Open the small Excel database that you have been using each week.
- With that database, create a 95% confidence interval for age—both by hand and using Excel to calculate the pieces you need to perform the calculation.
- Also, assuming that the distribution of age has a normal shape, determine the age percentile of the 72-year-old male in the data set – both by hand and using Excel to calculate the pieces you need to perform the calculation. See example 5.13. in your text book for additional help.
Expert Solution Preview
Introduction:
In this question, we are given a small Excel database and we are asked to create a 95% confidence interval for age and determine the age percentile of a 72-year-old male in the data set. We will be using both manual and Excel calculations for both parts of the question.
1. 95% confidence interval for age:
To calculate the confidence interval for age, we will be using the following formula:
Confidence Interval = mean ± (t-value x standard error)
First, we need to calculate the mean and standard error of age. In Excel, we can use the following formulas:
Mean = AVERAGE(data range)
Standard Error = STDEV(data range)/SQRT(COUNT(data range))
Once we have calculated the mean and standard error, we need to find the t-value for a 95% confidence level with n-1 degrees of freedom, where n is the sample size. In Excel, we can use the following formula:
t-value = T.INV.2T(0.05, COUNT(data range)-1)
Finally, we can calculate the confidence interval by plugging in the values into the formula. We can also use Excel to calculate the upper and lower bounds of the confidence interval.
2. Age percentile of the 72-year-old male:
To determine the age percentile of the 72-year-old male, we need to find the cumulative distribution function (CDF) of the normal distribution. In Excel, we can use the following formula:
Percentile = NORM.DIST(x, mean, standard deviation, TRUE) x 100%
Where x is the age of the 72-year-old male, mean is the mean age of the data set, standard deviation is the standard deviation of the data set, and TRUE indicates that we want to use the cumulative distribution function.
Once we have calculated the percentile, we can determine the age percentile of the 72-year-old male by comparing it to the percentiles of the normal distribution. We can also use Excel to calculate the exact age percentile of the 72-year-old male.
In conclusion, we can use manual calculations or Excel formulas to create a confidence interval for age and determine the age percentile of a 72-year-old male in the data set. These calculations are important in medical research as they help us to understand the distribution of relevant age groups in the population.
