Question

ch 16 a level 0.95 confidence interval is
a range of values computed from sample data that will contain the true value of the parameter of interest 95% of the time.
a range of values computed from sample data by a method that guarantees that the probability the interval computed contains the parameter of interest is 0.95.
any interval with margin of error ± 0.95.
a range of values with margin of error ± 0.95, which is also correct 95% of the time.
question 2
1 pts
ch 16* the national assessment of educational progress (naep) includes a mathematical test for eighth - grade students. scores on the test range from 0 to 500. suppose that you give the naep test to an srs of 900 eighth - graders from a large population in which the scores have mean μ = 285 and standard deviation σ = 125. the sample mean (x⁻) will vary if you take repeated samples.
the sampling distribution of x⁻ is approximately normal. it has mean μ = 285. what is its standard deviation of x⁻?
0.139
125
4.167

Explanation:

Question 1

A level - 0.95 confidence interval is a range of values compute from sample data by a method such that the probability the interval contains the true value of the parameter of interest is 0.95. It does not mean the margin of error is ±0.95.

Step1: Recall the formula for the standard deviation of the sample - mean

The standard deviation of the sample - mean (also known as the standard error) is given by the formula $\sigma_{\bar{X}}=\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard deviation and $n$ is the sample size.

Step2: Identify the values of $\sigma$ and $n$

We are given that $\sigma = 125$ and $n = 900$.

Step3: Calculate the standard deviation of the sample - mean

Substitute the values into the formula: $\sigma_{\bar{X}}=\frac{125}{\sqrt{900}}=\frac{125}{30}\approx4.167$.

Answer:

a range of values computed from sample data by a method that guarantees that the probability the interval computed contains the parameter of interest is 0.95.

Question 2