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Homework answers / question archive / 1)Suppose 30% of OSU students watch reality TV shows of some kind every week

1)Suppose 30% of OSU students watch reality TV shows of some kind every week

Statistics

1)Suppose 30% of OSU students watch reality TV shows of some kind every week. Ten OSU students are selected at random and asked if they watch reality TV of some kind each week. You want the probability that at least 4 of them say yes.

    1. What does X represent in this problem?
    2. Show BRIEFLY that X has a binomial distribution.
    3. Find the probability that at least 4 of the students say yes.
    4. Could a person use the normal approximation to answer this question? Explain briefly.

 

  1. Again suppose 30% of OSU students watch reality TV shows of some kind every week. Now 100 OSU students are selected at random and asked if they watch reality TV of some kind each week. X = number in the sample who watch reality TV of some kind each week.
    1. Find the mean and SD of X.
    2. Justify that X has an approximate normal distribution.
    3. Use the normal approximation to find the probability that at least 40 of the students in the sample say yes.
    4. Explain why being able to use the normal approximation for the previous question is a GOOD THING. (What would you have to do otherwise?)

 

  1. Suppose it is reported that 10% of OSU business students major in international marketing. You sample 200 OSU business students at random. Let X = the number of students in the sample who major in international marketing.
    1. How many students in your sample do you EXPECT to major in int’l marketing, according to the above information?
    2. What is the probability that your sample finds that at least 15 students major in international marketing?
    3. Are your findings typical of what you EXPECTED to get? (Think about your answers to parts a and b.)

 

  1. Suppose a media report claims that 25% of children are addicted to video games. You think the percentage is higher than that. You take a random sample of 200 children and find that at least 70 of them are addicted to video games.
    1. What is the chance of this result happening?
    2. Based on your results do you believe the claim that 25% of children are addicted to video games? Why or why not?

 

  1. Suppose X is binomial with p = .10. What does n have to be (at a minimum) to use the normal approximation for X?

 

  1. Suppose X is binomial with p = .90. What does n have to be (at a minimum) to use the normal approximation for X?

 

  1. Explain why the same n works for both of the previous problems.

 

 

 

  1. If X has a binomial distribution, X is counting the number of ‘successes’ found in the sample of size n. We know the variance is np(1-p).
    1. Choose a value of n, and graph the variance function f(p) = np(1-p) where the values of p go from 0 to 1. It should look like a parabola opening downwards.

 

    1. For which value(s) of p is the variance of X the largest? (Don’t change n.)
    2. Why does this make sense?
    3. For which value(s) of p is the variance of X the smallest? (Don’t change n.)

 

 

Sampling Distribution

  1. What do we call the set of all possible sample means from all possible samples of size n from a population?
  2. What does the symbol µx stand for?
  3. What does the symbol σx stand for?
  4.  What does the symbol  stand for?
  5. What does the symbol stand for?

 

  1. What is another name for
  2. What is the formula for

                       

 

  1. If the random variable X has a normal distribution, then the random variable has a

 

  1.  If you sample one test score at random, what is the chance that it will be less than 65?

 

 

 

  1. If you sample 36 test scores at random, what is the chanced that the average will be less than 65?

 

  1. Explain why the answer to #9 is less than #10. (Hint, draw a picture of the distribution of X for #9 and a picture of the sampling distribution of for #10, and compare them.)

 

 

 

 

 

 

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