Determination of the Cleanliness Attitudes - Statistics Assessment Answer

Internal Code: E_AI-DGFA_HC

Statistics Assessment Answer

TASK:

Scenario 1

A large food manufacturing company seeks to determine the cleanliness attitudes of their 250 employees, compared to the general population. You are tasked to compare the cleanliness attitudes of a sample of employees with the population cleanliness attitude.

You measure employees’ responses using the Happiness at Work Scale, which validly measures work happiness. This scale provides a number from 1 to 50, where 1 refers to very low happiness, and 50 signifies extreme happiness. The population mean for “work happiness” on this scale is 25, but you don’t have access to the population standard deviation.

Your analysis will examine happiness differences between the company employees and the population. You predict the employees will show a higher work happiness score than the population.

You randomly recruit 30 employees from the 250, and they all agree to complete the Happiness at Work Scale at the organisation’s head office on a Friday morning. The data you collect from the 30 participants is shown in Table 1.

Task 1

(1) Write a results section (“draft answer”). 1 mark for this “working out”

(2) What is the name of the statistical analysis you used?

(3) What is the mean age of male and female participants?

Female =

Male =

(4) Which (if any) participant was an outlier? (Provide their ID number, or write “no outlier” if you didn’t identify anyone). 

(5) If there was an outlier, what number did you change their score to? (write “Not applicable” if there was no outlier). 

(6) Was the assumption of normality met? (Yes/No). 

(7) What were the degrees of freedom for the test statistic? 

(8) What was the value of the test statistic? 

(9) What was the probability value associated with the test statistic? (use “p < 0.001” if the SPSS output shows “0.000” in the probability box). 

(10) What was the value of the Cohen’s d effect size? (write “Not applicable” if effect size is not relevant to the Scenario 1 analysis). 

(11) Based on the value of Cohen’s d you might have calculated, how would you describe the effect size? (small, medium, large or “not applicable”). 

TASK 2

Circle the number next to the statement which most accurately summarises the research findings.

(1) The mean happiness rating of the sample was significantly higher than the population mean.

(2) The mean happiness rating of the sample was statistically equivalent to the population mean

(3) The mean happiness rating of the sample was significantly lower than the population mean.

(4) Not enough information provided to determine an answer.

TASK 3

You’ve mistakenly allowed a single, obvious design flaw to potentially affect the validity of your results. What is it? (only write a single word, phrase or short sentence; for example, “lack of reliability” or “experimenter effect”)

Table 1

ID	Sex	Age	Score	ID	Sex	Age	Score
1	F	21	43	21	F	33	40
2	M	25	42	22	F	24	35
3	F	35	44	23	F	39	46
4	M	29	49	24	F	35	42
5	F	41	41	25	F	42	44
6	M	33	41	26	F	29	39
7	F	52	42	27	M	31	45
8	M	42	48	28	F	22	42
9	F	30	50	29	M	25	2
10	F	19	42	30	M	35	36
11	M	30	39
12	M	27	44
13	F	30	43
14	M	32	45
15	F	28	38
16	M	27	38
17	M	40	41
18	F	38	46
19	M	31	39
20	F	29	40

“Score” = Happiness at Work Scale score (1- 50)

Scenario 2

A health-food company is planning to advertise their (new) twelve-day weight-gain program to the public. The company executives believe the program will be effective in helping people who have lost weight (due to various chronic illnesses) gain a healthy and sustainable weight in a short period of time. However, the company requires scientific evidence that the program is successful, if they are to proceed with the marketing plan.

To help them gather this evidence, you compile a list of 177 patients who have been identified by medical professionals as having lost significant weight through disease (which is in remission). You contact these patients and ask them whether they’d be interested in participating in your study, and if they agree they are to meet you in the company’s training room on Friday morning so you can measure their weight (kg) and provide them with the diet program. This program consists of 36 pre-packaged meals that participants self-administer during the course of the study.

35 participants turn up to your meeting, and after weighing them you explain that the program consists of eating three of the pre-packaged meals a day; morning, noon and evening for 12 days. They cannot eat anything else (to ensure control of meal portion sizes).

All 35 participants begin the program on Monday, which you label Monday Week 1. The diet regime ends on the Friday of Week 2 (12 consecutive days x 3 meals a day = 36 pre-packaged meals). All the patients are very enthusiastic and keep a diet diary for the fortnight, and you later determine that they all correctly followed instructions and ate all the meals as specified.

On the first Saturday morning after the twelve-day program ends (“Day 13”) you have a return meeting with the participants in the training room and measure their weight a second time. You now analyse the data from these participants to answer the company’s question – did the program result in a significant increase in mean weight for the participant group?

TASK 1

(1) Write a results section (“draft answer”). 

(2) What is the name of the statistical analysis you used? 

(3) What are the standard deviations for the age of male and female participants?

Male =

Female =

(4) Which (if any) participant was an outlier? (Provide their ID number, or write “no outlier” if you didn’t identify anyone). 

(5) If there was an outlier, what number did you change their score to? (write “Not applicable” if there was no outlier). 

(6) Was the assumption of normality met for both sets of weight scores? (Yes/No).

(7) What were the degrees of freedom for the test statistic? 

(8) What was the value of the test statistic?

(9) What was the probability value associated with the test statistic? (use “p < 0.001” if the SPSS output shows “0.000” in the probability box). 

(10) What was the value of the r² effect size? (write “Not applicable” if effect size is not relevant to the Scenario 2 analysis). 

(11) Based on this r², how would you describe the effect size (small, medium, large or “Not applicable”)? 

TASK 2

Circle the number next to the statement which most accurately summarises the research findings. 

(1) Mean weight after the weight-gain program was significantly higher than mean weight before the weight-gain program.

(2) Mean weight after the weight-gain program was not significantly different to mean weight before the weight-gain program.

(3) Mean weight after the weight-gain program was significantly lower than mean weight before the weight-gain program.

(4) Not enough information provided to determine an answer.

TASK 3 

You’ve mistakenly allowed a single, obvious design flaw to potentially affect the validity of your results. What is it? (write a single word, phrase or simple sentence only; for example “lack of reliability” or “experimenter effect”).

Table 2

ID	Sex	Age	Start Weight	End Weight	ID	Sex	Age	Start Weight	End Weight
1	M	43	63	71	21	M	30	59	60
2	F	39	58	55	22	M	48	57	57
3	M	29	65	68	23	F	25	66	69
4	F	29	62	72	24	F	48	71	73
5	M	23	68	76	25	M	50	64	68
6	M	37	55	59	26	M	55	55	57
7	F	38	51	60	27	F	38	62	70
8	F	56	60		28	M	42	52	58
9	F	43	62	81	29	F	27	49	51
10	M	41	69	72	30	F	33	61	61
11	F	49	70	77	31	F	22	63	64
12	M	37	63	68	32	F	56	67	146
13	F	36	62	68	33	F	63	47	49
14	M	37	51	127	34	M	67	52	58
15	M	28	54	63	35	M	61	59	61
16	F	56	60	72
17	M	25	68	67
18	M	24	65	66
19	F	28	61	63
20	F	44	53	57

“Start weight” = weight of participants immediately before the two-week weight-gain program (kg). “End weight” = weight of participants at the end of the two-week program (kg). Empty cells indicate missing data.

Scenario 3

A manufacturing company is planning to remove sound-reducing mufflers from 60 machines in a factory that produces cardboard boxes. The rationale is that the machines will operate more quickly without the muffler, hence more cardboard boxes will be produced each week. However, the 60 workers in the factory who operate these machines (one person per machine) will now have to wear noise-reducing earmuffs in the new, louder factory environment. The trouble is, the company is concerned the earmuffs might inhibit productivity, since workers will be less able to hear instructions and signals from the machines while they are operating them.

This is the company’s conundrum; while the machines will operate much faster without a muffler (hence speeding-up production of boxes), any increase in productivity might be counteracted by the worker’s inability to hear instructions and signals from the machine, slowing production of boxes. Your task it to determine which combination of conditions allows the greatest weekly output of cardboard boxes;

(1) The current work practice; muffler installed on machine, and operator with no earmuffs (Condition 1)

(2) The newly-propose work practice; Muffler removed from machine and operator wearing earmuffs (Condition 2)

You randomly assign 30 workers to one of the two conditions (meaning all 60 workers take part in the study, but only in one of the two conditions). The experiment is performed at the same time in two identical - but isolated – locations in the factory.

The employees are required to work in their assigned conditions for a full five-day week, starting Monday morning. On Friday afternoon (at the close of business) you record the number of cardboard boxes each worker had produced that week.

(Note: As an experimental control measure, you have determined that before the study is conducted, the mean production output of the 30 workers assigned to Condition 1 was equivalent to the mean production output of the 30 workers assigned to Condition 2. That is, each condition begins at the same production level.)

Your task is to answer the following question; which condition (1 or 2) produces the most number of cardboard boxes during a working week?

(Hint: perform a frequency analysis for sex of worker, calculate the mean/standard deviations of age, and run a test of normality SEPARATELY for Condition 1 and Condition 2).

Task 1

(1) Write a results section (“draft answer”). 

(2) What is the name of the statistical analysis you used? 

(3) How many levels of the IV are there? 

(4) What is the mean age of Male and Female participants in Condition 1? 

Female =

Male =

(5) Was the assumption of normality met for both Condition 1 and Condition 2? (Yes/No). 

(6) Was the assumption of homogeneity of variance met for both conditions? (Yes/No/Not applicable) 

(7) What were the degrees of freedom for the test statistic?

(8) What was the value of the test statistic? 

(9) What was the probability value associated with the test statistic? (use “p < 0.001” if the SPSS output shows “0.000” in the probability box). 

(10) What was the value of the r² effect size? (write “Not applicable” if effect size is not relevant to the Scenario 3 analysis). 

(11) Based on this r², how would you describe the effect size (small, medium, large or “Not applicable”)? 

TASK 2

Circle the number next to the statement which most accurately summarises the research findings.  

(1) Mean output for Condition 1 was significantly higher than Condition 2.

(2) Mean output for Condition 1 was significantly lower than Condition 2.

(3) Mean output for Condition 1 was not significantly different to Condition 2.

(4) Not enough information provided to determine an answer.

TASK 3

There is a single, obvious design flaw associated with this scenario that will potentially affect the results of the analysis. What is it? (write a single word, phrase or simple sentence only; for example “lack of reliability” or “experimenter effect”) 

Table 3

ID	Sex	Age	Condition	Output	ID	Sex	Age	Condition	Output
1	F	64	1	420	21	F	22	1	690
2	M	43	1	720	22	M	37	1	820
3	F	32	1	820	23	M	64	1	730
4	M	29	1	550	24	F	28	1	920
5	F	39	1	760	25	M	54	1	750
6	M	31	1	970	26	F	64	1	640
7	M	56	1	620	27	M	55	1	670
8	F	56	1	830	28	M	30	1	500
9	M	25	1	960	29	F	38	1	730
10	F	29	1	770	30	M	31	1	860
11	F	34	1	780	31	F	54	2	1040
12	F	31	1	980	32	F	39	2	810
13	M	19	1	840	33	M	31	2	940
14	M	64	1	550	34	M	60	2	1010
15	F	37	1	1030	35	F	39	2
16	M	36	1	880	36	M	28	2	900
17	M	63	1	920	37	F	49	2	980
18	F	20	1	950	38	F	49	2
19	M	43	1	900	39	M	40	2	1020
20	F	42	1	850	40	F	49	2	920

Table 3 (cont.)

ID	Sex	Age	Condition	Output
41	F	42	2	1050
42	F	46	2
43	F	49	2
44	F	21	2	990
45	F	58	2	940
46	M	33	2	1000
47	M	25	2	1020
48	F	38	2	930
49	M	35	2	940
50	F	55	2
51	F	34	2	820
52	F	65	2	905
53	M	25	2	960
54	F	40	2	1100
55	M	34	2
56	M	50	2
57	M	27	2	1030
58	M	42	2
59	M	38	2	1010
60	M	21	2	1030

“Condition” = Muffler installed, no earmuffs (1) or muffler removed, earmuffs worn (2). Empty cells indicate missing data, meaning participant did not complete a week of work in their location. Output is personal production of carboard boxes (rounded to nearest “10” digit).

Scenario 4

Following completion of the last three scenarios, your next assignment seems a much simpler (and more interesting) to undertake.

A very busy coffee-shop is experimenting with two new coffee flavours. However they only have the finances to produce and serve one variety. Your task it to determine which coffee is the most preferred by customers.

In the space of a Wednesday morning you randomly recruit customers as they walk into the shop and offer them two large, free coffees. The variety you serve to all customers FIRST is called “Hot Chilli and Black Pepper”, and the second one you serve (in this order) to all customers is called “Creamy Marshmallow Sunday”. 43 random people agree to the offer and take a seat at your “testing table”. After each coffee, the customers are required to provide a score between 1 and 100 to signify their liking of the flavour (where 1 is “dislike intensely” and 100 is “The best coffee ever tasted”). That leaves you two liking scores for each person, which you can analyse and present to the shop-owners, allowing them to make a scientifically-informed decision about which new coffee flavour is liked the most, hence that will be the variety they should introduce.

TASK 1

(1) Write a results section (“draft answer”).

(2) What is the name of the statistical analysis you used? 

(3) What is the standard deviation of the age of female and male participants? 

Male =

Female =

(4) Which (if any) participant was an outlier? (Provide their ID number, or write “no outlier” if you didn’t identify anyone).

(5) Was the assumption of normality met for both coffee types? (Yes/No/Not applicable). 

(6) Was the assumption of homogeneity of variance met? (Yes/No/Not applicable). 

(7) What were the degrees of freedom for the test statistic? 

(8) What was the value of the test statistic? 

(9) What was the value of the r² effect size? (write “Not applicable” if effect size is not relevant to the Scenario 4 analysis). 

(10) Based on this r², how would you describe the effect size (small, medium, large or “Not applicable”)? 

(11) What are the upper and lower values for the 95% confidence intervals for mean difference? 

Upper =

Lower =

TASK 2

Circle the number next to the statement which most accurately summarises the research findings. 

(1) Mean liking for “Hot Chilli and Black Pepper” coffee flavour was significantly higher than for “Creamy Marshmallow Sunday” coffee flavour.

(2) Mean liking for “Hot Chilli and Black Pepper” coffee flavour was significantly lower than for “Creamy Marshmallow Sunday” coffee flavour.

(3) Mean liking for “Hot Chilli and Black Pepper” coffee flavour was not significantly different to “Creamy Marshmallow Sunday” coffee flavour.

(4) Not enough information provided to determine an answer.

TASK 3

You’ve mistakenly allowed a single, obvious design flaw to potentially affect the validity of your results. What is it? (write a single word, phrase or simple sentence only; for example “lack of reliability” or “experimenter effect”). 

Table 4

ID	Sex		Age		C1		C2
1	M		42		21		31
2	F		46		34		37
3	M		49		22		18
4	F		21		31		22
5	F		18		51		81
6	F		33		45		32
7	F		25		50		40
8	F		38		41		33
9	M		35		38		25
10	F		25		39		18
11	F		34		30		22
12	F		20		28		16
13	M		25		29		13
14	F		40		33		16
15	F		34		30		12
16	M		50		37		27
17	M		27		36		19
18	M		42		22		20
19	M		38		38		28
20	M		21		23		13
21	F		31		37		35
22	M		45		12		5
23	M		36		40		38
24	F		32		34		14
25	M		30		39		27
26	F		20		33		29
27	F		38		42		32
28	M		27		36		31
29	F		59		31		21
30	M		46		33		24
31	F		51		37		29
32	F		64		20		18
33	M		27		23		21
34	M		25		16		14
35	F		57		27		20
36	M		21		30		20
37	F		45		34		26
38	M		24		37		28
39	F		38		28		19
Table 4 (cont.)
40	M		31		25		21
41	M		27		31		25
42	F		38		36		25
43	M		33		33		26

“C” = Coffee type where C1 = liking score for Hot Chilli and Black Pepper, and C2 is liking score for Creamy Marshmallow Sunday.

Scenario 5

The IT (Information Technology) department of a very large accounting firm wants to know whether their employees’ work satisfaction is stronger NOW than it was 10 years ago. Specifically, department managers are hoping work satisfaction scores are higher than they were in 2009, measured using the validated “Satisfaction at Work” scale (a number from 1-100, where 1 is “extremely unhappy”, and 100 is “couldn’t be happier”).

Your task is to answer the firm’s question – are employees happier now in 2019 than in 2009? There were 38 employees in 2009, the (population) mean happiness score was 50 and the (population) standard deviation was 10 (the mean age of these employees was also 82 years).

You administer the “Satisfaction at Work” scale to the current 40 employees (the population) and compare their mean score with the 2009 employee group (no employee in the current 40 was working for the company back in 2009). Can you give management good news, that today’s employees are happier?

(Hint: the number 1.64 is important for this task – go to your lecture and tutorial notes to track down why)

TASK 1

(1) Write a results section (“draft answer”). 1 mark for this “working out”

(2) What is the name of the statistical analysis you used? 

(3) What is the mean age of the Male and Female participants? 

Female =

Male =

(4) What is the standard deviation for age of the Male and Female participants? 

Female =

Male =

(5) Which (if any) participant was an outlier? (Provide their ID number, or write “no outlier” if you didn’t identify anyone). 

(6) If there was an outlier, what number did you change their score to? (write “Not applicable” if there was no outlier). 

(7) Was the assumption of normality met for the set of sample scores? (Yes/No/Not applicable)

(8) Was the assumption of homogeneity of variance met? (Yes/No/Not applicable). 

(9) What was the value of the test statistic? 

(10) Was the probability value associated with the test statistic greater or less than 0.05? (greater/less than) 

(11) In this style of statistical test, the value of 1.64 is important. What probability does this correspond to? (Hint: provide a probability value here, rounded to two decimal places). 

TASK 2

Circle the number next to the statement which most accurately summarises the research findings. 

(1) Mean “work satisfaction” is significantly higher in 2019 employees compared to 2009 employees.

(2) Mean “work satisfaction” is significantly lower in 2019 employees compared to 2009 employees.

(3) Mean “work satisfaction” is not significantly different between 2019 employees and 2009 employees.

(4) Not enough information provided to determine an answer.

TASK 3

There is a single, obvious design flaw associated with this scenario that will potentially affect the results of the analysis. What is it? (write a single word, phrase or simple sentence only; for example “lack of reliability” or “experimenter effect”) 

Table 5

ID	Sex	Age	Score	ID	Sex	Age	Score
1	M	19	70	21	M	30	73
2	F	19	78	22	M	28	75
3	M	22	76	23	F	25	76
4	F	21	83	24	F	28	83
5	M	23	75	25	M	20	73
6	M	30	85	26	M	25	75
7	F	23	80	27	F	28	74
8	F	25	74	28	M	22	94
9	F	20	76	29	F	27	62
10	M	21	68	30	F	23	65
11	F	19	74	31	F	22	83
12	M	18	78	32	M	27	95
13	F	26	66	33	M	31	76
14	M	28	85	34	M	22	66
15	M	27	94	35	M	24	85
16	F	21	90	36	F	22	87
17	M	25	82	37	F	32	75
18	M	26	76	38	M	23	74
19	F	27	72	39	F	26	72
20	F	26	89	40	F	30	64

“Score” is score on the “Satisfaction at Work” scale (0 – 100).

Scenario 6

The same accounting firm is very happy with your work on the last project (Scenario 5). Now they want to know if their proposed “Love your Job” campaign will improve current employees’ work satisfaction in 2019. This applies to ALL employees, not just the 40 in the IT department you utilised in Scenario 5.

Specifically, at the completion of the “Love your Job” campaign, will those employees who were initially the least happy show an improved work satisfaction score that is now equivalent to the happiest employees?

Before the firm implements their campaign, you administer a validated survey to measure the “work satisfaction” of the 147 employees in the company. The survey measures employee’s attitudes about their current employment status, and their future in the firm, on a scale from 0-10; where a low score signifies low job satisfaction, and a high score signifies high job satisfaction.

From the 147 scores, you select the bottom-scoring 25 employees (indicating very low job satisfaction) and the top-scoring 25 employees (indicating very high job satisfaction). The bottom-scoring employees provide a mean score of approximately 4 out of 10. The top-scoring employees provide a mean score of approximately 9 out of 10.

The firm then implements the month-long “Love your Job” campaign (which involves daily activities employees must complete with the expectation that they’ll love their job more at the end of the month than they did at the beginning of the month).

At the conclusion of the month-long campaign you re-call the 50 employees (25 low satisfaction, 25 high satisfaction) and ask them to complete a second, equivalent “work satisfaction” survey which also uses a 0-10 scale, where the higher the score, the more positive the participant’s work satisfaction. You assume that the campaign will not necessarily improve scores for the high job satisfaction employees (since they’re as happy as they can ever be). However, you expect scores will improve for the low job satisfaction group.

Therefore, assuming the “Love your Work” campaign is valid and can improve employee work satisfaction, you predict that the mean score of the low satisfaction group following the campaign will increase and be equivalent to the mean score of the high satisfaction group.

(Hint: perform a frequency analysis for sex of employee, calculate the mean/standard deviations of age, and run a test of normality SEPARATELY for Condition 1 and Condition 2).

TASK 1

(1) Write a results section (“draft answer”). 1 mark for this “working out”

(2) What is the name of the statistical analysis you used? 

(3) What is the mean age of female and male participants in the high satisfaction group? 

Female =

Male =

(4) Which (if any) participant was an outlier? (Provide their ID number, or write “no outlier” if you didn’t identify anyone). 

(5) Was the assumption of normality met for both groups? (Yes/No) 

(6) Was the assumption of homogeneity of variance met? (Yes/No/ Not applicable). 

(7) What were the degrees of freedom for the test statistic? 

(8) What was the value of the test statistic? 

(9) What was the probability value associated with the test statistic? (use “p < 0.001” if the SPSS output shows “0.000” in the probability box) 

(10) What was the value of the r² effect size? (write “Not applicable” if effect size is not relevant to the Scenario 6 analysis). 

(11) Based on this r², how would you describe the effect size? (small, medium, large or “Not applicable”)?

TASK 2

Circle the number next to the statement which most accurately summarises the research findings. 2 marks

(1) Mean “work satisfaction” is significantly higher for the “low satisfaction” employee group compared to the mean for the “high satisfaction” employee group.

(2) Mean “work satisfaction” is significantly lower for the “low satisfaction” employee group compared to the mean for the “high satisfaction” employee group.

(3) Mean “work satisfaction” for the “low satisfaction” employee group is not significantly different to the mean for the “high satisfaction” employee group.

(4) Not enough information provided to determine an answer.

TASK 3

You’ve mistakenly allowed a single, obvious design flaw to potentially affect the validity of your results. What is it? (write a single word, phrase or simple sentence only; for example “lack of reliability” or “experimenter effect”)

Table 6

ID	Sex	Age	Group	Score	ID	Sex	Age	Group	Score
1	M	39	1	6	26	M	30	2	7
2	F	59	1	7	27	M	48	2	6
3	M	29	1	6	28	F	25	2	5
4	F	59	1	5	29	F	48	2	7
5	M	23	1	6	30	M	50	2	6
6	M	37	1	7	31	M	55	2	4
7	F	36	1	6	32	F	38	2	5
8	F	56	1	8	33	M	42	2	6
9	F	40	1	5	34	F	57	2	7
10	M	41	1	6	35	F	53	2	8
11	F	49	1	7	36	F	22	2	7
12	M	37	1	8	37	M	37	2	6
13	F	26	1	7	38	M	60	2	5
14	M	38	1	6	39	M	42	2	7
15	M	27	1	5	40	M	54	2	6
16	F	51	1	7	41	F	52	2	4
17	M	25	1	7	42	F	52	2	5
18	M	26	1	6	43	M	43	2	7
19	F	47	1	2	44	F	26	2	6
20	F	46	1	7	45	F	60	2	8
21	M	36	1	8	46	F	49	2	7
22	F	36	1	7	47	M	40	2	9
23	M	38	1	6	48	F	51	2	3
24	F	42	1	9	49	M	38	2	6
25	M	43	1	8	50	M	29	2	7

“Group” = Participation in either the low work or high work satisfaction groups, where 1 = Low satisfaction and 2 = High satisfaction. “Score” is score on the work satisfaction scale (0 – 10).

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