Early childhood development studies indicate that the more...

Early-childhood-development studies indicate that the more often a child is read to from birth, the earlier the child begins to read. A local parents’ group wants to test this theory and samples families with young children. They find the following results. Construct a 98% confidence interval to estimate the true difference between the proportions of children who read at an early age when they are read to frequently compared to those who were read to less often, as described in the table of results. Let Population 1 be the children who were read to frequently and Population 2 be the children who were read to less often. Round the endpoints of the interval to three decimal places, if necessary. Ages when Children Begin to Read Read to at Least Three Times per Week Read to Fewer than Three Times per Week Started Reading by age 4 29 48 Started Reading after age 4 53 51

Transcript

00:01 Hi, i'm david and i'm here to help you answer your question.

00:03 Now let me bring up your question here.

00:05 In the question here, we are going to discuss about the confidence interval for the difference between the two proportions.

00:12 Let me remind you that the confidence interval for the p1 minus the p2, the formula will be the phe1 minus the p h2, and then plus and minus the critical value z and 4 over 2, time with the square root of the phe 1 times 1 minus the p .h1 over n1 plus p h2 times 1 minus the p h2 over the n2.

00:38 In the question here, we're given the table on the summary for the reading here.

00:44 So we have the first one.

00:47 Let me summary the table here.

00:51 Now the first one will be started written by h4.

00:57 So, reading by 8 .4.

01:02 This one will be after 8 .4.

01:07 And we have on the top it will be 8 words students begin to read to under 3 times per week, reading to fewer than 3 times per week.

01:23 And then 8 .1 .1 .1.

01:25 Begin to read.

01:28 And then read to under 3 times per week.

01:32 So this one will be greater than equal to the three times per week.

01:38 And that this one will be less than the three times.

01:43 And we have the value here.

01:46 It will be this one 29 and this will be the 48.

01:53 And this will get equal to the 53 and this will go to the 51.

01:58 Now from here, once you've constructed the 98 % competitive to estimate the 2d000, difference between the proportion of the children who read at an earlier age when they are read too frequently so that will be the proportion of the children who root at the earlier age so we will have there will be the first group when they are 3d2 frequency compared to those who root too less often.

02:45 Compared to those who read less often.

02:52 So i believe this one will be the first population and this will be the second population who were root to less often.

03:05 So the next time we need to find the total for each of them...

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