Asked by Gisell Garcia on Jun 09, 2024
Verified
If you wish to estimate with 95% confidence the average number of miles that students living off-campus commute to classes every day, a random sample of 20 students produced a mean equal to 5.2 miles and a standard deviation of 3.05 miles. Then, the upper limit for a 95% confidence interval estimate for the true population mean is approximately:
A) 3.22
B) 6.63
C) 5.20
D) 2.15
E) 1.96
Population Mean
The average value of a property in a population, calculated by summing the values of all members of the population and dividing by the total number of members.
Confidence Interval
A range of values derived from sample statistics that is likely to cover the true parameter of the population with a certain level of confidence.
Standard Deviation
A statistic that measures the dispersion of a dataset relative to its mean.
- Acquire a deep comprehension of confidence intervals and the methods used to calculate them, highlighting the pivotal role played by t-distribution.
- Evaluate statistical data to approximate the parameters of populations.
- Understand the application of t-distribution in estimating population means from sample data.
Verified Answer
AD
Annierys DominguezJun 12, 2024
Final Answer :
B
Explanation :
Using the formula for confidence interval with a sample size less than 30, we have:
Upper limit = sample mean + (t-value * standard error)
where t-value for a 95% confidence level with 19 degrees of freedom (df=n-1) is 2.093.
Standard error = standard deviation / square root of sample size
= 3.05 / sqrt(20)
= 0.682
Therefore, upper limit = 5.2 + (2.093 * 0.682)
= 6.63
So, the best choice is B.
Upper limit = sample mean + (t-value * standard error)
where t-value for a 95% confidence level with 19 degrees of freedom (df=n-1) is 2.093.
Standard error = standard deviation / square root of sample size
= 3.05 / sqrt(20)
= 0.682
Therefore, upper limit = 5.2 + (2.093 * 0.682)
= 6.63
So, the best choice is B.
Learning Objectives
- Acquire a deep comprehension of confidence intervals and the methods used to calculate them, highlighting the pivotal role played by t-distribution.
- Evaluate statistical data to approximate the parameters of populations.
- Understand the application of t-distribution in estimating population means from sample data.