Solve the problem. 5) In constructing a confidence interval for or o2 , a table

Question

Solve the problem. 5) In constructing a confidence interval for or o2 , a table is used to find the critical values 2 and for values of n 101. For larger values of n.x? and using the following formula: can be approximated by 2 where k is the number of degrees of freedom and za/2 is the critical z score. Estimate the critical values and for a situation in which you wish to construct a 95% confidence interval for and in which the sample size is n-298. A) 2 250.692, : 346.150 A) L-250.692, R ~ 346.150 C) 257.795, #337.911 B) ~ 258.727, ~ 338.979 L. D) L 251.611, #347.230

Explanation / Answer

6.

Sample size is n=20

so degree of freedom for t distribution :df = 20-1 = 19

Therefore critical value of t for 95% confidence interval is 2.093

While critical value of z for 95% confidence inetravl is 1.96

That is for the given sample size critical value of t is greater than critical value of z. So confidence interval made using z critical value is samller than confidence interval made using t critical value. So confidence level of the interval smaller than 95%.

Hence, option C is correct.

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