A statistician believes that the scores on a standardized test fall into five ranges with proportions 0.06, 0.23, 0.38, 0.27, and 0.06. She recorded the scores of a random sample of 400 students and grouped them into these five ranges.
| Score range | Below 55 | 55 to 65 | 65 to 75 | 75 to 85 | 85 and above |
|---|---|---|---|---|---|
| Observed | 18 | 76 | 152 | 116 | 38 |
| Expected | 24 | 92 | 152 | 108 | 24 |
A chi-square goodness-of-fit test gives a statistic of 13.04 with 4 degrees of freedom and a p-value of about 0.011. Which of the following is the correct conclusion at the 0.05 level?