291 Words2 Pages

Technical Notes
Exploratory Analysis
The histogram, box plot and dot plot all show the data is slightly right skewed: the median (1088.65) is slightly less than the mean (1102.59) and the skewness statisti is a fairly small positive value (0.58).
Checking Assumptions
The independence of the observations appears to be satisfied from the data description.
The Shapiro-Wilk Normality test shws strong evidence gainst the hypothesis that the underlying distribution is normal (P-value=0.008103).
The Normal Q-Q plot shows a slight curve through the points indicating slight right skewness.
Although the data are slightly right skewed, because of the large sample size(n=152) our inference on the mean is valid, by the Central Limit Therom.
The Box Cox plot suggests a power transformation using a power, p= -0.5 would make the data more shaped like a normal distribution.
The Normal Q-Q plot shows the transformed data points lying close to the straight line and the box plot of the transformed data looks symmetric with two outliers.
The numerical summary of the transformed data confirms that the transformed data are symmetric (mean=1 and median=1).
A Shapiro-Wilk test on the transformed data provides no evidence against the transformed data having come fro a normal distribution (P-value=0.4286).
Statistical Inference
We can estimate both the population mean and median incomes. The P-values from the t-tests are not sensible here:
Executive Summary
Our interest in these data was to estimate both the mean and median lifetime (in hours) of light bulbs in a warehouse.
We estimate that the mean family income is between 1083 and 1122 hours, while the median family income is between 1074 and 1112

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