Question

There are four blood types, and not all are equally likely to be in blood banks. Records in a local blood bank show that, historically, 49% of donations are type O blood, 27% are type A blood, 20% are type B blood, and 4% are type AB blood. The blood bank takes a random sample of 40 donations from the past month, and finds that 25 were type O, 10 were type A, 4 were type B, and 1 was type AB. The blood bank will run a chi-square test for goodness of fit to determine if the sample shows evidence that the distribution of blood types this month differs from the historical distribution. Are the conditions for such a test met

Answer 1

Answer:

No, because all the expected frequencies must be higher than 5.

Step-by-step explanation:  

The chi-square test might be performed in those situations in which we need to know if a series of observations adjust or not to a theoretical function, such as the normal, Poisson, or binomial.

The chi-square test does not require the number of files to coincide with the number of columns in the table. It does not establish any restriction about the number of modalities per variable. However, the expected frequencies or counts should not be less than five.

In the exposed example, this unique rule is not accomplished, so the chi-square test can not be performed.