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Adults aged 16 or older were assessed in three types of literacy: prose, document, and quantitative. The scores in document literacy were the same for 19- to 24-year-olds and for 40- to 49-year-olds. A random sample of scores from a later year showed the following statistics.

Age group | Mean score | Population standard deviation | Sample size |
---|---|---|---|

19-24 | 280 | 56.2 | 40 |

40-49 | 315 | 52.1 | 35 |

Make a $95 \%$ confidence interval for the true difference in mean scores for these two groups. What does your interval say about the claim that there is no difference in mean scores? |

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