The problem asks us to estimate the chi-square value when $n=23$ and $p=99$, given a table of chi-square values for various $n$ and $p$ values.

1. Problem Description

The problem asks us to estimate the chi-square value when $n=23$ and $p=99$, given a table of chi-square values for various $n$ and $p$ values.

2. Solution Steps

We are given the following table:

| n/p | 95 | 99 | 99.9 |

|-----|-------|-------|-------|

| 20 | 31.41 | 37.57 | 45.31 |

| 22 | 33.92 | 40.29 | 51.18 |

| 24 | 36.42 | 42.98 | 54.05 |

We want to estimate the chi-square value for $n=23$ and $p=99$. We can use linear interpolation to estimate this value.

First, we interpolate between $n=22$ and $n=24$ for $p=99$. The corresponding chi-square values are $40.29$ and $42.98$, respectively.

Since 23 is exactly in the middle of 22 and 24, the interpolated value is the average of 40.29 and 42.

9

8.

Interpolated value $= \frac{40.29 + 42.98}{2} = \frac{83.27}{2} = 41.635$

So, the estimated chi-square value for $n=23$ and $p=99$ is $41.635$.

3. Final Answer

41.635