254 AN INTRODUCTION TO STATIST rom the chapter, a confidence interval is a diffe

Question

254 AN INTRODUCTION TO STATIST rom the chapter, a confidence interval is a different statistic owing the mean reading comprehension score of all r your students In this situation, you could use a TRODUCTION TO CONFIDENCE INTERVALS is a different statistical procedure that is or effect sizes. Its main purpose is As you know f a different purpose than hypothesis a population parameter. For example school district. Kn testing teacher in seniors in your scha district as well as of 50 seniors disti nleofscore for the en score meter. For example, suppose you just took a job as an heip yu would help you achievement goals fo ized reading comprehension scores population, Of course, we have used samples to represent to estimate the mean reading comprehension populations throughout t understand the current state of education in i th how much confidence should you have that the sample mean is a good estimate of the tion parameter? Confidence intervals answer this question. A confidence interval is a parameter with a specific degree of certainty or confi meh For a se, (Cis) for ple in this situation, you could compute a 95% confidence interval of 29 to 43. This would mean that you could be 95% confident that the actual mean reading comprehensi In this activity, you will compute and interpret 95% and 99% confidence intervals vidual means and for mean differences. However, there is some preliminary informa understand before you can start computing confidence intervals population of seniors in your district is between 29 and 43 you shoe Review of t Distributions As you know, scores in the middle of t distributions are more common than scores in the pe The following t curve represents all possible sample mean differences if the null hypothesisis true. The two vertical lines create three areas on the curve; if the middle section contains the middle 95% of all t scores (and all sample mean differences), what percentage of all t scores in the left and right tails of the distribution? a. 5% in the left and 5% in the right 1. 2.5% in the left and 2.5% in the right 1 % in the left and 1 % in the right b, c, Middle 95% -4 3 2 1 0 12 3

Explanation / Answer

Ans:

scenario 1)

10)point estimate=sample mean=M=59

11)N=15

df=15-1=14

critical t value=tinv(0.05,14)=2.145

Margin of error=2.145*4/sqrt(15)=2.22

12)Upper boundary=59+2.22=61.22

13)lower boundary=59-2.22=56.78

14)Option C is correct.

Scenario 2)

15)point estimate=sample mean=M=59

16)N=15

df=15-1=14

critical t value=tinv(0.01,14)=2.977

Margin of error=2.977*4/sqrt(15)=3.07

17)Upper boundary=59+3.07=62.07

18)lower boundary=59-3.07=55.93

19)Option C is correct.

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