STAT170 Workshop Notes prepared by Nan Carter for Numeracy ...

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QUESTION 3. A researcher wants to know the average sucrose content in a certain concentration of sugar-beet juice. There are two methods of measurement and the researcher wants to find out whether they both give the same mean dry weight. Ten sample containers of beet juice were randomly selected from ten different batches. Half the liquid in each container is measured using method A and the remaining half using method B. The measuring process yields the following data: METH OD 12 BATCH 1 2 3 4 5 6 7 8 9 10 A 11.0 5.0 9.8 5.7 6.5 8.2 5.9 6.0 7.5 5.4 B 11.1 5.6 9.7 5.3 6.7 8.5 5.6 5.8 7.1 5.5 Do these data support the hypothesis that both methods of measuring yield the same mean concentration? CHECKS: Q1: mean diffce = 9.267; s = 8.614; t=4.166; df=14; 0.0005
Week 8 H/Y. STAT170 workshop on the comparison of the means of two samples. (Prepared by Nan Carter for workshops at the Numeracy Centre; material taken from various sources and adapted for Stat170.) TWO INDEPENDENT RANDOM SAMPLES and the SAME VARIABLE OBSERVED ON BOTH SAMPLES We are interested in whether the two samples could come from two populations with the same mean: H0: μ1 = μ2 OR: to test if two samples come from the same population. THIS TEST IS ONLY VALID if both populations are NORMAL with the SAME SD. 13 POOL the two estimates of the unknown SD σ to find sp, then use the two-independent sample t-test. The SE(ybar1 - ybar2) = sp√(1/n1 + 1/n2), and t =(ybar1 ybar2)/SE(ybar1 ybar2) with (n1+n2–2) df QUESTION 1: The Chapin Social Insight Test is a psychological test designed to measure how accurately the subject appraises other people. The possible scores on the test range from 0 to 41. During the development of the Chapin Test, it was given to several groups of people. Here are the results for male and female students majoring in the liberal arts: Group Sex N X-bar S.D. 1 Male 133 25.34 5.05 2 Female 162 24.94 5.44 Do these data support the contention that female and male students differ in average social insight? QUESTION 2: Two groups of children were given visual acuity tests. Group 1 was composed of 11 children who receive their health care from private physicians. The mean score for this group was 26 with a standard deviation of 5. The second group, consisting of 14 children who receive their health care from the health department, had an average score of 21 with a standard deviation of 6. Assuming normally distributed scores for the populations of private and health department patients, find if the two groups of children have different scores on average. Find 90% and 95% confidence intervals for the difference between the mean scores of the two populations. QUESTION 3: An educator believes that new, directed reading activities in the classroom will help elementary school pupils improve some aspects of their reading ability. She arranges for a third grade class of 26 students to take part in these activities for an 8-week period. A control class room of 28 third graders follows the same curriculum without the activities. At the end of 8 weeks, all students are given a Degree of Reading Power (DRP) test, which measures the aspects of reading ability that the treatment is designed to improve. Nan Carter: workshop notes prepared for Numeracy Centre Macquarie University.
Page 1 and 2: STAT170 Workshop Notes prepared by
Page 3 and 4: Week 4 H/Y. Exercises for STAT170 w
Page 5 and 6: Week 5 H/Y. Questions on SAMPLING D
Page 7 and 8: EXAMPLES ON WORKING WITH PROPORTION
Page 9 and 10: EXERCISE 4. Suppose we wanted to pl
Page 11: We now have a single sample of diff
Page 15 and 16: Week 9 H/Y. Stat170 workshop on Hyp
Page 17 and 18: EXERCISE 11: In Q5 use a hypothesis
Page 19 and 20: PAIRED t-TEST: QUESTION 1. (from St
Page 21 and 22: QUESTION 4. “You can taste the lu
Page 23 and 24: sp =√[{(n1-1)s1 2 + (n2-1)s2 2 }
Page 25 and 26: a) Draw the scatterplot of the data
Page 27 and 28: Residual 20 15 10 5 0 -5 -10 -15 -2
Page 29 and 30: Residual Residual 1 0.8 0.6 0.4 0.2
Page 31 and 32: Relation: Monthly sales volume outc
Page 33 and 34: Unstandardized Residual 33 40 20 0
Page 35 and 36: mid-year exam paper (See below: the
Page 37 and 38: if the hypothesis is true. FOR EXAM
Page 39 and 40: sandwich, only 4 became ill. We wou
Page 41 and 42: Notice that a) 3.89 = 1/0.26, so if

STAT170 Workshop Notes prepared by Nan Carter for Numeracy ...

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