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A researcher was interested in the relationship between the number of texts sent in a day and the number ofe e-mails in a day by employees Yerpe at a certain compan...

Question

A researcher was interested in the relationship between the number of texts sent in a day and the number ofe e-mails in a day by employees Yerpe at a certain company_ Using 13 data values, percent confidence interval for the slope of a regression model was found to be The researcher claims that the interval would have been narrower with a different sample size if all other things remained the same_Which of the following sample sizes would make the researcher'$ claim NOT true?1000 16

A researcher was interested in the relationship between the number of texts sent in a day and the number ofe e-mails in a day by employees Yerpe at a certain company_ Using 13 data values, percent confidence interval for the slope of a regression model was found to be The researcher claims that the interval would have been narrower with a different sample size if all other things remained the same_ Which of the following sample sizes would make the researcher'$ claim NOT true? 100 0 16



Answers

Imagine that there are 100 different researchers each studying the sleeping habits of college freshmen. Each researcher takes a random sample of size 50 from the same population of freshmen. Each researcher is trying to estimate the mean hours of sleep that freshmen get at night, and each one constructs a $95 \%$ confidence interval for the mean. Approximately how many of these 100 confidence intervals will NOT capture the true mean? a. None b. 1 or 2 c. 3 to 7 d. about half e. 95 to 100 f. other

The following is a solution to number 17 and this is looking at a school administrator looked at the difference of upperclassmen and lower classman or underclassmen study time per week and he thinks that it's more for upperclassmen. So the upperclassmen of sample 35, it was an average of 15.6 hours of study with a standard deviation 2.9. And the underclassmen Sample size of 35 there. Uh Weekly studying was 12.3 hours and their standard deviation was 4.1, and we're supposed to test at the 1% level of significance if the difference is zero or if the difference is greater than zero, meaning upper minus the under. So in other words are saying there is no difference or there is a difference, in fact the upper being more. So I'm going to use the T. I 84 here and if you go to stat and then test, we're gonna go to the two samples t tests. The reason why we can use to sample Z test is because the sample sizes of 35 are large enough. Now, once you hit 30 then the T. And the Z essentially become pretty close to the same thing. So sample size of 35 is large enough. Just use the Z. interval. So the signal one sigma to just put in your S one and S two there, here's your X one bar and you're in one x two bar and you're into. So the only thing you really need to think about is the alternative and it's going to be greater than so this is the right tail test. And whenever we calculate this gives us 3.888 for our test value. And then R. P. Value it's not five. Alright P value is never going to be between are never gonna be more than one because it's a probability it's actually five times 10 to the negative fifth. So it's very very small number 4005. So that's going to be a reject for sure. So Z is equal to three point 888. And then the P value is just to give you know sometimes scientific notation doesn't give a clear picture but it's basically 0.5 which is significantly less than the alpha. And that's what you do with the P value explicitly compare the p value with the alpha. And if it's less than alpha if the P values less than alpha then you're gonna reject the H. Top. So you're rejecting that there is no difference. So there is going to be a difference it appears so and then part B of this it says what's the significance of the test? That's just the p value. So this is the significance of the test. Yes it's a two sample Z test for the difference of two population means

Here in question one. We are really tasked with understanding what a confidence interval is trying to communicate to us. So an important understanding about confidence intervals is that they give you a set of plausible values for the parameter that you're trying to estimate by collecting some data. And so in this problem I can see that the confidence interval goes from negative 1.32 to 0.18 And this is a confidence interval for slope and the slope being either positive or negative is really important in understanding the relationship between the variables and understanding that association. So typically when we are trying to make some judgments about an association, maybe we have a null hypothesis that um that there is just no relationship between the variables. So we say that the population slope is zero and then an alternative hypothesis might be something like that. The slope is not zero, that it's something else. Now in this confidence interval, since the lower boundary is negative and the upper boundary is positive, that means that A population slope of zero is located in this interval and therefore is a plausible value for the slope. And since zero is a plausible value for the slope, there would be no reason to reject a null hypothesis. That says that the population slope is zero. So this means that our data doesn't give us convincing evidence to say that there is an association. So unfortunately we can't say that there is an association. So the answer here would be choice. See which says that the association is not significant because zero is in the interval. Any confidence interval for slope, you should be looking for zero in there, especially if the lower end point is negative in the upper end point is positive. That's your signal that zero is in there. So the answer choice with BC.

Hello, everyone. Uh, you have a nice day this hour. Question Answer. This is a scatter diagram. Here is number three Number P. He was the final result. And here is number. The on here is number. He This is the final result. And thank you for watching.


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