Section 7 Lab Activity (1)

.docx

School

Clemson University *

*We aren’t endorsed by this school

Course

3090

Subject

Statistics

Date

Apr 3, 2024

Type

docx

Pages

Uploaded by CountRoseRhinoceros41

STAT 3090 S ECTION 7 L AB S PRING 2024 S AMPLING D ISTRIBUTIONS N AME : O BJECTIVES : Upon successful completion of this assignment, you will be able to…  Recognize and use different sampling methods  Describe the distribution of the sample mean and the sample proportion  Understand the Central Limit Theorem and its application  Understand the impact of Sample size on Sampling Variability  Interpret the probability of sampling distribution Part One: Sampling Techniques 1. A Beary Interesting Problem (18 points) To determine the effectiveness of jazz music in terms of bear attack prevention, a few students want to set up a study where they casually approach 7 bears while playing jazz music and then approach 7 bears with no music playing. Thus, they will need a sample of 14 bears. The students are near a wilderness area with 6 regions and they are also near to a zoo that has 5 bears. The 6 wilderness regions are approximately the same size and the number of bears in each area is approximately the same. Explain how the students could use each of the different types of sampling methods to gather their data. Note that some of the sampling methods would be nearly impossible to do. That is ok. Simply come up with a way they could use that particular method even if it is completely impractical. (Have fun with this) Disclaimer: Please do not try this experiment. a. Simple random sampling (3 pts) b. Stratified random sampling (3 pts) c. Cluster sampling (3 pts) d. Systematic sampling (3 pts) e. Convenience sampling (3 pts) f. Judgement sampling (3 pts) 1

STAT 3090 S ECTION 7 L AB S PRING 2024 S AMPLING D ISTRIBUTIONS Sampling Distribution of Sample Mean 2. Credit Card Debt (10 points) The mean credit card debt for a U.S. household is $7,115 with a standard deviation of $2,160. This mean is such a large value because of a few deeply indebted households. Consider a random sample of 50 U.S. households and let x represent the sample mean credit card debt. Use this information to answer the following questions. (5 pts each) (a) Describe the sampling distribution of sample mean x , i.e., its shape (normal or not), mean, and standard error. (Keep 2 decimal places.) (b) What is the probability that the mean credit card debt for a sample of 50 U.S. households is less than $6,500? Include probability notations and round your answer to 4 decimal places. 3. Hot Dog Fat Content (15 points) A hot dog manufacturer claims that its new lean beef hot dogs have an average of 3.5g of fat per hot dog. The fat content of these hot dogs is known to be approximately normally distributed with a standard deviation of 0.5g. (5 pts each) (a) What is the probability that one of these lean beef hot dogs has more than 4g of fat? Include probability notations and round your answer to 4 decimal places. (b) Describe the sampling distribution of the average fat content of a randomly selected package of 8 lean beef hot dogs, i.e., shape, mean, and standard error. Round to two decimal places if necessary. 2

STAT 3090 S ECTION 7 L AB S PRING 2024 S AMPLING D ISTRIBUTIONS (c) What is the probability that a randomly selected package of 8 lean beef hot dogs will have an average fat content greater than 4g? Use 4 decimal places in your final answer of the required probability and include probability notations. 4. WebAssign #1, 2, 3, 4, 8 (17 points) ****************************************************************************** Part 2: Sampling Distributions of sample proportion 5. College Degrees (9 points) A survey is conducted from a population of people of whom 40% have a college degree. Of the 60 people who were surveyed, 27 indicated that they have a college degree. (a) What is the sample proportion, p , of respondents who have a college degree in this survey? Include the correct symbol for the sample proportion in your answer. (4pts) (b) Find the probability of obtaining a sample proportion less than or equal to the one that you calculated in part (a) from a sample of size 60. (5pts) To get full credit, you need to:  Use the sampling distribution of sample proportion p .  Determine the shape, mean, and standard error of p .  Draw a sketch with appropriate area shaded.  Use the proper probability notations.  Get the correct answer with 4 decimal places. 3

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version