Question
Thensive Quiz
In a sample of 10 randomly selected women, it was found that their mean height was 63.4 inches. From previous studies, it can be assumed that the population standard
deviation
A.
B.
C.
D.
In a sample of 10 randomly selected women, it was found that their mean height was 63.4 inches. From previous studies, it can be assumed that the population standard
deviation
A.
B.
C.
D.
Ask by Lang Estrada. in the United States
Dec 13,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The
Solution
To construct a
Where:
-
is the sample mean -
is the z-score corresponding to the desired confidence level -
is the population standard deviation -
is the sample size
Given:
- Sample mean
inches - Population standard deviation
- Sample size
-
Find the z-score for a
confidence level:
The z-score for aconfidence level is approximately . -
Calculate the standard error (SE):
-
Calculate the margin of error (ME):
-
Construct the confidence interval:
Thus, the
The correct answer is:
A.
A.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To construct a
Where:
-
(sample mean) -
(population standard deviation) -
(sample size) -
is the z-value corresponding to the desired confidence level (approximately 1.96 for confidence)
Calculating the standard error (SE):
Now, using the z-score to calculate the margin of error:
Now, calculate the confidence interval:
Rounding to one decimal place, the
So the answer is A.
Confidence intervals give you a range of plausible values for the population mean based on your sample data. It’s like having a safety net—if you were to repeat the process many times, you expect the true mean to fall within this range in
Understanding how these intervals work in practice can be crucial, especially in fields like medicine or economics, where decisions depend on estimating values based on sample data. They’re not just numbers; they represent the uncertainty and reliability of our estimates!
