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These are the practice questions that will give you experience in tackling the methods we are discussing.  The ones you should be able to do at this stage are shown with numbers highlighted.... 

PLEASE NOTE: Some of these questions are presented in a "full" form- suitable for a longer working time (as in a take-home assignment).  The questions you will see in the exam will NOT be more complicated than these, and MOST of them will be much simpler, or have more of the answer already calculated for you.  

  The answers to these problems are given here. 

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1.  You are investigating risk factors for contracting Yersinia enterocolitica infection. A group of 22 patients has been identified as well as a group of 40 non-Yersinia controls.  The following data include possible exposures in the previous month.  The figures shown are the number in each group who answered 'yes'.

2. Before the analysis can proceed with data from a questionnaire, the age distribution of the two groups must be checked to help confirm unbiased sampling.  Type A respondents (N=120) have a mean age of 32.0 years, with a standard deviation of 7.2 years.  Type B respondents (N=130) have a mean age of 33.2 years with a standard deviation of 7.5 years. How likely is it that the differences in the mean ages occurred by chance?

3. Pre-testing and post-testing of knowledge at a patient-lifting training course for nurses has yielded the following summary.  Note that the differences (d) = post-test minus pre-test. The mean difference (đ) = 13 points, 22 df,  P>0.05      Which of the following is/are correct?

    [i] that is all but 5% of cases, there was a significant increase in knowledge of 13 points

   [ii] that more than 5% of the people scored 13 points more on the post-test than on the pre-test.

  [iii] that each of these 23 people could be expected to score 13 points more on the post test in 5% of repeated trials.

  [iv] that an overall mean improvement of 13 points could be expected (if the null hypothesis were correct) more than 5% of the time.

6.  The following data are taken from a food-specific attack rate table and represent one food (of many).  Display the values in a contingency table and choose a suitable method of testing the null hypothesis of "no association".  Report your findings in clear terms.

7.  The time between taking a water sample and having the sample analyzed is being investigated.  Beginning with a known suspension of coliforms, and with temperature remaining constant, the following data are collected.  [THE ADDITIONAL INFO HAS NOW BEEN ADDED TO THIS QUESTION]

 In addition, the following results have been obtained (meaning that you do NOT have to start the analysis from the beginning (although the practice is very valuable!)     

 On a scattergram, draw the regression line, and test the null hypothesis that beta=zero. (Don't forget to also check that the CL around the slope do NOT include the line of b=0 )   Predict the colony count after 20 hrs.  Is the count dependent upon time? summarize clearly.  [For a bonus point DRAW the confidence limits as lines on the scattergram; using any convenient (x,y) common point for all FOUR lines]  

8.   In buildings where very little fresh air is introduced the CO2 concentration increases over the working day.  You are studying the relationship, if any between (X) the CO2 conc. (in ppm) in the air of 16 government buildings, and (Y) the number of complaints about 'stale air', 'bad air', etc. per person, per year.  The regression is linear and is described by the following:  Y' = 324 + 0.016 (X)   The confidence limits are calculated as CL(95%) = 0.016 +/- (t _{0.05, 14df} )(0.11).

       (a) test the null hypothesis that Beta = zero

       (b) what is the estimated number of complaints/p/yr when CO2 is 300 ppm

       (c) How would you summarize the relationship?

9.   An excursion to Ethoipia has resulted in illness among a party of 22 Canadians.  The risk factors are shown, together with the number of people who were exposed to each factor, and the number ill in both exposed and non-exposed groups.  Calculate the odds ratio for each factor, and test the null hypothesis for the factor having the strongest association.

10.   The following figures represent results of a trial to measure the body length in cm (Y) of a rodent species as a function of age (X) in days after birth.

(a) draw the scattergram using suitable axes

(b) draw the regression line on the scattergram

(c) place upper and lower confidence limits around the regr line so as to pass through the MEAN of X

(d) Test the null hypothesis that beta =zero

(e) What is the probability that these results could have occurred by chance (in the absence of any real relationship)?

(f) Predict body length when age = 8 days

(g) Is body length dependent upon age for these animals in their first 17 days.  How would you summarize?

11.   In a workplace where lead solder is used, the concentration of lead fumes (Y) is being measured as a function of the number of hours (X) that soldering is being carried out.  The test begins on a Monday after two days of no operations, and runs for 30 hrs non-stop.  The lead measurements are in micrograms per litre of air and are taken each hour for 30 hrs.

The relationship is described by the model Y' = 24 + 5.1(X) and the 95% confidence limits are calculated as CL(95%)= b +/- (t_0.05,28df)(2.1).

(a) Draw the regression line and confidence limits on a suitable scattergram (even through you don't have the original data)

(b) Test the H_o: that beta = zero

(c) What is the estimated conc. of lead in the air at 10,20, and 30 hrs?

(d) How would you summarize the relationship shown?

13.   You are investigating the effects of lighting upon accidents in a car-assembly plant.  There are two assembly lines, identical, except for the lighting. Line B has been fitted with new, broad spectrum lighting at greater intensity.  Line A retains an older form of lighting.  The number of accidents per month are recorded for 2 years, and compared using a t-test. 

The results are summarized as follows:   meanA — meanB = 3.4       t = 2.104        df_____      P_________

    (i)  Complete the summary line by adding the df value, and the probability of such a difference occurring by chance alone

   (ii)  What is the value of the standard error of the difference between two means?

  (iii) Answer this question in clear, everyday language:  "Does the new lighting seem to be associated with a reduction in accidents?"

15.     A new device for measuring carbon dioxide is being compared with a standard device.  Nine trials are run, each involving a measurement with both devices.  The data are as follows:

16.      In an attempt to compare the bacteriological quality of two types of imported, bottled water, 20 bottles are sampled of each type.  The results show that standard deviation of bacterial counts from each type were the same:  16.0 cells/ml. but the mean counts were different: 105 cells/ml (type Y) and 85 cells/ml (type Z),    How would you summarise the findings?   

17.      Twelve medical students from University A are being compared with 11 medical students from University B in an pharmacology knowledge quiz scored out of a possible 20.   Is there convincing evidence that the two groups are different?

18.     Health programs are being evaluated for costs.  The rabies control program and the food safety program are being compared on average person-hours expended per incident.   There were 11 rabies control incidents and 9 food incidents in 2011.  Analyze the data and comment on the difference in hours, if any, between the program. 

19   An automated device for counting bacterial colonies on an agar plate is being compared to an experienced lab technician.  A series of six specially prepared petri dishes are counted by both methods and the results compared.  Are you able to determine if the machine and the lab technician differed to any significant degree?

20   After returning home from an international conference,  twenty-four delegates appear to have fallen victim to a mysterious respiratory ailment.  Possible risk factors for these people and those for forty non-ill conference attendees are being examined.  Calculate the odds ratios for each factor.  For the factor with the strongest association only, test the null hypothesis of "no association".  Summarize for the five factors fully.

21   After data collection, but before analysis, the data are checked to ensure that they are unbiased. Determine if the following figures are similar in the two groups prior to the commencement of a study:

22.   Is there evidence of a difference in monthly accidence rates at the following two plants between January and December 2009?  Both plants are of similar design in all respects except that "Epsilon" has 'non-slip' floors and "Omega" does not.

23.   Roach bait-and-trap stations are being evaluated.  A test-location is set up in each of five infested buildings.  At each station a carbohydrate-based bait and a protein-based bait are used, and the numbers of trapped roaches are recorded for each bait and at each station.  Analyse the data and report fully.

24.   Days to full recovery is the dependent variable in a trial of two treatment methods for 13 workers diagnosed with a spinal condition.  Analyse the data and determine if one method is significantly more efficient that the other:

25   Increased ventilation in the workplace is being examined as an aid to worker's respiratory health.  Ten cabinet makers working in an improved ventilation environment are compared with eight working in poorly-ventilated workshop under otherwise similar conditions.  Their lung functions are measured on a scale from 1 (poor) to 8 (perfect) as shown below.  Analyze the data and report on any apparent difference between the two groups.  What comments might you make about the design of this study?   What other factors would you need to know?

26   State the null hypothesis and summarize the following, giving a probability (P) value                      

27    State the null hypothesis and summarize the following, giving a probability (P) value

28   Workers in a fibre-glass production facility are being tested for hypersensitivity to the resin catalysts being used. Twenty workers exposed to fibre-glass resin and 40 workers not exposed to resins are given sensitivity tests.  Fifty-five percent of the exposed group are found to be sensitive, but only 12 of the not-exposed workers were found to be sensitive to the resins. Analyze and summarize fully.

29   An antiseptic cream is being used in a food plant in an attempt to control the presence of Staph. aureus bacteria.  After six weeks the wokers' handsare swabbed to compare the flora.  Of 40 workers who have used the cream, 36 were free from Staph. aureus on their hands.  Of 48 who had not used the cream, two-thirds were free from Staph. aureus. What can you state about the cream's effectiveness in controlling this bacterium?

30  The ability of a new ultra-violet flying insect trap to attract more insects that an ordinary 15 w light bulb is being investigated.  At the end of 10 days, the flies-per-day totals are compared as follows:

   Ultra-violet trap : mean: 74 flies (std.dev. : 16 )

  15w light bulb : mean: 42 flies (std.dev. : 18 )

How would you evaluate these results using an appropriate test of the null hypothesis?

31   Twelve (12)   samples of water are taken at each of two water storage reservoirs.  The nitrate content (in parts per million) was recorded as follows. Assuming unbiased data, state the null hypothesis, and test it at 0.05 level of significance.

34   The foods prepared in a commissary are being sampled to determine the incidence of Staphylococcus aureus, and to track the possible source of the bacteria.  The data collected include product (sandwiches [S], pies [P], wraps [W] ), production line (#1 or #2), and the shift (am, pm) in which the food was prepared. Analyse the data, and consider also the distribution of the dependent variable!

35.  The health unit is investigating the spread of a water-borne gastro-enteritis at a school.  The following data have been collected and your job is to test the association between water consumption and the risk of becoming ill.

                           * Total number of students who were ill: 37    

                          * Total number of students in the study: 89

                         * - of those 26 who usually drink more than 5 cups of water/day: 15 ill

                        * - of those 30 who usually drink more than 5 cups of water/day: 14 ill

                       * - the remainder usually drink less than one cup/day

38   The following are taken from different outbreaks. (So the totals are different). For each item, make an appropriate test of the null hypothesis, and include odds ratio results in your interpretation. (THREE separate discussions needed).

    Milk pudding    ate: 15,    (ill: 10),      did not eat: 18,    (ill: 9)    

    Ham Pie          ate: 31,    (ill: 13),      did not eat:  26,   (ill:20)

    Egg Salad        ate: 11,    (ill: 6),        did not eat: 7,      (ill:2)  

39   In a study of indoor air quality, workers are asked to rate air-"freshness" of thebuilding on a five-point scale in which '1' was 'very comfortable' and '5' was 'very uncomfortable'. Also collected at the same time are the relative humidity (RH%) and air velocity (VEL) in cm/sec.  Determine if any relationship exists between the reported rating and either of these two factors.  Also consider if these two factors might be themselves related; how would you test that idea?

40   You are attempting to determine the effects of acidified water on leaching of lead from plumbing fixtures.  The following trials are carried out using various pH levels in contact with lead-soldered fittings for 24 hrs.  Describe the effects, if any.

41   The following data are collected from a workplace because a suggestion has been made that exposure to styrene increases the risk of dermatitis. Carry out an appropriate analysis to determine if there is any convincing evidence of this association.  Of workers exposed to styrene vapour, 14 have dermatitis and 22 do not.  Of the workers not exposed to styrene vapour, only one in six suffer from dermatitis.  Total workers in the study: 72.

42   As part of the evaluation of a safety-education program, a pre- and post-test are administered.  The following scores were recorded from a class of eight persons. Determine the effectiveness of the knowledge-acquisition. (Dependent variable = percentage correct answers). Analyze and interpret fully.

43   In evaluating the effectiveness of different methods of presenting health and safety education sessions, fifteen learners are assigned at random into one of three methods of presentation.  Using ANOVA, test the null hypothesis that the methods are equal in teaching effectiveness.

46   The following data relate to the chlorine residual in a swimming pool at various times after it has been treated.

47   A bisulphite based formaldehyde-scavenging compound is being tested in eight houses containing urea-formaldehyde foam insulation.  A still-air measurement of formaldehyde vapour is taken prior to treatment and another measurement taken seven days after the treatment with bisulphite.  The following data are presented to you with the request to analyze and comment upon the effectiveness of the treatment.

49   In a study of dietary intake of metals, the following measurements for aluminum and zinc in the blood of 12 persons are recorded (micrograms/100 ml blood)

a. Make a scattergram of the data

b. Describe any relationship between the variables

c. Compute the correlation coefficient

d. Would you be justified in stating that there is a cause-and-effect mechanism operating here?

Test the correlation coefficient from (c) and determine if it differs significantly from zero

50   In 1963, an outbreak of type E botulism occurred in Kentucky and Alabama.  Antitoxin for type E botulism was used, one of the first trials in North America.  Of the 17 cases, five died. Of the twelve survivors, eight had been treated with type E antitoxin.  None of the five fatalities had received the antitoxin.     Arrange the data into a form suitable for analysis.  Test the null hypothesis that there was no association between survival and having received the antitoxin.

51    A new disinfectant compound is being evaluated for use in dairy plants.  Ten different types of stainless steel milk-contact surface are inoculated with a suspension of E. coli bacteria in milk.  The surfaces are treated on the left side with the new compound, and on the right side with the standard compound.   The counts are then compared after suitable incubation.  Use a suitable means of analysis on the data. (Dependent variable: percentage of live E coli cells remaining).

52     The mean number of dead insects (out of original 50) is shown for each pesticide.  Note that the ANOVA table has been largely completed.  Finish the table, and report fully. 

53   The results of a test of muscle strength are delivered to you.  You establish a null hypothesis and carry out an (unpaired) t-test on ten measures

  With treatment    Without treatment                     (five in each group) because nothing suggests that the data were paired. 

          7.8                     8.9                                     Later, you are told that the data were gathered from the SAME FIVE PERSONS,

          5.0                     7.1                                     before and after the treatment.  The correct analysis now becomes a t-test

          2.1                     4.5                                     for PAIRED data.  Carry out BOTH analyses.  Compare the two results.  What values

          5.5                     7.7                                     are the same?  Comment on the apparent discrepancy in statistical significance.  Why is this so?

        10.0                   11.9

54   The following foods are being examined for association with illness.  Deal with each food separately.  Calculate the odds ratio and test the null hypothesis by means of appropriate analytical methods.  Summarize fully. [Note: IF Fisher's test is required, please generate a complete and accurate "P" statement]

56   The effect, if any, of using iodophor hand-dips in supermarket delicatessen departments is being evaluated.  A total of 174 swab-tests are taken from the hands of employees working with no hand-dips, with Salmonellae species being reported as 'present' or 'absent'.  Eighty (80) swabs are taken from the hands of employees in stores where the dip has been introduced. Salmonellae are isolated from 24 non-dipped hands, and 22 "dipped" hands.  Comment on the effectiveness, if any, of the hand dips.