Stuart Bloom is a senior manager at a global accountancy and professional services firm. He has noticed that there appears to be a general feeling of dissatisfaction and low morale in the company and he would like to investigate this. As well as wanting to establish whether people are dissatisfied at work, he would also like to investigate whether the suspected low morale is affecting productivity. Although not a trained statistician, Stuart has taken some courses in data analysis, albeit quite a long time ago, and feels confident that he can carry out a quick bit of research to explore the issues. However, as a senior manager he is pressed for time so decides to ask just 10 employees from the company to rate their job satisfaction as a percentage, where a higher percentage indicates greater job satisfaction. Prior to doing this, he reviewed the employment records for these employees and assigned a productivity score to each of them. The productivity score is a calculated percentage based on achieved targets and outcomes. The data Stuart collected is shown in the Table. EMPLOYEE 1 2 3 4 5 6 7 8 9 10 SATISFACTION 37 29 44 56 61 83 37 52 26 67 PRODUCTIVITY 41 37 29 60 47 85 29 29 20 62 a)Using the data in Table 3.1, calculate the mean satisfaction score and the mean productivity score for the 10 employees. Clearly state the formula used. b) Stuart would like to feel confident that the mean satisfaction score calculated from his sample of 10 employees is an accurate estimate of the mean satisfaction score of all employees in the company (i.e. his population of interest). Specifically, he would like to be 95% certain that his estimate is within 10% of the true mean satisfaction score. If we estimate that the population standard deviation for satisfaction score is 18%, is Stuart’s sample size large enough to give him his desired level of accuracy? Show all steps of your calculations, including any formulas used. c) After collecting the data in Table , Stuart makes a quick decision to calculate the correlation between satisfaction score and productivity score for the 10 employees. He decides to calculate Spearman’s rank correlation coefficient as he remembers studying this in one of his data analysis courses. Critically discuss Stuart’s decisions at this point.
Stuart Bloom is a senior manager at a global accountancy and professional services firm. He has noticed that there appears to be a general feeling of dissatisfaction and low morale in the company and he would like to investigate this. As well as wanting to establish whether people are dissatisfied at work, he would also like to investigate whether the suspected low morale is affecting productivity.
Although not a trained statistician, Stuart has taken some courses in data analysis, albeit quite a long time ago, and feels confident that he can carry out a quick bit of research to explore the issues. However, as a senior manager he is pressed for time so decides to ask just 10 employees from the company to rate their job satisfaction as a percentage, where a higher percentage indicates greater job satisfaction. Prior to doing this, he reviewed the employment records for these employees and assigned a productivity score to each of them. The productivity score is a calculated percentage based on achieved targets and outcomes. The data Stuart collected is shown in the Table.
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EMPLOYEE 1 2 3 4 5 6 7 8 9 10 |
SATISFACTION 37 29 44 56 61 83 37 52 26 67 |
PRODUCTIVITY 41 37 29 60 47 85 29 29 20 62 |
a)Using the data in Table 3.1, calculate the mean satisfaction score and the mean productivity score for the 10 employees. Clearly state the formula used.
b) Stuart would like to feel confident that the mean satisfaction score calculated from his sample of 10 employees is an accurate estimate of the mean satisfaction score of all employees in the company (i.e. his population of interest). Specifically, he would like to be 95% certain that his estimate is within 10% of the true mean satisfaction score. If we estimate that the population standard deviation for satisfaction score is 18%, is Stuart’s
c) After collecting the data in Table , Stuart makes a quick decision to calculate the
d) Stuart recalls that in order to calculate Spearman’s correlation coefficient he must first convert his data into ranks. He has started to do this in Table 3.2 on the next page but has not yet completed the ranks for the satisfaction variable. By referring back to Table 3.1 (page 16), fill in the ranks in Table 3.2 for the satisfaction variable. The productivity scores have already been ranked.
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