Why are sampling distributions important to the study of inferential statistics? In your answer, demonstrate your understanding by providing an example of a sampling distribution from an area such as business, sports, medicine, social science, or another area with which you are familiar. Remember to cite your resources and use your own words in your explanation.

1) A manufacturer of cereal claims that the mean weight of a particular type of box of cereal is 1.2 pounds. A random sample of 71 boxes reveals a sample average of 1.186 pounds and a sample standard deviation of .117 pound. Using the .01 level of significance, is there evidence that the average weight of the boxes is different from 1.2 pounds?

Is the test statistic for this test Z or t?

Select one:

a. t

b. z

2) A manufacturer of cereal claims that the mean weight of a particular type of box of cereal is 1.2 pounds. A random sample of 71 boxes reveals a sample average of 1.186 pounds and a sample standard deviation of .117 pound. Using the .01 level of significance, is there evidence that the average weight of the boxes is different from 1.2 pounds?

What is the value of the test statistic of the test? ( Enter 0 if this value cannot be determined with the given information.)

3) A manufacturer of cereal claims that the mean weight of a particular type of box of cereal is 1.2 pounds. A random sample of 71 boxes reveals a sample average of 1.186 pounds and a sample standard deviation of .117 pound. Using the .01 level of significance, is there evidence that the average weight of the boxes is different from 1.2 pounds?

What is the pvalue of the test? (Enter 0 if this value cannot be determined with the given information.)

4) A manufacturer of cereal claims that the mean weight of a particular type of box of cereal is 1.2 pounds. A random sample of 71 boxes reveals a sample average of 1.186 pounds and a sample standard deviation of .117 pound. Using the .01 level of significance, is there evidence that the average weight of the boxes is different from 1.2 pounds?

What is the relevant bound of the rejection region? (Enter 0 if this value cannot be determined with the given information.)

5) A manufacturer of cereal claims that the mean weight of a particular type of box of cereal is 1.2 pounds. A random sample of 71 boxes reveals a sample average of 1.186 pounds and a sample standard deviation of .117 pound. Using the .01 level of significance, is there evidence that the average weight of the boxes is different from 1.2 pounds?

What decision should be made?

Select one:

a. Do not reject the null hypothesis

b. Can not be determined from given information

c. Accept the null hypothesis

d. Reject the null hypothesis

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

Twocombinationdrugtherapies(TreatmentAandTreatmentB)have been developed for eradicating Helicobacter pylori in human patients. The effectiveness of these treatments depends on whether or not the patient is resistant to the chemical compound Metronidazole, but apatient’s resistance status is not routinely determined before beginningtreatment. Treatment A successfully eradicates Helicobacter pylori in 92% of resistant patients and 87% of non-resistant patients. The corresponding proportions for Treatment B are 75% and 95%.

(i) Denote by θ (0 < θ < 1) the proportion of the affected population that is resistant. If a patient from this population is unsuccessfully treated with Treatment B, write down an expression for the probability that the patient is resistant.

(ii) For what values of θ would a greater proportion of patients from this population be successfully treated by Treatment B than by Treatment A?

(iii) Suppose that θ = 0.2. If 20 patients, selected at random from the affected population, are independently treated with Treatment B, find the probability that at least 18 of them will be treated successfully.

A survey conducted of 1,000 college students asked those who regularly drink alcohol, how many alcoholic beverages they consume each week. From this survey, on average (mean), these students consume five beverages each week. These data are normally distributed. The mean, median and mode are equal, and the standard deviation is 1.

1. How many of these students consume five or more alcoholic beverages each week?

2. What is the probability that a student in this study will consume five or more alcoholic beverages each week? (decimal)

3. How many of these adolescents consume five or less alcoholic beverages each week?

4. What is the probability that a student in this study will consume five or less alcoholic beverages each week? (decimal)

5. How many of these adolescents consume between four and six alcoholic beverages each week? 6. What is the probability that a student in this study will consume from four to six alcoholic beverages each week? (decimal)

Given their performance record and based on empirical rule what would be the lower bound of the range of sales values that contains 68% of the monthly sales?

The probability of winning in a certain state lottery is said to be about 1/9. If it is exactly 1/9, what a random variable represents the distribution of the number of tickets a person must purchase up to and including the first winning ticket? Plot the PMF of this random variable. the distribution of the number of tickets purchased up to and including the second winning ticket can be described by what distribution?

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.