Question

16 based on a random sample from a population, a researcher estimated that the mean value of a certain variable for the population is 20.5, with an associated margin of error of 1. which of the following is the most appropriate conclusion? a) it is plausible that the actual mean value of the variable for the population is between 19.5 and 21.5. b) it is not possible that the mean value of the variable for the population is less than 19.5 or greater than 21.5. c) every value of the variable in the population is between 19.5 and 21.5. d) the mean value of the variable for the population is 20.5. 17 7m = 5(n + p) the given equation relates the positive numbers m, n, and p. which equation correctly gives n in terms of m and p? a) n = \frac{5p}{7m} b) n = \frac{7m}{5}-p c) n = 5(7m)+p d) n = 7m - 5 - p

Explanation:

1. Solution for question 16

Step1: Recall margin - of - error concept

The confidence interval for the population mean $\mu$ is given by $\bar{x}\pm E$, where $\bar{x}$ is the sample - estimated mean and $E$ is the margin of error. Here, $\bar{x} = 20.5$ and $E = 1$.

Step2: Calculate the confidence interval

The lower limit of the confidence interval is $20.5−1=19.5$ and the upper limit is $20.5 + 1=21.5$. This means that it is plausible that the actual population mean lies within this interval.

Step1: Expand the given equation

We start with $7m = 5(n + p)$. Expand the right - hand side using the distributive property: $7m=5n+5p$.

Step2: Isolate $n$

Subtract $5p$ from both sides of the equation: $7m−5p = 5n$. Then divide both sides by 5 to solve for $n$: $n=\frac{7m}{5}-p$.

Answer:

A. It is plausible that the actual mean value of the variable for the population is between 19.5 and 21.5.

2. Solution for question 17