A simple random sample of size n is drawn from a population that is normally dis

Question

A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, , is found to be 107, and the sample standard deviation, s, is found to be 10. (a) Construct a 98% confidence interval about if the sample size, n, is 15. (b) Construct a 98% confidence interval about if the sample size, n, is 26 (c) Construct a 99% confidence interval about if the sample size, n, is 15. (d) Could we have computed the confidence intervals in parts (a-(c) if the population had not been normally distributed? Click the icon to view the table of areas under the t-distribution.

Explanation / Answer

Solution:- x = 107,s = 10

a) 98% confidence interval and n = 15 = 107 ± 2.624*(10/sqrt(15)

= ( 107 - 2.624*(10/sqrt(15) , 107 + 2.624*(10/sqrt(15)

= ( 100.2248 , 113.7751)

b) 98% confidence interval and n = 26 = 107 ± 2.624*(10/sqrt(26)

= ( 107 - 2.624*(10/sqrt(26) , 107 + 2.624*(10/sqrt(26)

= ( 101.8539 , 112.1461)

c) 99% confidence interval and n = 15 = 107 ± 2.977*(10/sqrt(15)

= ( 107 - 2.977*(10/sqrt(15) , 107 + 2.977*(10/sqrt(15)

= ( 99.3134 , 114.6866)

d) the confidence interval increase,the size of the interval increase.

=> no,The calculate the confidence interval parameter mu . Assume the normality of population

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