Using the “Example Dataset,” complete the following: Based on a normal distribution curve, calculate the probability of an individual being 60 years or older in this population. Show the Excel and SPSS formulas or your hand calculations. Include screenshots as needed to illustrate this. Using the sample standard deviation of age as an estimate of the population standard deviation, calculate by hand the standard error of the mean. Show your calculations and the answer. Calculate by hand a 95% confidence interval for “Age” based on the sample mean. Use SPSS to verify your answer. Include your calculations and screenshots of the SPSS output. Interpret the confidence interval for age and explain the three pieces of information needed to calculate a confidence interval.

Part 1.

Calculating mean, median and mode for Annual Income and Age variables

 

Table 1. Excel output of descriptive statistics for age and annual income

  Age Annual_Income
Mean 39.93 34766.67
Standard Error 2.17 4176.48
Median 41.00 28000.00
Mode 42.00 28000.00
Standard Deviation 11.90 22875.50
Kurtosis -0.79 -0.61
Skewness -0.09 0.64
Range 43.00 80000.00
Minimum 18.00 5000.00
Maximum 61.00 85000.00
Sum 1198.00 1043000.00
Count 30.00 30.00
Confidence level (95.0%) 4.44 8541.85

 

Table 2. SPSS output of descriptive statistics for age and annual income Practicing Application of Descriptive Statistics in Excel and SPSS

 

  Statistic Std. Error
Age Mean 39.93 2.173
95% Confidence Interval for Mean Lower Bound 35.49  
Upper Bound 44.38  
5% Trimmed Mean 39.98  
Median 41.00  
Variance 141.651  
Std. Deviation 11.902  
Minimum 18  
Maximum 61  
Range 43  
Interquartile Range 19  
Skewness -.091 .427
Kurtosis -.791 .833
Annual_Income* Mean 34766.67 4176.476
95% Confidence Interval for Mean Lower Bound 26224.81  
Upper Bound 43308.52  
5% Trimmed Mean 33759.26  
Median 28000.00  
Variance 5.233E8  
Std. Deviation 22875.500  
Minimum 5000  
Maximum 85000  
Range 80000  
Interquartile Range 37000  
Skewness .645 .427
Kurtosis -.610 .833

 

 

Histogram for age and annual income

 

Figure 1. Excel output of histogram for age

 

Figure 2. Excel output of histogram for annual income

 

Figure 3. SPSS output of histogram for age

 

Figure 4. SPSS output of histogram for annual income

Frequency tables of counts and percentage for smoking status, employment status, exercise level, and education level

 

Table 3. Excel output of frequency tables for smoking status

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  Frequency Percentage