Chapter 21, Problem 34E

(a)

To determine

To find out what is the probability that this test convinces her to use it anyway.

Answer to Problem 34E

  $4.64\%$ .

Explanation of Solution

It is given in the question that an artist experimenting with clay to create pottery with a special texture has been experiencing difficulty with these special pieces and about $40\%$ break in the kiln during firing. Thus, the probability that this test convinces her to use it anyway is calculated by using the calculator $\text{TI}-89$ using the Binomcdf command as,

  $\begin{array}{l}binomcdf(10,0.4,1)=0.0464\\ =4.64\%\end{array}$

(b)

To determine

To explain what kind of error did she commit.

Answer to Problem 34E

It is Type I error.

Explanation of Solution

It is given in the question that an artist experimenting with clay to create pottery with a special texture has been experiencing difficulty with these special pieces and about $40\%$ break in the kiln during firing. Thus, the error she committed is the Type I error because it is given that she decided to switch to the new clay and it is no better, so, when something seems true but it is actually false it is a Type I error.

(c)

To determine

To find out what is the probability that her test will not detect the improvement.

Answer to Problem 34E

  $0.6242$ .

Explanation of Solution

It is given in the question that an artist experimenting with clay to create pottery with a special texture has been experiencing difficulty with these special pieces and about $40\%$ break in the kiln during firing. Thus, the probability that her test will not detect the improvement is calculated as,

  $\begin{array}{l}=2^2\times 8^8+2^3\times 8^7+2^4\times 8^6+2^5\times 8^5+2^6\times 8^4+2^7\times 8^3+2^8\times 8^2+\\ 2^9\times 8^1+2^{10}\times 8^0\\ =0.6242\end{array}$

(d)

To determine

To explain how can she improve the power of her test by offering at least two suggestions.

Explanation of Solution

It is given in the question that an artist experimenting with clay to create pottery with a special texture has been experiencing difficulty with these special pieces and about $40\%$ break in the kiln during firing. Thus, she can improve the power of her test as she can fire more pieces of clay or lower standard of proof, so, $0,1\text{ or 2}$ pieces of broken clay will conceive the artist.