Chapter 24, Problem 7E

(a)

To determine

To find out what is the margin of error for this confidence interval.

Answer to Problem 7E

The margin of error is $2.927$ .

Explanation of Solution

The core plus mathematics program (CPMP) is an innovative approach to teaching mathematics. After field test in high schools over a three-year period, researchers compared the performances of CPMP students with those taught using traditional curriculum. The computer software is used to generate results i.e.

Confidence level: $95\%$

Confidence interval: $(5.573,11.427)$ .

Thus, the margin of error is calculated as:

  $\begin{array}{l}E=\frac{11.427-5.573}{2}\\ =2.927\end{array}$

(b)

To determine

To explain if you had created a $98\%$ confidence interval, would the margin of error be larger or smaller.

Answer to Problem 7E

The margin of error will increase.

Explanation of Solution

The core plus mathematics program (CPMP) is an innovative approach to teaching mathematics. After field test in high schools over a three-year period, researchers compared the performances of CPMP students with those taught using traditional curriculum. The computer software is used to generate results i.e.

Confidence level: $95\%$

Confidence interval: $(5.573,11.427)$ .

Now, if we increase the confidence interval from $95\%\text{ to 98\%}$ then,

We will be more confident that the confidence interval contains the true difference of the means. Thus, in order to become more confident, the confidence interval will then need to become wider and thus the margin of error will increase.

(c)

To determine

To explain what the calculated interval means in this context.

Explanation of Solution

The core plus mathematics program (CPMP) is an innovative approach to teaching mathematics. After field test in high schools over a three-year period, researchers compared the performances of CPMP students with those taught using traditional curriculum. The computer software is used to generate results i.e.

Confidence level: $95\%$

Confidence interval: $(5.573,11.427)$ .

Now, the calculated interval means in this context that we are $95\%$ confident that the true mean score for CPMP students is between $(5.573,11.427)$ than the true mean score for the control group of student in a traditional math program.

(d)

To determine

To explain does this result suggest that students who learn mathematics with CPMP will have significantly higher mean scores in algebra than those in traditional programs.

Answer to Problem 7E

Yes, it suggest this result.

Explanation of Solution

The core plus mathematics program (CPMP) is an innovative approach to teaching mathematics. After field test in high schools over a three-year period, researchers compared the performances of CPMP students with those taught using traditional curriculum. The computer software is used to generate results i.e.

Confidence level: $95\%$

Confidence interval: $(5.573,11.427)$ .

Thus, we conclude that this result suggest that students who learn mathematics with CPMP will have significantly higher mean scores in algebra than those in traditional programs because the confidence interval does not contain zero.