Question 1

Use the following 
Consider taking samples of size 100 from a population with proportion 0.33.
-Find the mean of the distribution of sample proportions.

Accepted Answer

The mean of the distribution of sample proportions is equal to the population proportion, which is 0.33.

Question 2

Use the following 
Consider taking samples of size 100 from a population with proportion 0.33.
-Find the standard error of the distribution of sample proportions.

Accepted Answer

The standard error of the distribution of sample proportions is calculated using the formula SE = sqrt[(p(1-p))/n], where p is the population proportion and n is the sample size. Here, SE = sqrt[(0.33(1-0.33))/100] = 0.047.

Question 3

Use the following 
Consider taking samples of size 100 from a population with proportion 0.33.
-Is the sample size large enough for the Central Limit Theorem to apply so that the sample proportions follow a normal distribution?

Accepted Answer

The sample size is large enough because np = 100 * 0.33 = 33 and n(1-p) = 100 * 0.67 = 67, both of which are greater than 5, satisfying the conditions for the Central Limit Theorem.

Question 4

Use the following 
Consider taking samples of size 25 from a population with proportion 0.65.
-Find the mean of the distribution of sample proportions.

Accepted Answer

The mean of the distribution of sample proportions is equal to the population proportion, which is 0.65.

Question 5

Use the following 
Consider taking samples of size 25 from a population with proportion 0.65.
-Find the standard error of the distribution of sample proportions.

Accepted Answer

The standard error of the distribution of sample proportions is given by the formula:SE = sqrt(p(1-p)/n)where p is the population proportion and n is the sample size.In this case, p = 0.65 and n = 25, so the standard error is:SE = sqrt(0.65(1-0.65)/25) = 0.0954Therefore, the correct answer is A.

Question 6

Use the following 
Consider taking samples of size 25 from a population with proportion 0.65.
-Is the sample size large enough for the Central Limit Theorem to apply so that the sample proportions follow a normal distribution?

Accepted Answer

The answer of Use the following 
Consider taking samples of...

Question 7

Use the following 
Suppose that the makers of M&M's claim that 24% of their Milk Chocolate M&M's are blue.
-Assume that Fun-Size bags of Milk Chocolate M&M's hold 20 candies. Find the mean and standard error of the distribution of sample proportions of blue candies for Fun-Size bags (i.e., samples of size 20). Use four decimal places when reporting the standard error.

Accepted Answer

The answer of Use the following 
Suppose that the makers...

Question 8

Use the following 
Suppose that the makers of M&M's claim that 24% of their Milk Chocolate M&M's are blue.
-Assume that the bags of Milk Chocolate M&M's sold in vending machines have 55 candies. Find the mean and standard error of the distribution of sample proportions of blue candies for vending machine bags (i.e., samples of size 55). Use four decimal places when reporting the standard error.

Accepted Answer

The answer of Use the following 
Suppose that the makers...

Question 9

Use the following 
Suppose that the makers of M&M's claim that 24% of their Milk Chocolate M&M's are blue.
-Assume that bags of Milk Chocolate M&M's labeled as "Medium"
size contain 415 candies. Find the mean and standard error of the distribution of sample proportions of blue candies for Medium bags (i.e., samples of size 415). Use four decimal places when reporting the standard error.

Accepted Answer

The answer of Use the following 
Suppose that the makers...

Question 10

Use the following 
Suppose that the makers of M&M's claim that 24% of their Milk Chocolate M&M's are blue.
-Would you expect using bags of Milk Chocolate M&M's labeled as "Large" size, which contain more candies than the "Medium"
Size bags, to result in a larger or smaller standard error?

Accepted Answer

A larger sample size (more candies in the "Large" size bags) results in a smaller standard error because the standard error is inversely proportional to the square root of the sample size.

Question 11

Use the following 
Suppose that the makers of M&M's claim that 24% of their Milk Chocolate M&M's are blue.
-For which sample sizes (Fun-Size with 20, Vending Machine with 55, or Medium with 415) would the Central Limit Theorem apply?

Accepted Answer

The answer of Use the following 
Suppose that the makers...

Question 12

Use the following 
Suppose that the makers of M&M's claim that 24% of their Milk Chocolate M&M's are blue.
-Suppose you purchase a bag of Milk Chocolate M&M's from a vending machine and only 8 of your 55 candies are blue. Assuming that the sample proportions are normally distributed, what percent of vending machine bags (i.e., samples of size 55) will have a sample proportion smaller than 0.145? Use two decimal places when reporting your answer.

Accepted Answer

The answer of Use the following 
Suppose that the makers...

Question 13

Use the following 
Admissions records at a small university indicates that 6.7% of the students enrolled are international students.
-Find the mean and standard error of the sample proportion of international students in random samples of size 50. Use four decimal places when reporting the standard error.

Accepted Answer

The answer of Use the following 
Admissions records at a...

Question 14

Use the following 
Admissions records at a small university indicates that 6.7% of the students enrolled are international students.
-Find the mean and standard error of the sample proportion of international students in random samples of size 100. Use four decimal places when reporting the standard error.

Accepted Answer

The answer of Use the following 
Admissions records at a...

Question 15

Use the following 
Admissions records at a small university indicates that 6.7% of the students enrolled are international students.
-Find the mean and standard error of the sample proportion of international students in random samples of size 200. Use four decimal places when reporting the standard error.

Accepted Answer

The answer of Use the following 
Admissions records at a...

Question 16

Use the following 
Admissions records at a small university indicates that 6.7% of the students enrolled are international students.
-For which sample sizes (n = 50, n = 100, and n = 200) would the Central Limit Theorem apply?

Accepted Answer

The answer of Use the following 
Admissions records at a...

Question 17

Use the following 
Admissions records at a small university indicates that 6.7% of the students enrolled are international students.
-What proportion of samples of 200 randomly selected students will have at least 8% international students? Use three decimal places when reporting your answer.

Accepted Answer

The answer of Use the following 
Admissions records at a...

Question 18

Use the following 
A 2009 study to investigate the dominant paws in cats was described in Animal Behaviour (Volume 78, Issue 2). The researchers used a random sample of 42 domestic cats. In this study, each cat was shown a treat (5 grams of tuna), and while the cat watched, the food was placed inside a jar. The opening of the jar was small enough that the cat could not stick its head inside to remove the treat. The researcher recorded the paw that was first used by the cat to try to retrieve the treat. This was repeated 100 times for each cat (over a span of several days). The paw used most often was deemed the dominant paw (note that one cat used both paws equally and was classified as "ambidextrous"). Of the 42 cats studied, 20 were classified as "left-pawed".
-Verify that the sample is large enough to use the normal formula to find a confidence interval for the proportion of domestic cats that are "left-pawed".

Accepted Answer

The answer of Use the following 
A 2009 study to...

Question 19

Use the following 
A 2009 study to investigate the dominant paws in cats was described in Animal Behaviour (Volume 78, Issue 2). The researchers used a random sample of 42 domestic cats. In this study, each cat was shown a treat (5 grams of tuna), and while the cat watched, the food was placed inside a jar. The opening of the jar was small enough that the cat could not stick its head inside to remove the treat. The researcher recorded the paw that was first used by the cat to try to retrieve the treat. This was repeated 100 times for each cat (over a span of several days). The paw used most often was deemed the dominant paw (note that one cat used both paws equally and was classified as "ambidextrous"). Of the 42 cats studied, 20 were classified as "left-pawed".
-Construct a 95% confidence interval for the proportion of domestic cats that are "left-pawed". Use three decimal places in your margin of error.

Accepted Answer

The answer of Use the following 
A 2009 study to...

Question 20

Use the following 
A 2009 study to investigate the dominant paws in cats was described in Animal Behaviour (Volume 78, Issue 2). The researchers used a random sample of 42 domestic cats. In this study, each cat was shown a treat (5 grams of tuna), and while the cat watched, the food was placed inside a jar. The opening of the jar was small enough that the cat could not stick its head inside to remove the treat. The researcher recorded the paw that was first used by the cat to try to retrieve the treat. This was repeated 100 times for each cat (over a span of several days). The paw used most often was deemed the dominant paw (note that one cat used both paws equally and was classified as "ambidextrous"). Of the 42 cats studied, 20 were classified as "left-pawed".
-Provide an interpretation of your interval in the context of this data situation.

Accepted Answer

The answer of Use the following 
A 2009 study to...

Quiz 6: Inference for Means and Proportions

Use the following Consider taking samples of size 100 from a population with proportion 0.33. -Find the mean of the distribution of sample proportions.

Use the following Consider taking samples of size 100 from a population with proportion 0.33. -Find the standard error of the distribution of sample proportions.

Use the following Consider taking samples of size 100 from a population with proportion 0.33. -Is the sample size large enough for the Central Limit Theorem to apply so that the sample proportions follow a normal distribution?

Use the following Consider taking samples of size 25 from a population with proportion 0.65. -Find the mean of the distribution of sample proportions.

Use the following Consider taking samples of size 25 from a population with proportion 0.65. -Find the standard error of the distribution of sample proportions.

Use the following Consider taking samples of size 25 from a population with proportion 0.65. -Is the sample size large enough for the Central Limit Theorem to apply so that the sample proportions follow a normal distribution?

Use the following Suppose that the makers of M&M's claim that 24% of their Milk Chocolate M&M's are blue. -Would you expect using bags of Milk Chocolate M&M's labeled as "Large" size, which contain more candies than the "Medium" Size bags, to result in a larger or smaller standard error?

Use the following Suppose that the makers of M&M's claim that 24% of their Milk Chocolate M&M's are blue. -For which sample sizes (Fun-Size with 20, Vending Machine with 55, or Medium with 415) would the Central Limit Theorem apply?

Use the following Admissions records at a small university indicates that 6.7% of the students enrolled are international students. -For which sample sizes (n = 50, n = 100, and n = 200) would the Central Limit Theorem apply?

Use the following Admissions records at a small university indicates that 6.7% of the students enrolled are international students. -What proportion of samples of 200 randomly selected students will have at least 8% international students? Use three decimal places when reporting your answer.