A new species of sea crab has been discovered, and a study was conducted to determine whether or not the animal can regulate its temperature. If the animal can maintain a body temperature different from the surroundings, this would be considered evidence of regulating capability. Ten of these sea crabs were exposed to ambient temperatures of 24 degrees Celsius and their body temperatures were measured. The sample mean was $24.694$ degrees, and the standard deviation $0.277$ degrees.

For purposes of this example, assume that it is reasonable to regard these 10 crabs as a random sample from the population of all crabs of this species. A plot of the data indicated that the assumption of approximately normal body temperatures was credible.
a) Construct and interpret a $99 \%$ confidence interval for the mean body temperature, $\mu$.

b) Based on your answer to part (a), does it appear that the crabs are able to regulate their body temperature? Provide statistical justification for your response.

Question

A new species of sea crab has been discovered, and a study was conducted to determine whether or not the animal can regulate its temperature. If the animal can maintain a body temperature different from the surroundings, this would be considered evidence of regulating capability. Ten of these sea crabs were exposed to ambient temperatures of 24 degrees Celsius and their body temperatures were measured. The sample mean was $24.694$ degrees, and the standard deviation $0.277$ degrees.

For purposes of this example, assume that it is reasonable to regard these 10 crabs as a random sample from the population of all crabs of this species. A plot of the data indicated that the assumption of approximately normal body temperatures was credible.
a) Construct and interpret a $99 \%$ confidence interval for the mean body temperature, $\mu$.

b) Based on your answer to part (a), does it appear that the crabs are able to regulate their body temperature? Provide statistical justification for your response.

Quizplus · Accepted Answer

The Answer of A new species of sea crab has been discovered, and a study was conducted to determine whether or not the animal can regulate its temperature. If the animal can maintain a body temperature different from the surroundings, this would be considered evidence of regulating capability. Ten of these sea crabs were exposed to ambient temperatures of 24 degrees Celsius and their body temperatures were measured. The sample mean was $24.694$ degrees, and the standard deviation $0.277$ degrees.

For purposes of this example, assume that it is reasonable to regard these 10 crabs as a random sample from the population of all crabs of this species. A plot of the data indicated that the assumption of approximately normal body temperatures was credible.
a) Construct and interpret a $99 \%$ confidence interval for the mean body temperature, $\mu$.

b) Based on your answer to part (a), does it appear that the crabs are able to regulate their body temperature? Provide statistical justification for your response.

A New Species of Sea Crab Has Been Discovered, and a Study