The Head Start program, begun in the 1960s, was designed to...

The Head Start program, begun in the 1960s, was designed to promote future academic success and includes a focus on O children's physical health O improving the parents' standard of living O ethics and values O getting children into elite private schools

Transcript

00:01 For this problem, to begin, i'll note that our null hypothesis is that the proportions do not differ, and the alternate hypothesis will be that the proportions differ.

00:24 Specifically, proportions do not differ from that of the program, and proportions do not differ.

00:30 Or, pardon me, proportions do not differ from that of the program, versus proportions differ.

00:36 Pardon me, my pen is glitching out a little bit here.

00:39 Hopefully that's not going to be too much of a problem.

00:41 All right.

00:42 Additionally, we are asked to identify the claim.

00:45 We're specifically being asked, is there sufficient evidence that the proportions differ? so, the claim then would be that the proportions differ, and we are trying to determine whether there is sufficient evidence to support that.

01:00 So, our claim is the alternative hypothesis.

01:04 Now, what we'll do here is do this using a chi -squared test, where for our chi -squared statistic, we take the sum over all of the categories of the observed frequency minus the expected frequency, squared, divided by the expected frequency, where the expected frequency for each category is going to be equal to the null hypothesized proportion times the total sample size.

01:31 So, i'm going to jump over into excel just to make this a little bit, or make the numbers a little bit easier to deal with here.

01:37 So, first we have our observed frequencies.

01:40 We have 11 were 5 years old, 93 were 4 years old, 83 were 3 years old, 13 were under 3 years old.

01:47 Now, note that i'm not labeling the categories just because it doesn't actually matter for calculating our statistic.

01:54 Now, we'll have the expected proportion, which i'll label as e .p.

01:59 We know that the expected proportion were 0 .04 as the proportion of 5 -year -olds, 0 .52 as the proportion of 4 -year -olds, 0 .34 as the proportion of 3 -year -olds, and 0 .1 as the proportion of under 3 -year -olds...

Question

The Head Start program, begun in the 1960s, was designed to promote future academic success and includes a focus on O children's physical health O improving the parents' standard of living O ethics and values O getting children into elite private schools

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