Asked by Zaria Howard on Jul 11, 2024
Verified
How tall is your average statistics classmate? To determine this,you measure the height of a random sample of 15 of your 200 fellow students,finding a mean height of 166.6 cm and a standard deviation of 5.64 cm.Construct a 90% confidence interval for the mean height of your classmates.
A) (163.73,169.27)
B) (164.04,169.16)
C) (165.992,167.01)
D) (164.02,168.98)
E) (164.91,170.09)
Mean Height
The average height of a group of individuals.
- Achieve understanding of how to calculate confidence intervals for assorted confidence levels and sample sizes.
- Learn to apply and calculate confidence intervals in scenarios encountered in the real world.
Verified Answer
GF
Grace FleetwoodJul 11, 2024
Final Answer :
B
Explanation :
Using the formula for a confidence interval for a population mean with a known standard deviation and a 90% confidence level, we have:
Margin of error = z* (standard deviation / square root of sample size)
where z* is the z-score associated with the 90% confidence level, which can be found using a standard normal distribution table or calculator. For a two-tailed 90% confidence level, we have:
z* = 1.645
Plugging in the values from the problem, we get:
Margin of error = 1.645 * (5.64 / sqrt(15)) ≈ 2.31
Therefore, the 90% confidence interval for the mean height of the population of statistics classmates is:
166.6 ± 2.31
or
(164.29, 168.91)
Among the answer choices, the closest one to this interval is B, (164.04,169.16), so that is the best choice.
Margin of error = z* (standard deviation / square root of sample size)
where z* is the z-score associated with the 90% confidence level, which can be found using a standard normal distribution table or calculator. For a two-tailed 90% confidence level, we have:
z* = 1.645
Plugging in the values from the problem, we get:
Margin of error = 1.645 * (5.64 / sqrt(15)) ≈ 2.31
Therefore, the 90% confidence interval for the mean height of the population of statistics classmates is:
166.6 ± 2.31
or
(164.29, 168.91)
Among the answer choices, the closest one to this interval is B, (164.04,169.16), so that is the best choice.
Learning Objectives
- Achieve understanding of how to calculate confidence intervals for assorted confidence levels and sample sizes.
- Learn to apply and calculate confidence intervals in scenarios encountered in the real world.