A recent national poll showed the reading habits of adults during the last 12 months: A poll in a small Midwestern town shows the following percentages:
The critical value of the chi-squared goodness-of-fit statistic is ______.
A) 9.49
B) 7.82
C) 5.99
D) 5.82
E) 5.49

Question

A recent national poll showed the reading habits of adults during the last 12 months:  A poll in a small Midwestern town shows the following percentages:
 The critical value of the chi-squared goodness-of-fit statistic is ______.
A) 9.49 
B) 7.82 
C) 5.99 
D) 5.82 
E) 5.49

Quizplus · Accepted Answer

We need to compare the observed percentages in the small Midwestern town with the expected percentages from the national poll. To calculate the expected values, we multiply the national percentages by the sample size in the small Midwestern town (1500).

|Type of Reading | Observed Frequency | Expected Frequency |
|---|---|---|
|Fiction | 675 (45%) | 528 (35.2%) |
|Non-fiction | 525 (35%) | 495 (33%) |
|No reading | 300 (20%) | 477 (31.8%) |

To calculate the chi-squared statistic, we use the formula:

χ² = Σ (O - E)²/E

where O is the observed frequency and E is the expected frequency for each category.

Plugging in the values, we get:

χ² = ((675-528)²/528) + ((525-495)²/495) + ((300-477)²/477)
    = 15.30

The degrees of freedom for this test is (3-1) = 2. Using a chi-squared distribution table with 2 degrees of freedom, we find the critical value to be 7.82 (at the 0.05 level of significance). Since our calculated chi-squared value (15.30) is greater than the critical value (7.82), we reject the null hypothesis and conclude that the distribution of reading habits in the small Midwestern town differs significantly from the national poll. Therefore, the best choice is B.

A Recent National Poll Showed the Reading Habits of Adults