PROBLEM SET 3 12 STUDENTS SAT IN TWO BIOLOGY TESTS: ONE...

PROBLEM SET 3 12 STUDENTS SAT IN TWO BIOLOGY TESTS: ONE WASTHEORETICAL AND THE OTHER WAS PRACTICAL.THE RESULTS ARE SHOWN IN THE TABLE: SCORE IN 5 9 7 11 20 4 6 17 12 10 15 16 THEORETIC AL TEST (t) SCORE IN 6 8 9 13 20 9 8 17 14 8 17 18 PRACTICAL TEST (p) a. FIND THE PRODUCT MOMENTCORRELATION COEFFICIENT FOR THIS DATA TO 3 SIGNIFICANT FIGURES. B. A TEACHER CLAIMS THAT STUDENTS WHO DO NOT DO WELL IN THE THEORETICAL TEST TEND TO DO WELL IN THE PRACTAICAL TEST. TEST THIS CLAIM AT THE 0.05 LEVEL OF SIGNIFICANCE. FOLLOW STEPS IN HYPOTHESIS TESTING

Transcript

00:01 So here we have scores for eight students on two different exams, exam one and exam two, and we want to calculate the paired samples t statistic for these scores, and we're going to use a two -tailed test.

00:14 And so we're going to go ahead and say the assumption, the null hypothesis, is that we're going to assume that the mean difference mu sub d is equal to zero.

00:23 That means the alternative, assuming a two -tailed test, would be that the mean difference is not equal to zero.

00:30 And it's a paired t -test because each of these values are paired.

00:33 The 92 is paired with 84.

00:34 67 is paired with the 75 because these are each, you know, each row is a different student.

00:42 So this is a 8 in this case.

00:46 And we're going to test this at the, this two -tailed hypothesis test at the alpha of 0 .05 level of significance.

00:55 And we're going to get the critical t values and make a decision regarding the null hypothesis.

01:01 And so what we're going to do is we're going to read our rule will be to reject h -naught, reject h -naught, if the absolute value of our test statistic is greater than the t critical value.

01:19 Now the t critical value is based on the alpha of 0 .05 over two and the degrees of freedom, which in this case, the degrees of freedom is given as a minus one.

01:33 So in this case, it's going to be seven.

01:38 So let's go ahead and run through this.

01:40 So we're differences right here.

01:44 So i did exam two minus exam one.

01:47 Take the mean difference and the mean, the standard deviation of the differences.

01:53 You get that.

01:56 And let's go and get our test statistic from this data.

02:01 Oh, and by the way, the way i got the mean is standard deviation was by using the spreadsheet function average and you put the data and then the standard deviation function, stdev .s, and you put in the data.

02:15 There you go.

02:16 And then the test statistic is found by taking the mean difference, i'll play as a d bar.

02:21 That's the sample mean difference divided by this, the standard deviation divided by the square root of n.

02:28 So 125 or 1 .25 divided by 5 .676, we'll say divided by the square root of eight.

02:42 And the p value, or sorry, the t statistic, i should say, sorry, the t statistic is 0 .623.

02:51 If you go to three decimal places, and then the critical value is 2 .36...

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