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Completing this self-test and the connections section, and then checking your answers by clicking on the answer button or by looking in Appendix B, will provide imm...

Question

Completing this self-test and the connections section, and then checking your answers by clicking on the answer button or by looking in Appendix B, will provide immediate feedback and helpful practice for exams.Discuss Hans Eysenck's contribution to theories of personality.

Completing this self-test and the connections section, and then checking your answers by clicking on the answer button or by looking in Appendix B, will provide immediate feedback and helpful practice for exams.Discuss Hans Eysenck's contribution to theories of personality.



Answers

Completing this self-test and the connections section, and then checking your answers by clicking on the answer button or by looking in Appendix B, will provide immediate feedback and helpful practice for exams.Discuss Hans Eysenck's contribution to theories of personality.

The relationship here, as demonstrated by the axes, describes the relationship between the distance between that hydrogen atoms and the potential energy of the H two molecule.

This question. We're looking at times for a seven lap run, and we're specifically looking at the times for lap one for a given athlete. And we have samples from scenarios that air races and scenarios that air practices. And we're interested to test whether there's a difference in the mean lap time for the race setting and the practice setting. And so, if I have summarized the samples for lap one in this table here and to do this, I used Excel, So I copied the data from the textbook question into Excel. So this is it here and then to find the mean of each sample, we can use the average function. It's like that. So here I have this information summarised in the table, and so we begin by stating our head, pa theses on no hypothesis is that there is no difference in the mean lap times between races and practices, and it follows that the alternative hypothesis is that there is some difference. In other words, the difference between the mean times is not zero. And for this test, let's a Seema Significance level of Alfa equals 0.5 and now we proceed to calculate our test statistic. And so we since we don't have a standard deviation of the entire population of lap times, we're relying on the sample standard deviations. And so our test statistic is distributed according to the student's T distribution and we calculated as follows and this comes out to negative 4.70 to then go in calculator P value. We need to know the degrees of freedom and that's found according to this formula. And I calculated it using software and it came out to 20.32 so we can use Excel to calculate the P value so equals t dot d. I s t dot to t and X is the test statistic, So I will put 4.7 even though we had minus 4.7. This is a two tailed test so we can use either plus or the minus test statistic and the degrees of freedom 20.32 and we get a P value of just a bit bigger than 0.1 and therefore because a P value is less than Alfa, we reject the no hypothesis and we can conclude that at the 5% level at the 55% significance level, there is sufficient evidence to suggest that the meantime to complete a lap during races is different from the meantime to complete a lap during practices.

For this question, we're looking to see if the lap time for a runner it's different in the racing context than in the practice context and were asked to use the data for Lap five from a seven lap run given in the appendix of the textbook. And I've summarises data for races and practices in terms of the sample size, the average sample time for the lap and the sample standard deviation. And I actually did this in Excel. So I copied the data for lap five out of the text book and put it here and then to calculate the mean I used this formula, the average formula and to calculate thesis sample standard deviation. I used this formula here, so let's state our hypotheses. So the no hypothesis is that there is no difference in the average lap time for races and for practices. In other words, the difference is equal to zero, and the alternative hypothesis is that there is some difference. And as we can see based on this not equal to operator, this is going to be a two tailed test, and let's decide up front that we're going to do this test at the Alfa equals 0.5 significance level, and the next step is to calculator test statistic. And because we don't have the standard e standard deviation of the population off lap times, we're relying on the sample standard deviations. And so our test statistic is distributed according to the student's T distribution, which looks like this and so we can put the valleys from the table. We're from the samples into this equation and this comes out to minors 3.307 And now, to find the corresponding P Valley, we must also have the degrees of freedom and that's given by this equation and solving that using a calculator or software, you should get a vote 20 0.32 degrees of freedom, and then we can sell for the P Value and Excel. He's the function t dot the i s t dot to t. And instead of putting minus 3.307 I'm going to put plus 3.307 which is fine because this is a two tailed test, but also because this to tail distribution in Excel is looking for the right or the positive end of the test statistic. So it's looking for the positive test statistic. So 3.307 and the degrees of freedom was 20.32 and we get a P value of 0.35 and now we can compare the P value to the significance level. And the P Valley is indeed less than Alfa. So therefore, we reject the no hypothesis and we can conclude that at the 5% significance level, there is sufficient evidence to suggest a difference in the meantime for laps in the race sitting and in the practice setting.

Interested to see if the average lap times for a certain runner are different when that person is running a race compared to when that person is running for practice. And this time we're asked to combine the sample data for Lap one and Lap five out of the appendix in the textbook. So I've gone ahead and done that and summarized the sample data in this table. So I have the sample size sample, average running time for the lapse and the sample standard deviations and actually did this in Excel. So I copied all the data from laps one and five and put into two columns race in practice. And then I calculated the mean and sample standard deviations. So for the mean, I used this formula, the average formula and for the sample standard deviation. I use this formula so we can begin by starting off with our hypotheses. So the no hypothesis is that there is no difference in the average lap time for races and for practices, or that the difference is zero. And so the alternative hypothesis is that there is some difference, and let's decide up front that we will use a significance level for this test of 5%. And now we're ready to calculate our test statistic. And because we do not have the population standard deviations for lap times, we're relying on the sample standard deviations and therefore our test statistic is distributed according to the student's T distribution, and it looks like this. So if we plug in our sample values from the table, we get a value of minus 5.8 Now, before we can calculate RPI value, we must find our degrees of freedom for the situation which is given by this formula. And if you calculate that with a calculator or software, you should get 40.94 degrees of freedom. And so this value and our test statistic give us a P value and we can find that an excel as well. We use the function equals t dot d. I s t dot to t. This is a two tailed distribution because it's a two tailed hypothesis. We're hypothesizing that the difference in the means is not equal to zero. And so the formula in excel wants the positive test statistics. So our test statistic was minus 5.8 so we can just put in positive 5.8 and then the degrees of freedom which was 40.94 and we get a tiny number. You can see if this is of the order of 10 to the minus six or 10 to the minus five, approximately. So we can say that RPI value is approximately zero and therefore we reject the no hypothesis and we can come claim at the 5% significance level. There is sufficient evidence to suggest that there is a difference in the mean lap times in the race setting versus the practice city.


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