Question

QUESTION 5 In a goodness-of-fit test to see if a set of 100 values were randomly drawn from a normal distribution, the quartiles and median (i.e., the 0.25, 0.5, and 0.75 quantiles) for the normal distribution were used to determine intervals for sorting the data. What is the expected number of values that fall into each interval assuming the 100 numbers were drawn from the normal distribution? QUESTION 6 Consider again the goodness-of-fit described in the previous problem. Assuming that the mean and variance are known and do NOT need to be estimated from the sample, how many degrees of freedom does the chi-square distribution used to find the P-value of the observed test statistic have?

Answer 1

Question 5

Since quartiles divide the data into 4 equal parts , in each interval there should be equal number of observation. 100 numbers are drawn from the population , so expected number of values fall into each interval is 25 .

Question 6

For chi square goodness of fit test for normality (if mean and variance are to be estimated from sample)

degrees of freedom = number of intervals -1 - 2

For chi square goodness of fit test for normality (if population mean and variance are known)

degrees of freedom = number of intervals -1

in the above case , number of intervals =4 and mean and variance are known

degrees of freedom = 4-1= 3