Chapter 19, Problem 6E

(a)

To determine

To explain what does this mean and are the conclusions correct or not.

Answer to Problem 6E

It is incorrect.

Explanation of Solution

It is given in the question that two students made worldwide headlines by spinning a Belgian euro $\text{250}$ times. Thus, the conclusion is given on the confidence interval calculated of the proportion of spins as: between $\text{51\% and 61\%}$ of all euros are unfair. This is simply incorrect as the interval is about the proportion of heads, not individual coins.

(b)

To determine

To explain what does this mean and are the conclusions correct or not.

Answer to Problem 6E

It is incorrect.

Explanation of Solution

It is given in the question that two students made worldwide headlines by spinning a Belgian euro $\text{250}$ times. Thus, the conclusion is given on the confidence interval calculated of the proportion of spins as: we are $\text{90\%}$ sure that in this experiment this euro landed heads between $\text{51\% and 61\%}$ of the spins. This conclusion is incorrect because we know in this sample that $\text{56\%}$ of the spins were heads.

(c)

To determine

To explain what does this mean and are the conclusions correct or not.

Answer to Problem 6E

It is correct.

Explanation of Solution

It is given in the question that two students made worldwide headlines by spinning a Belgian euro $\text{250}$ times. Thus, the conclusion is given on the confidence interval calculated of the proportion of spins as: we are $\text{90\%}$ sure that spun euros will land heads between $\text{51\% and 61\%}$ of the time. This conclusion is correct because the interval is about the parameter, not about individual spins.

(d)

To determine

To explain what does this mean and are the conclusions correct or not.

Answer to Problem 6E

It is correct.

Explanation of Solution

It is given in the question that two students made worldwide headlines by spinning a Belgian euro $\text{250}$ times. Thus, the conclusion is given on the confidence interval calculated of the proportion of spins as: if you spin an euro many times, you can be $\text{90\%}$ sure of getting between $\text{51\% and 61\%}$ heads. This statement is correct because the interval is about the individual spins.

(e)

To determine

To explain what does this mean and are the conclusions correct or not.

Answer to Problem 6E

It is incorrect.

Explanation of Solution

It is given in the question that two students made worldwide headlines by spinning a Belgian euro $\text{250}$ times. Thus, the conclusion is given on the confidence interval calculated of the proportion of spins as: $\text{90\%}$ of all spun euros will land head between $\text{51\% and 61\%}$ of all time. This conclusion is incorrect because the interval is about the proportion of heads, not about the percentage of euros.