At 8 weeks of age kittens at a specific shelter are assessed. A vet previously noted that the average weight of kittens (deemed healthy) at 8 weeks is 696.8 grams. A random sample of 9 kittens had an average weight of 664.2 grams and a sample standard deviation of 71.5. She calls a colleague at an affiliated rescue in another county to see if anything is happening with their kittens at 8 weeks of age. They observe that from a sample of 22 healthy independent kittens an average weight of 735.1g with a sample standard deviation of 82.5g. Assume the distribution of kitten weights at 8 weeks is sufficiently close to the normal distribution to use the central limit theorem, and that kittens are independent (statistically, not literally). Question 5: Suppose we anticipate an equal number of kittens in shelter A and shelter B. The true difference in the average weights of kittens is 10.0g, and the true standard deviations were 100.0g and 120.0g, respectively. Calculate the total sample size required in both shelters if a two-sided test is used with a 5% significance level and an 80% power is desired. If using R, round the critical value to two decimal places to ensure you obtain an answer that matches what you would get if using the textbook method to get the critical value. I think since we're assuming equal sample sizes in this question, we may not need to use the sample-specific numbers provided at the beginning. Thanks in advance for the help!
At 8 weeks of age kittens at a specific shelter are assessed. A vet previously noted that the average weight of kittens (deemed healthy) at 8 weeks is 696.8 grams. A random sample of 9 kittens had an average weight of 664.2 grams and a sample standard deviation of 71.5. She calls a colleague at an affiliated rescue in another county to see if anything is happening with their kittens at 8 weeks of age. They observe that from a sample of 22 healthy independent kittens an average weight of 735.1g with a sample standard deviation of 82.5g. Assume the distribution of kitten weights at 8 weeks is sufficiently close to the
Question 5: Suppose we anticipate an equal number of kittens in shelter A and shelter B. The true difference
in the average weights of kittens is 10.0g, and the true standard deviations were 100.0g and 120.0g,
respectively. Calculate the total
5% significance level and an 80% power is desired. If using R, round the critical value to two decimal
places to ensure you obtain an answer that matches what you would get if using the textbook method to
get the critical value.
I think since we're assuming equal sample sizes in this question, we may not need to use the sample-specific numbers provided at the beginning. Thanks in advance for the help!
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