Question Two: The Educational Testing Service conducted a...

Question Two: The Educational Testing Service conducted a study to investigate differences between the scores of males and females on the SAT. The study identified a random sample of 562 females and 852 males that had achieved the same high score on the math portion of the test. That is, both females and males were viewed as having similar high abilities in Math. The SAT verbal scores for the two samples are: Females Males ?x1 = 547 ?x2 = 525 S1 = 83 S2 = 78 Do the data support the conclusion that given a population of females and a population of males with similar high mathematical abilities, the females will have a significantly higher verbal ability? Test at a 0.02 level of significance. What is your conclusion?

Transcript

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

00:04 Now let me bring up your question here.

00:06 In this question we're going to perform the hybrid testing.

00:11 And we have the two groups and the first will be female, the second will be male.

00:16 And we want to know that is the female, we'll have a significant high verbal ability than the male.

00:25 And here we have the female in we have the total and equal to the 562 and the end for the male and one doesn't be the n2 equal to the 8152 and want to test the arch note that the mean of the one will equal to the mean of the two versus the arch one here want to test if the female will have a significant higher than ability than the male mean that the mean of the 2 will be mean of the 1 it will be greater than mean under 2 now to proceed to the next step we need to compute the test statistics and test statistic here will be the z by definition the z will equal to the x par 1 minus x part 2 divided by the square root of the n1 minus 1 times the s1 square then plus n2 minus 1 times the s2 square divided by n1 plus n2 minus 2 now if we are plug in the value here we should get that the x by 1 equal to the 5 47 x bar 2 equal to the 525 over the square root of n1 will be 562 minus 1 be 561 times when the s 1 square will be the 83 square plus and 2 minus 1 will be the 851 times when the s 2 square 52 minus 2 if we compute this one we should get now 561 times 83 square plus 851 times the 78 square dividing by the 6562 plus 852 minus 2 taking the square root and then we will have that on the time will be 547 minus the 525 dividing by that we get equal to the 0 .2749 and that's will be the g test for this question and then the next time we will compute the critical value and critical value here we have the alpha equal to this one we have the one sided test or sometimes we call the one tell test here and therefore we will compute the z on the alpha so unfa we have equal to the zb102 to compute this z here i will bring up the z table for you and let me copy the table here i will put the table on the right here and we need to look at the value on the 0 .002 and it will look for the 0 .0 2.

04:12 We see the closest one it will be the this one and it corresponds to the z score equal to the 2 .05...

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