Collect one set of data from the real world. Data will be collected from a large number of observations (at least 100) for a continuous random variable from a population that is suspected to be normally distributed. Examples of such data include the body weight of people, the circumferences of oranges, the extension length of rubber bands at the point at which they burst, etc.
Descriptive Statistics: Do the following:
Calculate the sample mean.
Calculate the sample standard deviation.
Calculate the quartiles Q1, Q2, and Q3.
Construct a histogram.
Chi-Square Goodness of Fit Test: Using a Chi-Square Goodness of Fit Test with a significance level of 0.05, test the hypothesis that data is sampled from a Normal Distribution with a population mean equal to the sample mean and a population standard deviation equal to the sample standard deviation. For the test, start with the data classes from your histogram and merge them to ensure each class has a sufficient number of observations. Then, calculate the following:
Numbers of observations in the data.
Class probability.
Class expected value.
Chi-square component values.
Finally, calculate the chi-square value, describe the degrees of freedom, and explain your conclusion. Note that since you are using the sample means and standard deviations, you will need to adjust your degrees of freedom accordingly.