1. Two streams (Brimer and Standifer creeks) located in the same watershed are similar in size/shape and most habitat conditions (e.g., temperature, dissolved oxygen, channel substrate); however, they exhibit different pH values. Brimer Creek has a mean pH of 6.1, whereas Standifer Creek has a pH of 5.6. A stream ecologist wishes to determine whether the pH has an influence on the local distributions of benthic macroinvertebrates (annelids, crustaceans, insects) in the two streams. Two study sites were established (one in each stream) that are in close proximity to each other (~50 m apart, separated by a ridge) and located near the mouths of their respective streams. Benthic invertebrates were collected at the two sites using a standardized kick-sampling technique (equal sampling times and areas). Invertebrates were counted in samples from the two sites. The data are summarized below. Number of invertebrates per sample: Brimer Creek, n = 1373 individuals Standifer Creek, n = 955 individuals Perform a G-test for goodness of fit (α = 0.05) to test the ecologist’s hypothesis.

Each of the distributions below could be used to model the time spent studying for an exam. Take 1,000 random samples of size 25 from each of the distributions below. 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)

Suppose that cholesterol levels for women in the U.S. have a mean of 188 and a standard deviation of 24. A random sample of 20 women in the U.S. is selected. Assume that the distribution of this data is normally distributed.

Are you more likely to randomly select one woman with a cholesterol level of more than 200 or are you more likely to select a random sample of 20 women with a mean cholesterol level of more than 200? Explain.

There were 49.7 million people with some type of long-lasting condition or disability living in the United States in 2000. This represented 19.3 percent of the majority of civilians aged five and over (http://factfinder.census.gov). A sample of 1000 persons is selected at random. Use normal approximation. Round the answers to four decimal places (e.g. 98.7654).

(a) Approximate the probability that more than 201 persons in the sample have a disability. (answer is not .274) round 4 decimal plzzzzz on a and b

(b) Approximate the probability that between 180 and 300 people in the sample have a disability. (answer is not .860

Bonus

Using permutation test SAS code , do the following:

Trauma data

Metabolic Expenditure

Nontrauma patients: 20.1 22.9 18.8 20.9 20.9 22.7 21.4 20

trauma patients: 38.5 25.8 22 23 37.6 30 24.5

Part A

Build the permutation distribution (using 5,000 permutations) for the rank sum statistic for the Trauma

data used above. Use SAS to fit/overlay a normal curve to the resulting histogram. Compare the mean and

standard deviation of this normal curve that was fit to the permutation/randomization distribution to the

mu and sigma you found earlier in the homework.

Part B

Compare the one-sided p-value found in this permutation distribution with the one found in prior questions.

Find an equation of the line satisfying the given conditions.

Through (6,4); perpendicular to 9x+4y=70

A man purchased a $23,000, 1-year term-life insurance policy for $375. Assuming that the probability that he will live for another year is 0.989, find the company's expected gain.

At the beginning of 2007, the population of a certain state was 55.4% rural and 44.6% urban. Based on past trends, it is expected that 13% of the population currently residing in the rural areas will move into the urban areas, while 21% of the population currently residing in the urban areas will move into the rural areas in the next decade. What was the population distribution in that state at the beginning of 2017? (Round your answers to one decimal place.)

In a study of the domestic market share of the three major automobile manufacturers A, B, and C in a certain country, it was found that their current market shares were 50%, 20%, and 30%, respectively. Furthermore, it was found that of the customers who bought a car manufactured by A, 75% would again buy a car manufactured by A, 15% would buy a car manufactured by B, and 10% would buy a car manufactured by C. Of the customers who bought a car manufactured by B, 90% would again buy a car manufactured by B, whereas 5% each would buy cars manufactured by A and C. Finally, of the customers who bought a car manufactured by C, 85% would again buy a car manufactured by C, 5% would buy a car manufactured by A, and 10% would buy a car manufactured by B. Assuming that these sentiments reflect the buying habits of customers in the future, determine the market share that will be held by each manufacturer after the next two model years. (Round your answers to the nearest percent.)

Suppose there is a bag containing 20 red marbles (R), 20 green marbles (G), 20 pink marbles (P), and violet marbles(V).

Someone mixes the marbles​ thoroughly, draws one marble at​ random, puts the marble back in the​ bag, mixes the bag​ thoroughly, and draws another marble at random. Complete parts​ (a) and​ (b) below

a. List all possible outcomes of this process. Choose the correct answer below

A. RR,RG, RP, RV, GG, GP, GV, PP, PV, W

B. RR, RG, RP, RV, GR, GG, GP, GV, PR, PG, PP, PV, VR, VG, VP, W

C. RG, RP, RV, GP, GV, PV

D. R, G, P, V

b. Make the probability distribution showing the probability of drawing​ 0, 1, and 2 green marbles.

Find the odds for and the odds against the event rolling a fair die and getting a 6 or a 2.

a. The odds for the event are __ to __ ​(Simplify your​ answers.)

b. The odds against the event are __ to __ . ​(Simplify your​ answers.)

The liquid chlorine added to swimming pools to combat algae has a relatively short shelf life before it losesits effectiveness. Records indicate that the mean shelf life of a jug of chlorine is 2180 hours. An experiment was conducted in which an additive, 'Holdlonger' was added to the jugs of chlorine in an attempt to increase its shelf life. The following data represent the shelf life (in hours) of nine jugs of chlorine with the Holdlonger added:

2172
2153
2157
2158
2179
2164
2154
2178
2168

(a)What assumption is required in order to proceed with a hypothesis test with this data? (Check all that apply)

A. Is dependent
B. Comes from a standard normal population
C. Comes from a normal population
D. Comes from a random sample

(b) Will the data follow a normal distribution?  ? Yes No
Report the P-value of the normality test:
(c)State the hypotheses which would be tested in this experiment.

A. H0:μ=2180H0:μ=2180, HA:μ>2180HA:μ>2180
B. H0:μ≥2180H0:μ≥2180, HA:μ<2180HA:μ<2180
C. H0:μ=2180H0:μ=2180, HA:μ≠2180HA:μ≠2180
D. H0:μ=2180H0:μ=2180, HA:μ<2180HA:μ<2180
(d) Reject the null hypothesis (α=0.08α=0.08) if the test statistic (x¯−2180s/n√x¯−2180s/n) is  ? greater than less than  

. Use three decimals.

(e) Calculate the test statistic from this data.

Use two decimals.

(f) What is the p-value?

Input numerical answers to four decimal places.

(g) Should you reject the null hypothesis?  ? Yes No

The Excel data for this assignment shows the annual energy usage in kWh for a random sample of 250 detached single-family homes in the Southeast. A contractor building a new housing development in Town A hypothesizes that mean annual energy usage will be below 16,500 kWh per household. Use the data to run a single mean hypothesis test and calculate a test statistic in Excel. In your method summary, state the hypothesis and your assumptions. In your resulting conclusions, state your conclusion regarding the hypothesis in words, using a 99% confidence level.

The Mean of the data is 14651.548

The Standard Deviation is 7980.99357

Of 250 adults who tried a new multi-grain cereal, "Wow!", 187 rated it excellent; of 100 children sampled, 66 rated it excellent. Using the 0.1 significance level and the alternate hypothesis π1 not equal to π2 , what is the null hypothesis? Select one: a. π1 = π2 b. π1 ≠ π2 c. π1 < π2 d. π1 > π2

A typical adult's resting heart rate is 79 BPM with a standard deviation of 12. If the heart rate of 9 randomly selected adults are taken, what average heart rate is at the 75th percentile? Round answer to 1 decimal place (i.e. 10.2)

Portfolio returns. The Capital Asset Pricing Model is a financial model that assumes returns on a portfolio are normally distributed. Suppose a portfolio has an average annual return of 11.1% (i.e. an average gain of 11.1%) with a standard deviation of 40%. A return of 0% means the value of the portfolio doesn't change, a negative return means that the portfolio loses money, and a positive return means that the portfolio gains money. Round all answers to 4 decimal places.

a. What percent of years does this portfolio lose money, i.e. have a return less than 0%?

b. What is the cutoff for the highest 13% of annual returns with this portfolio?

Changes in demographic outcomes can occur because of changes in within-group rates and/or changes in composition. First, explain what that sentence means. Then take the example of falling rates of death due to heart disease. How might changes in within-group rates account for that outcome? What about changes in composition? Can you think of any way to sort out the effects of changes in within-group rates vs. changes in composition?