Let's solve the problem step by step to find the expected value for characteristic D.
1. Understanding the frequencies:
We have given frequencies for six characteristics: A, B, C, D, E, and F.
[tex]\[
\begin{array}{c|cccccc}
\text{Characteristic} & A & B & C & D & E & F \\
\hline
\text{Frequency} & 28 & 30 & 45 & 48 & 39 & 39 \\
\end{array}
\][/tex]
2. Calculate the total number of occurrences:
To find the total number of occurrences, sum up all the given frequencies:
[tex]\[
28 + 30 + 45 + 48 + 39 + 39 = 229
\][/tex]
3. Determine the null hypothesis (equal frequencies):
Under the null hypothesis, we assume that each characteristic occurs with equal frequency.
4. Calculate the expected frequency for each characteristic:
Since the total number of occurrences is 229 and there are 6 characteristics, the expected frequency for each characteristic is:
[tex]\[
\text{Expected Frequency} = \frac{\text{Total Occurrences}}{\text{Number of Characteristics}} = \frac{229}{6} \approx 38.1667
\][/tex]
The expected value for characteristic D (and all other characteristics under the null hypothesis) is [tex]\( \approx 38.1667 \)[/tex].
Based on this calculation, the closest option from the provided choices is:
A. 38
Hence, the expected value for D is 38.
