High School

The small round holes you often see in sea shells were drilled by other sea creatures, who ate the former dwellers of the shells. Whelks often drill into mussels, but this behavior appears to be more or less common in different locations. Researchers collected whelk eggs from the coast of Oregon, raised the whelks in the laboratory, and then put each whelk in a container with some mussels. Only 9 of 98 whelks drilled into a mussel.

Check to see if the conditions for calculating a confidence interval for [tex]p[/tex] are met, where [tex]p[/tex] is the proportion of all Oregon whelks that will spontaneously drill into mussels.

A. Random? Collected 98 whelk eggs (not sure if random) √
Large Counts? [tex]98 \left(\frac{9}{98}\right) = 9 \geq 10[/tex] and [tex]98 \left(\frac{89}{98}\right) = 89 \geq 10[/tex] √

B. Fails Random and Large Counts

C. Fails Large Counts

D. Not Random

Answer :

The conditions for calculating a confidence interval for p are met. Hence, Option A is the correct answer.

The question demands to check the conditions for calculating a confidence interval for p, where p = the proportion of all Oregon whelks that will spontaneously drill into mussels. The proportion of the 98 whelks that drilled into a mussel is given as pˆ = 9/98. To calculate a confidence interval for the proportion p, there are certain conditions that need to be met.

The sample needs to be random, and in this case, the whelk eggs collected were indeed a random sample. Large counts must be observed. This condition is met because 9(98/9) and 89(98/89) are greater than or equal to 10. Hence, the conditions for calculating a confidence interval for p are met.Therefore, Option A is the correct answer.

Learn more about confidence interval here:

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