The Arithmetic Mean: Definition, Formula & Examples

Question 1 

1.  

	Age (years)	Annual income ($)	BMI (kg/m^2)	PHQ-9 depression score (points)	HDL cholesterol (mg/dL)
Mean	37.6	62000.0	28.4	11.7	46.7
Standard Deviation	10.6	22920.3	2.6	3.5	10.2

The arithmetic mean estimates the central position of the data as summation of all data values divided by the number of data entries. On the other hand, the standard deviation measures the spread of data around the mean. Although the mean is sensitive to outliers unlike the median, it remains fairly constant for different samples calculated from the same population. The standard deviations for BMI and PHQ-9 depression score are relatively small indicating that data is arranged closely around the mean. The standard deviation for income, age, and HDL cholesterol are moderate implying that data is fairly spread around the mean. 

Question 2 

Fill in the blanks in the following statement: 

If the study sample size is too ___ large _____, data analysis can yield a statistically significant result even in the absence of practical or clinically meaningful significance. 

However, if the study sample size is too _____ small ____, data analysis can yield a nonsignificant result even though the null hypothesis is false. 

Question 3 

1.  

The aim of the study is find the correlation between the attitudes of Norwegian nurses about evidence based practice (EBP) and its implementation. EBP involves utilizing various ways of collecting the most relevant clinical evidence while integrating patients’ preferences and values and finally assessing the outcomes and decision making process. The dependent variable, BELIEFS ABOUT EBP, estimates nurses’ attitude about the importance of EBP and their ability to implement. The respondents were asked to respond to 16 statements about EBP beliefs on a 5 point scale ranging from 1 to 5 where 1 stands for strongly disagree and 5 is strongly agree. 

1.  

The researcher used multiple linear regression analysis to evaluate the statistical significance of the independent variables on the beliefs and implementation of evidence based practice. 

The significant independent variables include learning about EBP (B = 2.7, p-value = 0.04), taking part in EBP working groups (B = 3.2, p-value 0.05) had statistically significant impact of increasing the beliefs about EBP. Registered nurse qualifications (B= -4.2, p-value = 0.04) is also significantly related to beliefs about EBP although the relationship is inverse. 

The survey received a low response rate of 52% despite lack of difference in age or education level among the study participants and those that did not participate. Possibility that those that did not participate in the study have a different view about EBP lowers the generalizability of the study. The data was collected from a specific hospital at specific time hence the risk that the data is not representative of the situation in other hospitals. 

Question 4 

1.  

The average MRSA lie closely around the grand mean and within the upper and lower control limits implying that the average number of MRSA cases process is “in-control” 

Question 5 

The aim of the project is to evaluate the patients’ projections about lumbar spine surgery and to suggest, implement and assess an education program that aligns patients’ expectations to those of healthcare providers. 

The study utilized a sample of 23 patients of between ages 25 and 71 years. 22 of the 23 patients sampled were males and only 1 female. 

Participants in the study had to be patients requiring special surgery lumbar spine surgery. The study was conducted between 11 th June 2015 and 10 th September 2015 where participants had to fill in demographic information, pre-surgery expectations and feelings about post- surgery satisfaction. 

The research utilized primary data obtained from a survey in which the participants responded to questions about their demographic information, pre-surgery expectations and post-surgery experience. A nurse then reviewed the responses to allow for modifications. 

The relationship between pre and post expectation scores, demographic information such age, BMI, race, sex, education status, work and marital status and information about surgery such as type of surgery, therapies and surgical diagnosis. 

The data analysis process used descriptive statistics including means, standard deviations, frequencies, percentages, scatter graphs and ranges to understand data distribution. Paired t-test used to evaluate change in mean expectation scores pre and post-surgery. 

The analysis fails to test whether the change in mean expectation scores pre and post-surgery was significant. The sample size used was too small hence the risk of accepting the null hypothesis when it is actually wrong. 

The survey may be improved by using a larger sample from different facilities with the aim of enhancing generalizability as the results would be a better representation of the population. 

Question 6 

The study would test the null hypothesis which assumes that the mean HbA1c (%) remains the same after 12 months. 

Null hypothesis, H0: 

Null hypothesis, H0: 

We use single factor ANOVA and hence the need to reorganize the data into to groups as shown in the table below. 

Patient No.	HbA1c (%) in month 0	HbA1c (%) after 12 months
1	5.3	5.5
2	4.8	5.1
3	4.6	4.6
4	6.8	6.7
5	11.2	10.4
6	4.8	4.6
7	6.3	6.8
8	7.1	6.4
9	8.9	9.2
10	10.1	9.6

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
HbA1c (%) in month 0	10	69.9	6.99	5.525444
HbA1c (%) after 12 months	10	68.9	6.89	4.545444
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	0.05	1	0.05	0.00993	0.921726	4.413873
Within Groups	90.638	18	5.035444
Total	90.688	19

The F-statistic= 0.00993 while the p-value is 0.921726. We fail to reject the null hypothesis since the p-value> than assumed level of significance 0.05. We conclude that the mean HbA1c (%) remains the same after 12 months. 

Question 7 

		T-test	Bonferroni ( 6 tests)
0 months	after 12 months	0.921725666	0.008333333
	α	0.05

The adjustment is 0.05/6 tests = 0 .008333333 

Question 8 

ME = 0.10 

  0.67 

  =0.05 

n =  (  ) ^2 

Where n is the minimum sample required. 

Standard normal distribution table  = 1.96 

n = 0.67 * (1-0.67) * (  ) ^2 = 84.9378 

p ̃	0.67
(1-p ̃)	0.33
	1.96
p ̃(1-p ̃)	0.2211
ME	0.1
(Z(α/2)/ME) ^2	384.16
n = p ̃(1-p ̃)*(Z(α/2)/ME) ^2	84.9378

Question 9 

The standardized mean difference, SMD = −0.30 with a 95% confidence interval of between −1.17 and 0.48. The pooled results indicated non-significant difference between the treatment and control pain intensity.