The Golden Retriever Club of America conducted a study of 64 golden retrievers,

Question

The Golden Retriever Club of America conducted a study of 64 golden retrievers, and found the average age at death in the sample to be 11.0 years old. Let’s assume the standard deviation of golden retriever lifespan is known to be 1.2 years (this is consistent with studies and with some other dog breeds). Give three confidence interval estimates for the unknown mean age at death for golden retrievers: first using 90% confidence, then 95%, and finally 99%. Please report your intervals in parenthesis notation, and please round your final values to the nearest tenth for simplicity. Be sure to notice the size of the intervals with the different confidence levels.

Explanation / Answer

here n=64, sample mean=11, sd=1.2

(1-alpha)*100% confidence interval for sample mean=mean± z(alpha/2)*sd/sqrt(n)

90% confidence interval for sample mean=mean±z(0.1/2)*sd/sqrt(n)=11±1.645*1.2/sqrt(64)=11±0.25=(10.75,11.25)

95% confidence interval for sample mean=mean±z(0.05/2)*sd/sqrt(n)=11±1.96*1.2/sqrt(64)=11±0.29=(10.71,11.29)

90% confidence interval for sample mean=mean±z(0.01/2)*sd/sqrt(n)=11±2.58*1.2/sqrt(64)=11±0.39=((10.61,11.39)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.