Question

In: Statistics and Probability

A team of dermatological researchers were studying skin cancer among 60-70 year old American men. Suppose...

A team of dermatological researchers were studying skin cancer among 60-70 year old American men. Suppose you were a part of the research team and take a sample of n=70 men from this age group and calculate the mean number of skin cancer spots in the sample. Also suppose that it is known that the distribution of the number of cancer spots is right-skewed.

1. How is the standard deviation of the distribution of sample means related to the population standard deviation of the number of cancer spots?

The standard deviation of the distribution of sample means is less than the population standard deviation of the number of cancer spots.

The standard deviation of the distribution of sample means is equal to the population standard deviation of the number of cancer spots.

The standard deviation of the distribution of sample means is greater than the population standard deviation of the number of cancer spots.

We cannot be sure of any of the above answers until we examine the data.

2. How is the mean of the distribution of sample means related to the population mean of the number of cancer spots?

The mean of the distribution of sample means is less than the mean of the number of cancer spots.

The mean of the distribution of sample means is equal to the mean of the number of cancer spots.

The mean of the distribution of sample means is greater than the mean of the number of cancer spots.

We cannot be sure of any of the above answers until we examine the data.

3. The numbers of skin cancer spots of 60-70 year old men are right-skewed. Assuming the sample size is large, which of the following best describes the shape of the distribution of sample means?

It is approximately normal.

It is right-skewed.

It has more than one mode.

We cannot be sure until we examine the data.

4. Suppose the sample size for this study was n=2 instead of n=70. What would be the shape of the distribution of sample means?

Skewed right

Normal

Skewed left

We cannot be sure until we examine the data.

Solutions

Expert Solution

Solution:

1. How is the standard deviation of the distribution of sample means related to the population standard deviation of the number of cancer spots?

Answer: The standard deviation of the distribution of sample means is less than the population standard deviation of the number of cancer spots.

2. How is the mean of the distribution of sample means related to the population mean of the number of cancer spots?

Answer: The mean of the distribution of sample means is equal to the mean of the number of cancer spots.

3. The numbers of skin cancer spots of 60-70 year old men are right-skewed. Assuming the sample size is large, which of the following best describes the shape of the distribution of sample means?

Answer: It is approximately normal.

4. Suppose the sample size for this study was n=2 instead of n=70. What would be the shape of the distribution of sample means?

Answer: Skewed right

orchestra answered 2 years ago

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