The standard deviation for a population is \sigma=14.8. A sample of 21 obs

Khaleesi Herbert

Khaleesi Herbert

Answered question

2021-10-02

The standard deviation for a population is σ=14.8. This population's sample of 21 observations yielded a mean value of 139.05. It is well known that the population has a normal distribution.
Round your answers to two decimal places. 
1) Make a 99% confidence interval for μ. ( Enter your answer; 99% confidence interval, lower bound ,Enter your answer; 99% confidence interval, upper bound ) 
2) Construct a 97% confidence interval for μ. ( Enter your answer; 97% confidence interval, lower bound ,Enter your answer; 97% confidence interval, upper bound ) 
3) Determine a 95% confidence interval for μ. ( Enter your answer; 95% confidence interval, lower bound ,Enter your answer; 95% confidence interval, upper bound )

Answer & Explanation

lobeflepnoumni

lobeflepnoumni

Skilled2021-10-03Added 99 answers

Step 1
Considering the data provided,
Population standard deviation (σ)=14.8
Sample size (n)=21
Sample mean (x)=139.05
1) Because we know the population standard deviation, we will use the z distribution.
The z value at 99% confidence level from the standard normal table is 2.58.
The required 99% confidence interval for µ can be obtained as:
CI=x±zα2σn
=139.05±(2.58)14.821
=139.05±8.33
=(130.72, 147.38)
Thus, the lower bound of 99% confidence interval is 130.72 and the upper bound is 147.38.
Step 2
2) The z value at 97% confidence level from the standard normal table is 2.17.
The required 97% confidence interval for μ can be obtained as:
CI=x¯±zα/2σn
139.05±(2.17)14.821
=139.50±7.01
(132.04, 146.06)
Thus, the lower bound of 97% confidence interval is 132.04 an the upper bound is 146.06
Step 3
3) The z value at 95% confidence level from the standard normal table is 1.96.
The required 95% confidence interval for μ can be obtained as:
CI=x±zα2σn
139.05±(1.96)14.821
=139.05±6.33
=(132.72, 145.38)
As a result, the 95% confidence interval's lower and upper bounds, respectively, are 132.72 and 145.38. 

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