Chapter 24, Problem 8E

(a)

To determine

To interpret your interval in context.

Answer to Problem 8E

We are $90\%$ confident that the true mean time for the NV group is between $0.55\text{ seconds and }5.47\text{ seconds}$ higher than the true mean time for the VV group.

Explanation of Solution

In the question, stereograms appear to be composed entirely of random dots. However, they contain separate images that a viewer can “fuse” into a three-dimensional image by staring at the dots while defocusing the eyes. Thus, an experiment was performed to determine whether knowledge of the form of the embedded image affected the time required for subjects to fuse the images. It is also given that,

Confidence level: $90\%$

  $df=70$

Confidence interval: $(0.55,5.47)$ .

Thus, the interval interprets that we are $90\%$ confident that the true mean time for the NV group is between $0.55\text{ seconds and }5.47\text{ seconds}$ higher than the true mean time for the VV group.

(b)

To determine

To explain does it appear that viewing a picture of the image helps people “see” the $3\text{D}$ image in a stereogram.

Answer to Problem 8E

It appears that viewing a picture of the image helps people “see” the $3\text{D}$ image in a stereogram.

Explanation of Solution

In the question, stereograms appear to be composed entirely of random dots. However, they contain separate images that a viewer can “fuse” into a three-dimensional image by staring at the dots while defocusing the eyes. Thus, an experiment was performed to determine whether knowledge of the form of the embedded image affected the time required for subjects to fuse the images. It is also given that,

Confidence level: $90\%$

  $df=70$

Confidence interval: $(0.55,5.47)$ .

Thus, it appear that viewing a picture of the image helps people “see” the $3\text{D}$ image in a stereogram because the confidence interval does not contain zero and the confidence interval only contains values above zero.

(c)

To determine

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

Answer to Problem 8E

The margin of error is $2.46$ .

Explanation of Solution

In the question, stereograms appear to be composed entirely of random dots. However, they contain separate images that a viewer can “fuse” into a three-dimensional image by staring at the dots while defocusing the eyes. Thus, an experiment was performed to determine whether knowledge of the form of the embedded image affected the time required for subjects to fuse the images. It is also given that,

Confidence level: $90\%$

  $df=70$

Confidence interval: $(0.55,5.47)$ .

Thus, the margin of error will be as:

  $\begin{array}{l}E=\frac{5.47-0.55}{2}\\ =2.46\end{array}$

(d)

To determine

To explain what does the $90\%$ confidence interval means.

Explanation of Solution

In the question, stereograms appear to be composed entirely of random dots. However, they contain separate images that a viewer can “fuse” into a three-dimensional image by staring at the dots while defocusing the eyes. Thus, an experiment was performed to determine whether knowledge of the form of the embedded image affected the time required for subjects to fuse the images. It is also given that,

Confidence level: $90\%$

  $df=70$

Confidence interval: $(0.55,5.47)$ .

Thus, the $90\%$ confidence interval means that the confidence interval contains the true population value in $90\%$ of all possible samples.

(e)

To determine

To explain would you expect a $99\%$ confidence level to be wider or narrower.

Answer to Problem 8E

It will become wider.

Explanation of Solution

In the question, stereograms appear to be composed entirely of random dots. However, they contain separate images that a viewer can “fuse” into a three-dimensional image by staring at the dots while defocusing the eyes. Thus, an experiment was performed to determine whether knowledge of the form of the embedded image affected the time required for subjects to fuse the images. It is also given that,

Confidence level: $90\%$

  $df=70$

Confidence interval: $(0.55,5.47)$ .

Now, if we increase the confidence level from $90\%\text{ to 99\%}$ , then

We will be more confident that the confident that the confidence level contains the true difference of the means. In order to become more confident, the confidence interval will then need to become wider.

(f)

To determine

To explain might that change your conclusion in part (b).

Answer to Problem 8E

Yes, it might change.

Explanation of Solution

In the question, stereograms appear to be composed entirely of random dots. However, they contain separate images that a viewer can “fuse” into a three-dimensional image by staring at the dots while defocusing the eyes. Thus, an experiment was performed to determine whether knowledge of the form of the embedded image affected the time required for subjects to fuse the images. It is also given that,

Confidence level: $90\%$

  $df=70$

Confidence interval: $(0.55,5.47)$ .

Thus, yes, it might change the conclusion in part (b) because if the confidence interval becomes wider, then it is possible that the confidence interval contains zero and then we would conclude "No" instead of "Yes".