Math 135 Review Test 1
Answer key
1) a) C-Q
b)
c) Yes, a relationship appears to exist between job satisfaction and job class. Hourly craft employees generally have lower job satisfaction survey scores than either salaried employees or clerical employees.
d)
Summary statistics:
Mean / Std. Dev. / Median / Range / Min / Max / Q1 / Q3HrlyCrft / 54.875 / 14.798045 / 60 / 38 / 32 / 70 / 41.5 / 67
HrlyClerical / 63.75 / 15.80913 / 60.5 / 50 / 44 / 94 / 53.5 / 72
Salaried / 66.25 / 19.88359 / 71 / 52 / 37 / 89 / 48 / 83
Yes…this confirms our conclusions from part c. The mean satisfaction survey score for hourly craft employees is lower than the mean survey scores of the other two job classes (with a standard deviation that is less than the other two – indicating that the scores are less variable for the hourly craft employees as well)
2) a) Histogram or stemplot would be appropriate here. Shape: Roughly symmetric with a slight right skew and a high outlier (confirmed by the fact that the mean is over 3 points higher than the median). If the outlier remains in the data set for analysis, we should report the median as the measure of center and the 5# summary as the measure of spread.
b) Bar Graph* using percents : Hourly Craft – 71%; Hourly Clerical -- 17%; Salaried – 13% The majority of employees at this company are hourly craft employees. Salaried employees represent the smallest classification for the North Trust Bank. *we will construct the bar graph in class if necessary.
c) The company should work to improve job satisfaction for the hourly craft employees – since these employees comprise the largest group and they are the most dissatisfied with their jobs.
3) a) QQ b) Scatterplot is shown below. Roughly linear with an outlier (employee with 38 years of service and a salary of $47,000); direction is positive, strength: moderate to weak based on the visual)
c) y-hat = 44.178 + 0.458x ; correlation, r = 0.4168; r^2 = 17.4% the correlation value of 0.4168 (since it is close to 0.4) confirms our suspicion that the relationship is a positive, moderate to weak linear association. Interpretation of the slope: for each additional year of tenure a person will make on average (according to the model) $458 more per year.
d) yes, there is an outlier; yes, the outlier is influential since by removing that individual (employee #47) the new recomputed correlation value, r = 0.772 (which is substantially higher than the original value of 0.4168. The new regression equation is y-hat = 36.332 + 1.25x. Using the new regression equation, the predicted annual salary for an employee who has been working for North Trust for 17 years would be 36.332 + 1.25*17 = 57.582 in thousands (i.e. approx. $57,582)
e) The residual plot shows a fairly random scatter of points – i.e. there is not discernable pattern present in the plot (indicating that the linear model is a good fit).
4) a) Explanatory Variable is the Treatment Type and the Response Variable is whether the patient had a Cocaine Relapse
b) Create 3 bar graphs* one for each treatment type. Use percents based on the row totals for each treatment. *We will construct in class if necessary.
c) Yes; Desipramine appears to have the greatest success rate 58% compared with Lithium’s success rate of 25% (which was only slightly better than the success rate of the placebo – 17%);
5) Ho: The average wattage of the shipment of bulbs is equal to 60 watts.
Ha: The average wattage of the shipment of bulbs is not equal to 60 watts.
6) Patient Name: C Illness Type: C
Pain Level: Q Pulse Rate: Q
Insurance: C
7) The conversion formula for Celsius to Fahrenheit is F = 1.8*C + 32; When computing the new mean – the old mean would change exactly according to the conversion – that is NewMean = 1.8*OldMean + 32; the standard deviation would be unaffected by the addition, so the NewStdDev = 1.8*OldStdDev.
8) a) %X > 40
%Z > (40-44.6)/14.5
%Z > -.32
= 100% - 37.45%
= 62.55 %
b) %X < 50
%Z < (50-44.6)/14.5
%Z < .37
= 64.43 %
c) 50 < %X < 60
(50-44.6)/14.5 < %Z < (60-44.6)/14.5
.37 < %Z < 1.06
= 85.54 % - 64.43 %
= 21.11%
Part II Multiple Choice:
1. c 2. c 3. b 4. a 5. c 6. c 7. b 8. a 9. a 10. a 11. a 12. b
13. b 14. c 15. a