Assume that 1600 births are randomly selected and 1575 of the births are girls. Use subjective judgment to describe the number of girls as significantly high, significantly low, or neither significantly low nor significantly high.
Choose the correct answer below.
A. The number of girls is significantly high.
B. The number of girls is significantly low.
C. The number of girls is neither significantly low nor significantly high.
D. It is impossible to make a judgment with the given information.
Answer (2)
Calculate the proportion of girls: p = 1600 1575 = 0.984375 .
Compare the observed proportion with the expected proportion (0.5).
The proportion of girls is significantly higher than expected.
Conclude that the number of girls is significantly high: A .
Explanation
Analyze the problem We are given that out of 1600 births, 1575 are girls. We need to determine if this number is significantly high, significantly low, or neither, using subjective judgment.
Calculate the proportion of girls First, let's calculate the proportion of girls: p = 1600 1575 = 0.984375
Compare with the expected proportion The expected proportion of girls is typically assumed to be 0.5 (50%). Now, let's compare the observed proportion (0.984375) with the expected proportion (0.5). The difference is: d = 0.984375 − 0.5 = 0.484375
Draw a conclusion The proportion of girls is 0.984375, which is significantly higher than the expected proportion of 0.5. This suggests that the number of girls is significantly high.
Examples
In a real-world scenario, if a study found a significantly higher proportion of girls born in a specific region compared to the expected 50%, it might prompt further investigation into environmental or genetic factors influencing sex ratios. For example, if a town of 1600 births had 1575 girls, the proportion of girls p = 1600 1575 = 0.984375 is much higher than the expected 0.5. This could lead to research on potential causes.
The proportion of girls born (0.984375) is significantly higher than the expected 0.5. Therefore, we conclude that the number of girls is significantly high. The chosen answer is A.
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