Answer:
Explanation:
To calculate the chi-squared statistic for a chi-squared test of independence, you can use the following formula:
�
2
=
∑
(
�
−
�
)
2
�
χ
2
=∑
E
(O−E)
2
Where:
�
2
χ
2
is the chi-squared statistic.
�
O represents the observed frequency (the actual number of students in each category).
�
E represents the expected frequency (the number of students that would be expected in each category if there was no association between the format of the book and the students' choices).
In your case, you have the following observed frequencies:
76 students bought a hard copy.
28 students printed it out from the web.
27 students read it online.
To calculate the expected frequencies, you'll assume that the format choice is independent of the students' choices. You can calculate the expected frequencies based on the overall proportions predicted by the professor.
The total number of students is 131, and the predicted proportions are:
60% buy a hard copy (0.60 * 131 = 78.6 expected in this category).
25% print it out from the web (0.25 * 131 = 32.75 expected in this category).
15% read it online (0.15 * 131 = 19.65 expected in this category).
Now, use the formula to calculate the chi-squared statistic:
�
2
=
(
76
−
78.6
)
2
78.6
+
(
28
−
32.75
)
2
32.75
+
(
27
−
19.65
)
2
19.65
χ
2
=
78.6
(76−78.6)
2
+
32.75
(28−32.75)
2
+
19.65
(27−19.65)
2
Calculate each of these terms, then sum them up:
�
2
≈
0.66
χ
2
≈0.66
So, the chi-squared statistic is approximately 0.66 when rounded to two decimal places.