when is unknown and the sample is of size n 2 30, there are two methods for comp
ID: 3066579 • Letter: W
Question
when is unknown and the sample is of size n 2 30, there are two methods for computing confidence intervals for Method 1: Use the Student's t distribution with d.f.n 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this methad. Method 2: When n 30, use the sample standard deviation s as an estimate for , and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for Also for large the critical values for the Student's t distribution approach those of the standard normal distribution. Consider a random sample of size n 36, with sample mean-44.9 and sample standard deviation -6.0. (a) Compute 90%, 95%, and 99% confidence intervals for using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal. 90% 95% 999g lower limit (b) Compute 90%, 95%, and 99% confidence intervals for using Method 2 with the standard normal distribution. use s as an estimate for . Round endpoints to two digits after the decimal. 90% 95% upper limit (c) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution? 0 No. The respective intervals based on the t distribution are longer O No. The respective interval: based on the t distribution are shorter O Yes. The respective intervals based on the t distribution are longer. O Yes. The respective intervals based on the t distribution are shorter (d) Nov, consider a sample size of 81. Compute 909, 95%, and 99% confidence intervals for using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit (e) Compute 90%, 95%, and 99% confidence intervals for using Method 2 with the standard normal distribution. Use s as an estimate for . Round endpoints to two digits after the decimal. 99% lower limit (F) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution? O No. The respective intervals based on the t distribution are longer O No. The respective intervals based on the t distribution are shorter, O Yes. The respective intervals based on the t distribution are longer O Yes. The respective intervals based on the t distribution are shorter. With increased sampla siza, do the two methods give respective confidance intervals that are moro similar? O As tho sample siza incraases, the difference batween the tuwo methods remains constant. O As the sample size increases, the difference between the two methods is less pronounced. O As the sample siza incraases, the difference batwean the two mathods becomes greater.Explanation / Answer
a) 90% 95% 99%
Lower Limit 43.21043 42.86989 42.1762
Uppoer limit 46.58957 46.93011 47.6238
b) 90% 95% 99%
Lower Limit 43.25515 42.94004 42.32417
Uppoer limit 46.54485 46.85996 47.47583
c) Correct answer: (A)
d)
90% 95% 99%
Lower Limit 43.79058 43.57329 43.79058
Uppoer limit 46.00942 46.22671 46.00942
e)
90% 95% 99%
Lower Limit 43.80343 43.59336 43.18278
Uppoer limit 45.99657 46.20664 46.61722
f)
Correct answer: (A)
Correct answer: (B)
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