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# Lesson 6: Sampling Distributions

Answer the following questions showing all work. Full credit will not be given to answers without

work shown. If you use StatKey or Minitab Express include the appropriate output (copy + paste) along

with an explanation. Output without explanation will not receive full credit. Round all answers to at

least 3 decimal places. If you have any questions, post them to the course discussion board.

1. According to U.S. News and World Reports, 18.60% of all Penn State World Campus students have

military experience. In a random sample of 45 students enrolled in World Campus sections of STAT

200, 6 reported having military experience. [30 points]

A. Compute the sample proportion (p-hat) for this sample of n=45 STAT 200 students.

B. Should the exact method or normal approximation method be used to construct a sampling

distribution in this situation? Explain your reasoning.

C. Using StatKey, construct a sampling distribution for p=0.1860 and n=45. Generate at least

5,000 samples. Take a screenshot of your sampling distribution and paste it here.

D. If the population proportion is 18.60%, what is the probability of taking a random sample of

n=45 and finding a sample proportion more extreme than the one observed in this sample?

Use StatKey to determine this proportion. Include a screenshot of your sampling distribution

with this proportion highlighted.

E. Given your results from part D, do you think that the proportion of all STAT 200 students

who have military experience is different from the overall population of World Campus

students where p=0.1860? Explain your reasoning. 2. For the following questions, assume a normally distributed population. [20 points]

A. Given μ=40, σ=12, and n=25, compute the standard error of the mean.

B. Given μ=40, σ=12, and n=400, compute the standard error of the mean.

C. Given μ=40, σ=3, and n=25, compute the standard error of the mean.

D. Given μ=400, σ=12, and n=25, compute the standard error of the mean.

E. How does the standard error of the mean change when the population mean, population

standard deviation, and sample size change? Lesson 6: Sampling Distributions NAME Due Monday February 20, 2017, 11:59 EDT 3. Using StatKey you are going to construct a sampling distribution for a mean. Select a population

distribution that is NOT normal (e.g., the built in Hollywood Movies, Rock Bands, or Baseball Players

datasets, or a skewed distribution of your own). Using the same population distribution for each,

construct the distribution of sample means for N=5 and N=30. Take at least 5,000 samples. [20 points]

A. Include a screen shots of your parent population and your two sampling distributions here.

B. How are your two distributions of sample means similar? How are they different?

C. Describe how your results relate to the Central Limit Theorem. 4. In the population ACT scores are normally distributed with a mean of 18 and a standard deviation of

6. Suppose that we are taking a simple random sample of 60 students from one high school. [30

points]

A. Calculate the standard error of the mean.

B. If we were to repeatedly pull samples of 60 individuals from the population of all ACT test

takers, the distribution of sample means would have a mean of ____ and a standard deviation

of ____.

C. Given the values from part B, 95% of random samples of n=60 will have sample means

between ___ and ___.

D. What is the probability that you would pull a random sample of 60 individuals from the

population of all test takers and they would have a sample mean of 19 or higher?

E. Suppose that the high school in question boasts that their students (i.e., the population of

all of their students) have an average ACT score above the national average of 18. Given your

results from part D, do you believe that there is evidence that the mean ACT score at this high

school is greater than 18? Explain your reasoning.

work shown. If you use StatKey or Minitab Express include the appropriate output (copy + paste) along

with an explanation. Output without explanation will not receive full credit. Round all answers to at

least 3 decimal places. If you have any questions, post them to the course discussion board.

1. According to U.S. News and World Reports, 18.60% of all Penn State World Campus students have

military experience. In a random sample of 45 students enrolled in World Campus sections of STAT

200, 6 reported having military experience. [30 points]

A. Compute the sample proportion (p-hat) for this sample of n=45 STAT 200 students.

B. Should the exact method or normal approximation method be used to construct a sampling

distribution in this situation? Explain your reasoning.

C. Using StatKey, construct a sampling distribution for p=0.1860 and n=45. Generate at least

5,000 samples. Take a screenshot of your sampling distribution and paste it here.

D. If the population proportion is 18.60%, what is the probability of taking a random sample of

n=45 and finding a sample proportion more extreme than the one observed in this sample?

Use StatKey to determine this proportion. Include a screenshot of your sampling distribution

with this proportion highlighted.

E. Given your results from part D, do you think that the proportion of all STAT 200 students

who have military experience is different from the overall population of World Campus

students where p=0.1860? Explain your reasoning. 2. For the following questions, assume a normally distributed population. [20 points]

A. Given μ=40, σ=12, and n=25, compute the standard error of the mean.

B. Given μ=40, σ=12, and n=400, compute the standard error of the mean.

C. Given μ=40, σ=3, and n=25, compute the standard error of the mean.

D. Given μ=400, σ=12, and n=25, compute the standard error of the mean.

E. How does the standard error of the mean change when the population mean, population

standard deviation, and sample size change? Lesson 6: Sampling Distributions NAME Due Monday February 20, 2017, 11:59 EDT 3. Using StatKey you are going to construct a sampling distribution for a mean. Select a population

distribution that is NOT normal (e.g., the built in Hollywood Movies, Rock Bands, or Baseball Players

datasets, or a skewed distribution of your own). Using the same population distribution for each,

construct the distribution of sample means for N=5 and N=30. Take at least 5,000 samples. [20 points]

A. Include a screen shots of your parent population and your two sampling distributions here.

B. How are your two distributions of sample means similar? How are they different?

C. Describe how your results relate to the Central Limit Theorem. 4. In the population ACT scores are normally distributed with a mean of 18 and a standard deviation of

6. Suppose that we are taking a simple random sample of 60 students from one high school. [30

points]

A. Calculate the standard error of the mean.

B. If we were to repeatedly pull samples of 60 individuals from the population of all ACT test

takers, the distribution of sample means would have a mean of ____ and a standard deviation

of ____.

C. Given the values from part B, 95% of random samples of n=60 will have sample means

between ___ and ___.

D. What is the probability that you would pull a random sample of 60 individuals from the

population of all test takers and they would have a sample mean of 19 or higher?

E. Suppose that the high school in question boasts that their students (i.e., the population of

all of their students) have an average ACT score above the national average of 18. Given your

results from part D, do you believe that there is evidence that the mean ACT score at this high

school is greater than 18? Explain your reasoning.

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