7.(16 pts) The first exam grades of last semester\'s Stats class had a mean of 6

Question

7.(16 pts) The first exam grades of last semester's Stats class had a mean of 67 with a a. Jenny received a score of 80. What is her z-score? Is it positive or negative? the average? How c. Anne's z-score was a 0. What does this tell you about her score in relation to the d. John received a score of 65. What is his z-score? Is it positive or negative? standard deviation of 5 points. Answer the following questions Why? b. Michael's z-score was a -1.5. Did he do better or worse than t can you tell? And by how many points? mean Why? For the students in the first part of this question (Jenny, Michael, Anne, and John): e, which (if any) students fall into the middle 68% of the distribution? f, which (if any) students fall outside ofthe middle 68% of the distribution? g, which (if any) students fall into the top 5% of the distribution? e, h, which (if any) students fall into the bottom 5% of the distribution? 8. (10 pts) SPSS: For the following data: x={ 3, 4, 7, 6, 5, 1, 4, 3, 4, 4, 5, 4, 0, 3, 5, 4, 4, 4: a. Use SPSS to find the Mean, Median, Mode and Standard Deviation. Paste your b. Construct a frequency histogram of this data, with a discrete x-axis that starts at c. Describe the distribution (modes, skew, etc) and indicate how the relationship d. Using SPSS, convert each score in this distribution into a z-score. Then output: 0 and ends with 7. Paste below between the mean and median also reflects the observation you have made construct a frequency histogram of the z-scores (x-axis should span from-3 to 2, because you should not have any z-score values outside of this range). Paste below: e. Describe the similarities between the raw-score histogram you created and the z- score histogram. What are the differences, if there are any? 9.4 pts) SPSS: For the following set of J 2014 temperature (in Fahrenheit) data: x = { 26, 45, 31, 28, 52, 7, 40, 34) Find the mean, median, mode, range, standard deviation, and variance in SPSS. Paste below ONE table which contains all of the above statistics. Indicate the steps you took to construct this table

Explanation / Answer

mean = 67
std. dev. = 5

As per central limit theorem,
z = (x - mu)/sigma

a) for x = 80
z = (80 - 67)/5 = 2.6
The score is positive because value of x is greater than the mean

b) for z = -1.5
x = 67 - 1.5*5 = 59.5
He did worse than the average as he scored 59.5 which is less than 67 by 7.5 points

c) As Anne's z-score is 0, she scored same as mean i.e. 67 because we get z = 0 in the CLT formula when x = mu

d) for x = 65
z = (65 - 67)/5 = -0.4
The score is negative because value of x is less than the mean

e) In order to fall into middle 68%, score should be within 1*sigma level from the mean i.e. 67 +/- 5. Hence Anne and John fall in this.

f) Jenny and Michael fall outside this

g) For top 5%, z-value = 1.64 or greater
Hence Jenny falls in this

h) For bottom 5%, z-value = -1.64 or less
Hence none falls in this

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