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Births: Sampling Distribution of Sample Proportion When
Chapter 6, Problem 16BSC(choose chapter or problem)
Problem 16BSC
Births: Sampling Distribution of Sample Proportion When three births are randomly selected, the sample space for genders is bbb, bbg, bgb, bgg, gbb, gbg, ggb, and ggg. Assume that those eight outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from three births. Does the mean of the sample proportions equal the proportion of girls in three births?
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QUESTION:
Problem 16BSC
Births: Sampling Distribution of Sample Proportion When three births are randomly selected, the sample space for genders is bbb, bbg, bgb, bgg, gbb, gbg, ggb, and ggg. Assume that those eight outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from three births. Does the mean of the sample proportions equal the proportion of girls in three births?
ANSWER:Answer :
Step 1 of 1 :
The sample space for genders is bbb, bbg, bgb, bgg, gbb, gbg, ggb, and ggg.
We assume that those eight outcomes are equally likely.
We have to construct a table that describes the sampling distribution of the sample proportion of girls from three births.
The sample proportion is the number of girls divided by the number of individual in the sample.
Assign every sample as an equal probability.
Add the probabilities for each sample value.
Then the table is given below.
Sample |
Sample Proportion |
Probability |
bbb |
0 |
1/8 |
bbg |
1/3 |
1/8 |
bgb |
1/3 |
1/8 |