(b) What is the 95% confidence interval estimate of the population mean examination score if a sample of 100 applications provided a sample mean x = 833? A confidence interval for a population mean, u, is found by adding and subtracting the margin of error, E, to the given sample mean, as follows. Recall that z, is the standard normal random variable corresponding to a particular level of confidence and n is the sample size. x+ E, where E = z2 A sample of 100 applications provided a mean of 833 and the standard deviation is known to be 150. Thus, n = and . Now the value of za is needed. A 95% confidence interval is to be found. The margin of error corresponding to a 95% confidence level is needed, which is calculated using z2. Common values for z, for various confidence levels are given below. * Za/2 Confidence Level a 90% 0.10 0.05 1.645 95% 0.05 0.025 1.960 99% 0.01 0.005 2.576 For a 95% confidence level, the necessary value for z/2 is
(b) What is the 95% confidence interval estimate of the population mean examination score if a sample of 100 applications provided a sample mean x = 833? A confidence interval for a population mean, u, is found by adding and subtracting the margin of error, E, to the given sample mean, as follows. Recall that z, is the standard normal random variable corresponding to a particular level of confidence and n is the sample size. x+ E, where E = z2 A sample of 100 applications provided a mean of 833 and the standard deviation is known to be 150. Thus, n = and . Now the value of za is needed. A 95% confidence interval is to be found. The margin of error corresponding to a 95% confidence level is needed, which is calculated using z2. Common values for z, for various confidence levels are given below. * Za/2 Confidence Level a 90% 0.10 0.05 1.645 95% 0.05 0.025 1.960 99% 0.01 0.005 2.576 For a 95% confidence level, the necessary value for z/2 is
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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At a university the historical mean of scholarship examination scores for freshman applications is 800. A historical population standard deviation ? = 150 is assumed known. Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.
Transcribed Image Text:(b) What is the 95% confidence interval estimate of the population mean examination score if a sample of 100 applications provided a sample mean x = 833?
A confidence interval for a population mean, u, is found by adding and subtracting the margin of error, E, to the given sample mean, as follows. Recall that z, is the standard
normal random variable corresponding to a particular level of confidence and n is the sample size.
x+ E, where E = z
A sample of 100 applications provided a mean of 833 and the standard deviation is known to be 150. Thus, n =
and
Now the value of za is needed.
A 95% confidence interval is to be found. The margin of error corresponding to a 95% confidence level is needed, which is calculated using z2: Common values for z2
for
various confidence levels are given below.
Confidence Level
Za/2
a
90%
0.10
0.05
1.645
95%
0.05
0.025
1.960
99%
0.01
0.005
2.576
For a 95% confidence level, the necessary value for z12
is
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