8. Data on fifth-grade test scores (reading and mathematics)...

8. Data on fifth-grade test scores (reading and mathematics) for 420 school districts in California yield Ÿ = 646.2 and standard deviation s? = 19.5. (a) Construct a 95% confidence interval for the mean test score in the population. When the districts were divided into districts with small classes (< 20 students per teacher) and large classes (? 20 students per teacher), the following results were found: Class Size Average Score (Ÿ) Standard Deviation (s?) n Small 657.4 19.4 238 Large 650.0 17.9 182 (b) Is there statistically significant evidence (at the 5% level, using a z- statistic) that the districts with smaller classes have higher average test scores? Explain.

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

00:03 In the question here we have the question a to put the two part a and b.

00:07 Now let me answer the part a for you.

00:09 Here we want to find the 95 % confidence interval for the mean.

00:13 Let me remind you that the 95 % confidence interval for the mean, it will be the x bar plus or minus the critical value for the 95 % confidence equal to the 1 .96 and then times the s, the 1bis square root of the end.

00:30 Here we use the notation of the y, instant of the x.

00:34 And here in this question we're given the y -bore equal to the 646 .2 plus and minus 1 .96 the xy equal to the 19 .5 of a square root of the 420.

00:49 Now if we compute the quantity on the right, we have the 1 .96 times 19 .5 the 1b square root of 420 equal to the 1 .689 and if we use the minus we have the 646 .2 minus the answer we go to the 64 .335 and if we use the plus 1 .8649 get equal to the 648 .065 and that's will be the answer for the a.

01:30 Now for the b, we need to perform the hypothesis testing.

01:33 That we have the smaller classes, have the higher average test scores.

01:39 I will define the smaller classes will be the m1 and equal to the m2 will be the larger class size versus the alternative hypothesis that the m1 will be greater than the m2.

01:53 Notice that it needs the right -tale test.

01:56 Here we will give you a good hypothesis.

01:58 The n1 equal to the 2 38 and then the x part 1 equal to the x part 2 this will be i will be the y1 and y1 equal to the 657 .4 and the s1 equal to the 19 .4 the n2 equal to the 182 the n2 the and 50 the s2 equal to the 17 .9...

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