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0l 35Arandom sample of 22 eighth grade students watched television for an average of 19.6 hours per week p0 normally distribuled.Whal is Ihe 90% confidence Interval...

Question

0l 35Arandom sample of 22 eighth grade students watched television for an average of 19.6 hours per week p0 normally distribuled.Whal is Ihe 90% confidence Interval for the mean hours of television watched per week by eighth grade st (17.5.21.7) (18.6 20.9) (19.6,23.1) (19.0,20.2)

0l 35 Arandom sample of 22 eighth grade students watched television for an average of 19.6 hours per week p0 normally distribuled. Whal is Ihe 90% confidence Interval for the mean hours of television watched per week by eighth grade st (17.5.21.7) (18.6 20.9) (19.6,23.1) (19.0,20.2)



Answers


A Gallup poll conducted January $17-$ February $6,2005,$ asked 1028 teenagers aged 13 to $17,$ "Typically, how many hours per week do you spend watching TV?" Survey results indicate that $\bar{x}=13.0$ hours and $s=2.3$ hours. Construct a $95 \%$ confidence interval for the number of hours of TV teenagers watch each week. Interpret the interval.

All right. This question gives us a population standard deviation, and it tells us where to find a data file. So from there, putting our data file into Excel, we confined that the average equals 8.5 and there are 300 cells and we'll need both of these numbers and computing our interval. So no, it wants the 95% confidence interval. So remember, confidence intervals, our point estimate plus or minus a special Z score times the standard error. And we know all of these values now, thanks to our Excel spreadsheet. So it's 8.5 plus or minus. We're dealing with 95% confidence. So if you look in your C score table Z star value for 95 is 1.96 times are standard air, which is 3.5 over square root of 300. And this gives us an interval from 8.1 to 8.9 as our 95% confidence interval

In question 45. It says 108 Americans were surveyed to determine the number of hours they spend watching television each month. It was revealed that they watch an average of 151 hours each month with a standard deviation of 32 hours. Assume that the underlying population distribution is normal to find the random variable X bar in words. So because we're talking about the average number of hours that these Americans were watching television, the X Bar represents the average number of hours of television watched, but this simple of 108 Americans.

We want to construct a confidence interval about the population, mean you for a sample, the sample mean expire equals 4.76 sample size and equals 20 sample standard deviation S equals 2.297 And confidence level 90%. To start off with, let's identify the T score needed to compute this interval to find this T score, we need to know the degree of freedom 19 And the confidence level .9. We can use a tea table which maps for these two variables the direct T score needed in this case T C equals 1.7 to 9. Next let's calculate the margin of error. E. Given by the formula. The left equals two times as of a root and plugging in these three variables for this problem we obtain equals 1.25. Finally we can compute the margin of error or rather the confidence interval from that margin of error using X bar minus is less than you. Is that the next plus? E plugging in? Our expert in R. E Gives 3.51 is less than meal is less than 6.01. Finally, we can interpret this to mean that we can say with 90 confidence that the mean is between 35.1 3.51 and 6.01. Yeah.

All right, let's look a question to we have to numbers. And first, we're going to sort this number in the ascending order from the smallest to the largest. So how I'll just write down the sorted numbers. 1st 1 is 66 and then 75 80 82 80 more candy paint on the next flight. E anyone? 94 100. Okay, so in this question, the sample size can iss 10 because we have 10 numbers. And according Teoh, the questions were interested in the 90% confidence interval. So, um, point and I is equal to one minus Alfa here so we can tell Alfa sequel Teoh point point one. Um and we just need to look at Thea table tall in the in our appendix B. Um and we need to find out the critical go for K. Um, and we have done is equal to 10 and 12 is because 2.1. So we have K. Aziz one. Um, now we know that we just need to drop, uh, one from each. Ich tell off the sorted number sequence. So we're going to drop the 1st 1 and the last one So now hear this number and this number is going to be our bound for, um, for this confidence interval. So I'll just write. It cured our 90% companies interval far the median. The media number of hours of the television watching per week by Chavez is from 75 to 94. That's that.


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