Question

An SRS of size n was taken to estimate mean body mass index (BMI) for girls between 13 and 19 years of age. The 95% confidence interval obtained had lower limit 19.5 and upper limit 26.3. Which of the following is NOT true? 1. A total of 95% of all teenage girls have BMI between 19.5 and 26.3. 2. The margin of error is 34. 3. The value z in the margin of error is 1.96. 4. A total of 95% of all SRS of size n contain the true mean BMI

Answer 1

Answer:

Option 1) A total of 95% of all teenage girls have body mass index between 19.5 and 26.3.  

Step-by-step explanation:

We are given the following in the question:

95% confidence interval of mean body mass index (BMI) for girls between 13 and 19 years of age is:

$(19.5, 26.3)$

Lower limit = 19.5

Upper limit = 26.3

1. A total of 95% of all teenage girls have body mass index between 19.5 and 26.3.

The given statement is false. This is not the right interpretation for confidence interval.

2. The margin of error is 3.4

The confidence interval can be found as

$\text{sample mean}\pm \text{Margin of error}$

Let x be the sample mean and y be the margin of error, thus, we can write

$x - y =19.5\\x + y = 26.3\\2x =45.8 \\x = 22.9\\y = 22.9 - 19.5\\y = 3.4$

Thus, the margin of error is 3.4

Thus, the given statement is true.

3. The value z in the margin of error is 1.96.

The statement is true.

The z-multiplier for a 95% confidence interval used is 1.96

4. A total of 95% of all SRS of size n contain the true mean body mass index

The given statement is true. It is the right interpretation of 95% confidence interval.