Question

1. a biology professor claims that, on the average, 15% of her students get a grade of a, 20% get a b, 35% get a c, 15% get a d, and 10% get an f. the grades of a random sample of 115 students were recorded. the following table presents the results.

grade	1	2	3	4	5

how many degrees of freedom are there?
a) 6
b) 5
c) 15
d) 4

Explanation:

Step1: Recall the formula for degrees of freedom in a chi - square goodness - of - fit test

The formula for the degrees of freedom (\(df\)) in a chi - square goodness - of - fit test is \(df = k-1\), where \(k\) is the number of categories (or groups).

Step2: Determine the number of categories (\(k\))

From the table, the grades are in 5 categories (since there are 5 rows for the grade: 1, 2, 3, 4, 5). So \(k = 5\).

Step3: Calculate the degrees of freedom

Using the formula \(df=k - 1\), substitute \(k = 5\) into the formula. We get \(df=5 - 1=4\).

Answer:

D) 4