Suppose a population consists of the following values: 1, 2, 3, 5, 7, 9. If random samples of size 3 are to be selected without replacement and order not important, then how many samples can be taken from this population?

Q1) Below find the records of 12 randomly selected used pickup trucks (none used commercially) and 11 randomly selected used passenger cars, the time (in years) that they were kept by the original owner before being sold: Used pickup trucks | 3 | 2.5 2.9 5 4.2 3.1 3.3 4 5.3 3.8 4.5 Used passenger cars | 2.2 3 2.8 4.3 4 3.3 2.9 2.1 2 3.1 3 It is known that the standard deviation of used pickup trucks is 2 years and of used passenger cars is 1 year. (a) Investigate, at the 5% significant level, whether the mean time (in years) that used pickup trucks were kept by the original owner before sold is larger than used passenger cars. (b) What assumption is needed to perform the test in (a). (c) Construct the 96% confidence interval for the mean difference of time (in years) were kept by the original owner before sold between used passenger cars and used pickup trucks. Use this confidence interval to tell whether there is difference in the mean time (in years) between these 2 tynes of…

2. In a population it is estimated that 20% have a desired trait of interest for the researcher. The researcher wants to know how many people on average he has to draw from a population to get 2 people with the trait. Use rows 20-24 of the Random Number Table to carry out the simulation. Explain clearly how you set up the problem and report your findings. Answer:

2.4.4 A bag contains 1 red, 1 black and 1 green marble. I randomly select 1 of the marbles and record its color. I then replace it in the bag, shake the bag, and randomly select a second marble, again recording its color. The second marble is then replaced and a third marble is randomly selected and its color recorded. How many different samples of 3 colors could occur?

3. An integer is randomly chosen from the set 1, 2,..., 100. If this integer is divisible by 2 we let Y = 0, and if it is not divisible by 2 but is divisible by 3 then Y = 1. We let Y = 2 in all other cases. Find mean and variance of Y.

Find the number of ways in which one A, three B’s, two C’s, and one F can be distributed among seven stu-dents taking a course in statistics.

Here is a sample of amounts of weight change (kg) of college students in their freshman year: 13, 7, -3, -5, where -5 represents a loss of 5 kg and positive values represent weight gained. Here are ten bootstrap samples: {13, 13, 13, -3), (13, -5, -3, 13}, {13, 5, 7, 3), (7, 5, 3, 13), {-3, -3, -3, 7}, {7, 5, 7, 5), (13, 7, 5, 3}, {-5, 7, 5, 7), {-5, -3, -5, 7}, {7, 13, 13, 13). Complete parts (a) and (b) below. a. Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the mean weight change for the population. (Round to one decimal place as needed.)

A single strand of a DNA molecule is a sequence of nucleotides. There are four possible nucleotides in eachposition (step), one of which is cytosine (C). In a particular long strand, it has been observed that C appearsin 34.1% of the positions. Also, in 36.8% of the cases where C appears in one position along the strand, italso appears in the next position.1. What is the probability that a randomly chosen pair of adjacent nucleotides is CC (that has cytosinein both locations).2. If a position along the strand is not C, then what is the probability that the next position is C?3. If a position n along the strand is C, what is the probability that position n + 2 is also C? How aboutposition n + 4?4. Answer parts (a)- (c) if C appeared independently in any one position with probability 0.341.

were Classified 2. Pg, 36-7, 1.4.33. At the beginning of a Study individuals, 3% were Classified as heavy Smokers, 25.1. Smokers, and 72% were classified as as light In the 5 year study, it was determined. that the death rates of the heavy and light Smokers were 6 and 3 times that of non smokers. non- of Smokers, respectively. A randomly selected Participant died over the Syear period: Calculate the probability that the participant а nonsmorcer? was

A candy maker offers Child and Adult bags of jelly beans with different color mixes. The company claims that the Child mix has 30% red jelly beans, while the Adult mix contains 15% red jelly beans. Assume that the candy maker’s claim is true. Suppose we take a random sample of 50 jelly beans from the Child mixand a separate random sample of 100 jelly beans from the Adult mix. Let ?^ and ?^ be the sample ??proportions of red jelly beans from the Child and Adult mixes, respectively.a. What is the shape of the sampling distribution of ?^ − ?^ ? Why???b. Find the mean of the sampling distribution. Show your work.c. Find the standard deviation of the sampling distribution. Show your work.