million dollars, obtain a 99% confidence interval for the mean gross earnings of all Rolling Stones concerts (in millions).

Confidence interval: ( __________________ , __________________ ).

Please explain steps to find these answers on the TI 84 plus calculator:

A machine used to fill gallon sized paint cans is regulated so that the amount of paint dispensed has a mean of 128 ounces and a standard deviation of 0.20 ounce. You randomly select 40 cans and carefully measure the contents. The same mean of the cans is 127.9 ounces. Does the machine need to be reset? Explain your reasoning.

1. Use the diamond data:

Is there enough evidence in the data that population average price of diamond for color “E” is more than 1500.

Please solve using R please.

Thank you

indicate the term not synonymous with the others

How is the rejection region defined, and how is that related to the p value? When do you reject or fail to reject the null hypothesis? Why do you think statisticians are asked to complete hypothesis testing? Can you think of examples in courts, in medicine, or in your area?

Type “ineffective charts,” “ineffective graphs,” “unethical charts,” or some version thereof into Google Images. Find two or three differently-designed graphs and charts and discuss why the data visualizations are not effective.

Suppose your research assistant screwed up and lost the information that linked the person’s identity across the two weight loss periods. This makes it impossible to run a paired t-test. Rather than start over:

a) Compute the mean and standard deviation of the two samples (2-pts)

b) Compute the two sample t-statistic (2pts)

c) How many degrees of freedom do you have(3pts)?

d) compute the P-value (4pts)

e) How does this P-value compare to the one you just computed using the paired ttest? (3pts))

Two Sample t-test (16pts):

Suppose you are interested in deciding if the 1990 Toyota Four Runner has been equally reliable as the 1990 Honda Passport. You go out a randomly sample of 5 people who own a 1990 Toyota and 5 other people who own a 1990 Honda and you ask them how often they have to take their vehicles in for maintenance. Here are your data (in thousands of miles):

Toyota: 30 35 32 34 30

Honda: 29 33 28 31 27

a) State the null and alternative hypotheses (2pts)

b) Compute the means and standard deviations of the two samples (2-pts)

c) Compute the two sample t-statistic (2 pts)

c) How many degrees of freedom do you have? (3pts)

d) Compute the P-value (4pts)

e) At an alpha = 0.05 would you accept or reject the null hypothesis? (3pts)

Please show work! thank you!

8. A fair coin is tossed 60 times. Find the probability that the head appears between 22 and 40 times by using

a. binomial distribution,

b. approximation of Binomial distribution by normal distribution. Discuss why b. is better in practice.

ID      Year    CornYield       SoyBeanYield
1       1957    48.3    23.2
2       1958    52.8    24.2
3       1959    53.1    23.5
4       1960    54.7    23.5
5       1961    62.4    25.1
6       1962    64.7    24.2
7       1963    67.9    24.4
8       1964    62.9    22.8
9       1965    74.1    24.5
10      1966    73.1    25.4
11      1967    80.1    24.5
12      1968    79.5    26.7
13      1969    85.9    27.4
14      1970    72.4    26.7
15      1971    88.1    27.5
16      1972    97      27.8
17      1973    91.3    27.8
18      1974    71.9    23.7
19      1975    86.4    28.9
20      1976    88      26.1
21      1977    90.8    30.6
22      1978    101     29.4

23      1979    109.5   32.1
24      1980    91      26.5
25      1981    108.9   30.1
26      1982    113.2   31.5

27      1983    81.1    26.2
28      1984    106.7   28.1
29      1985    118     34.1
30      1986    119.4   33.3
31      1987    119.8   33.9
32      1988    84.6    27.0
33      1989    116.3   32.3
34      1990    118.5   34.1
35      1991    108.6   34.2
36      1992    131.5   37.6
37      1993    100.7   32.6
38      1994    138.6   41.4
39      1995    113.5   35.3
40      1996    127.1   37.6
41      1997    126.7   38.9
42      1998    134.4   38.9
43      1999    133.8   36.6
44      2000    136.9   38.1
45      2001    138.2   39.6
46      2002    129.3   38.0
47      2003    142.2   33.9
48      2004    160.3   42.2
49      2005    147.9   43.1
50      2006    149.1   42.9
51      2007    150.7   41.7

Use both predictors. From the previous two exercises, we conclude that year and soybean may be useful together in a model for predicting corn yield. Run this multiple regression.

a)       Explain the results of the ANOVA F test. Give the null and alternate hypothesis, test statistic with degrees of freedom, and p-value. What do you conclude?

b)      What percent of the variation in corn yield in explained by these two variables? Compare it with the percent explained in the previous simple linear regression models.

c)       State the regression model. Why do the coefficients for year and soybean differ from those in the previous exercises?

d)      Summarize the significance test results for the regression coefficients for year and soybean yield.

e)      Give a 95% confidence interval for each of these coefficients.

f)        Plot the residual versus year and soybean yield. What do you conclude?

Complete the following by writing a response to three of the four following questions. For each question, your response should be 2 or more paragraphs.
Describe how you could use confidence intervalsto help make a decision in your current job, a past job, or life situation. Include a description of the decision, how the interval would impact the decision, and how data could ideally be collected to determine the interval.