Question: A developmental psychologist would like to determine how much fine motor skill improves for children from age 3 to age 4. A random sample of \(n=153\) -year-old children and a second sample of \(n=154\) -year-olds are obtained, Each child is given a manual dexterity test that measures fine motor skills. The average score for the older children was \(M=40.6\) with \(SS=430\) and the average for the younger children was \(M=35.4\) with \(SS =410\). Using these data,

1. Make a point estimate of the population mean difference in fine motor skills.
2. Make an interval estimate so you are \(95 \%\) confident that the real mean difference is in your interval.
3. Make an interval estimate so you are \(99 \%\) confident that the real mean difference is in your interval,
4. Based on your answers from b and c, do these data indicate a significant change using a two-tailed test with \(\alpha=.05\) Is the difference significant with \(\alpha=.01\) ?

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