7. For the table that follows, answer the following questions: x y 1-1/4 2-1/2 3-3/4 4

Size: px

Start display at page:

Download "7. For the table that follows, answer the following questions: x y 1-1/4 2-1/2 3-3/4 4"

Eleanor Bishop
5 years ago
Views:

1 7. For the table that follows, answer the following questions: x y 1-1/4 2-1/2 3-3/4 4 - Would the correlation between x and y in the table above be positive or negative? The correlation is negative. - Find the missing value of y in the table. The most obvious estimated y value for x=4 is y = 1. - How would the values of this table be interpreted in terms of linear regression? These values form a perfectly straight line, so the best-fit line would pass through the points exactly. - If a line of best fit is placed among these points plotted on a coordinate system, would the slope of this line be positive or negative? The slope of the best fit line would be negative: slope = 1/4.

2 8. Determine whether each of the distributions given below represents a probability distribution. Justify your answer. (A) x P(x) /12 1/3 1/6 (B) x P(x) 0.1 3/5 0.3 (C) x P(x) A and C both sum to greater than 1, while B sums to 1 exactly, so B is the only candidate for a probability distribution.

3 9. A set of 50 data values has a mean of 25 and a variance of 36. I. Find the standard score (z) for a data value = 31. z = x µ = σ 36 = 1 II. Find the probability of a data value > is 1 standard deviation away. Thus, P x µ > σ ( ) = = III. Find the probability of a data value < 31. Show all work. P = =

4 10. Answer the following: (A) Find the binomial probability P(x = 5), where n = 14 and p = P(k) = n! k!(n k)! pk (1 p) n k P(5) = 14! = = = 2,002 5! 9! ,384 = (B) Set up, without solving, the binomial probability P(x is at most 5) using probability notation. The probability of k successes out of n trials, when the probability of success on a single trial is p, is n! P(x) = k!(n k)! pk (1 p) n k (C) How would you find the normal approximation to the binomial probability P(x = 5) in part A? Please show how you would calculate µ and s in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations. We can approximate the binomial probability distribution with a normal distribution with the following mean and variance: µ = np s 2 = np(1 p) We compute the z-score for some value k as: z = (k µ) ± 1 2 s

5 7. For the table that follows, answer the following questions: x y 1-1/4 2-1/2 3-3/4 4 - Would the correlation between x and y in the table above be positive or negative? The correlation is negative. - Find the missing value of y in the table. The most obvious estimated y value for x=4 is y = 1. - How would the values of this table be interpreted in terms of linear regression? These values form a perfectly straight line, so the best-fit line would pass through the points exactly. - If a line of best fit is placed among these points plotted on a coordinate system, would the slope of this line be positive or negative? The slope of the best fit line would be negative: slope = 1/4.

6 8. Determine whether each of the distributions given below represents a probability distribution. Justify your answer. (A) x P(x) /12 1/3 1/6 (B) x P(x) 0.1 3/5 0.3 (C) x P(x) A and C both sum to greater than 1, while B sums to 1 exactly, so B is the only candidate for a probability distribution.

7 9. A set of 50 data values has a mean of 25 and a variance of 36. I. Find the standard score (z) for a data value = 31. z = x µ = σ 36 = 1 II. Find the probability of a data value > is 1 standard deviation away. Thus, P x µ > σ ( ) = = III. Find the probability of a data value < 31. Show all work. P = =

8 10. Answer the following: (A) Find the binomial probability P(x = 5), where n = 14 and p = P(k) = n! k!(n k)! pk (1 p) n k P(5) = 14! = = = 2,002 5! 9! ,384 = (B) Set up, without solving, the binomial probability P(x is at most 5) using probability notation. The probability of k successes out of n trials, when the probability of success on a single trial is p, is n! P(x) = k!(n k)! pk (1 p) n k (C) How would you find the normal approximation to the binomial probability P(x = 5) in part A? Please show how you would calculate µ and s in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations. We can approximate the binomial probability distribution with a normal distribution with the following mean and variance: µ = np s 2 = np(1 p) We compute the z-score for some value k as: z = (k µ) ± 1 2 s

9 11. Assume that the population of heights of male college students is approximately normally distributed with mean of inches and standard deviation of 6.86 inches. A random sample of 93 heights is obtained. Show all work. (A) Find (B) Find the mean and standard error of the distribution (C) Find (D) Why is the formula required to solve (A) different than (C)? This problem is missing some key parts. B) Mean is 72.83, with standard error = 6.86 / sqrt(93) =

10 12. Determine the critical region and critical values for z that would be used to test the null hypothesis at the given level of significance, as described in each of the following: (A) and, a= 0.10 (B) and, a= 0.05 (C) and, a= 0.01 Missing data, can t answer.

11 13. Describe what a type I and type II error would be for each of the following null hypotheses: : There is no difference between the two sports. Type I error: rejects the null hypothesis when it is in fact true. So in this case, a Type I error would be to conclude that there is a difference, when in fact there is none. Type II error: don t reject a null hypothesis when it is in fact false. So, in this case, a Type II error would be to conclude there is no difference, when in fact there is a difference.

12 14. A researcher claims that the average age of people who buy lottery tickets is 60. A sample of 30 is selected and their ages are recorded as shown below. The standard deviation is 7. At? = 0.01 is there enough evidence to reject the researcher s claim? Show all work Computed mean = 62.9 Number of samples = 30 Standard deviation = 7 (not what I compute, but OK) This gives a p-value of , so the hypothesis that the mean is 60 is not rejected at the 1% level.

13 15. Write a correct null and alternative hypothesis for testing the claim that the mean life of a battery for a cell phone is at least 90 hours. Let µ be the mean life of the cell phone battery. Null hypothesis: µ < 90 hours. Alternative hypothesis: µ >= 90 hours.

No, because np = 100(0.02) = 2. The value of np must be greater than or equal to 5 to use the normal approximation.

No, because np = 100(0.02) = 2. The value of np must be greater than or equal to 5 to use the normal approximation. 1) If n 100 and p 0.02 in a binomial experiment, does this satisfy the rule for a normal approximation? Why or why not? No, because np 100(0.02) 2. The value of np must be greater than or equal to 5 to