## Description

**Assignment 7**

Started: Oct 24 at 1:14am

**Quiz Instructions**

For Assignment 7 you will input your answers into this Canvas assignment.

All your normal distribution curves must be drawn by hand with the mean AND two standard deviations identified.

You will need this document to answer questions that involve z-scores: __Z-table for Assignment 7.pdf__

**You can use the following document to help you answer the Hypothesis Testing Questions. This document will not be uploaded. It is only a template to help you complete questions 7- 38. Fall 2018 Assignment 7 Template to Help You Complete Questions 7- 38.pdf**

You can open and close this assignment as many times as necessary throughout the week and the course staff will not see your work until you click “Submit”. Please do not submit the assignment until you have finished it completely. To begin, click “Take the Quiz” below. Please disregard the “quiz” title. This assignment will be treated as all other assignments.

Canvas may add additional zeros to the end of your answer. For example, if you input 0.25, Canvas may correct it to 0.2500 automatically. We will grade this as 0.25. Please disregard this Canvas glitch. Read each question to know how to enter your answers.

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**Questions 1-3**

In a given population of males, it is found that the mean weight is 170 lbs. Furthermore, the calculated standard deviation is 22.4 pounds. Assume the distribution of weights is normal.

**Question 1****5 pts**

Draw a normal distribution curve of the normal distribution of male weights. You will need to show the mean, the values for plus or minus 1 standard deviation and 2 standard deviations, along with the rough and ready percentages that apply. Be sure to indicate, with label arrows, 1 and 2 standard deviations. *There is no need to show three standard deviations.*

Upload your drawing.

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**Question 2****4 pts**

Use the Z score tables in the PDF document you downloaded to calculate the percentage of males who have weights between 140 lbs and 170 lbs? __You will need to round twice: once right before using the z-tables, and again when presenting your final answer. Both times round to one decimal place.__

**Question 3****5 pts**

Use the Z score tables in the PDF document you downloaded to calculate the percentage of males who have weights between 155 lbsand 195 lbs. __You will need to round twice: once right before using the z-tables, and again when presenting your final answer. Both times round to one decimal place.__

*Hint: Break this question up into two parts. First, find the z-score between 155 lbs and the mean. Second, find the z-score between 195 and the mean. From there calculate the total percentages. *

**Questions 4-6**

Suppose the scores on the Graduate Record Exam (GRE) are normally distributed with a mean of 500 and a standard deviation of 110.

**Question 4****5 pts**

Draw by hand a normal distribution curve of the GRE scores. You will need to show the mean, the values for plus or minus 1 standard deviation and 2 standard deviations, along with the rough and ready percentages that apply. Be sure to indicate, with label arrows, 1 and 2 standard deviations. *There is no need to show three standard deviations.*

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**Question 5****2 pts**

If the graduate school you are interested in attending requires a GRE score of 630 for admission, how many standard deviations above the mean do you need to score? __Round to one decimal place.__

**Question 6****4 pts**

If the admission’s officer chooses an applicant at random, what is the probability of finding a student who scores a grade over 700 on the GRE? Use the Z score tables in the PDF document you downloaded to calculate the percentage. __You will need to round twice: once right before using the z-tables, and again when presenting your final answer. Both times round to one decimal place.__

**Hypothesis Testing Questions **

For questions 7 through 38, assume all samples were randomly chosen even if not stated in the problem.

Make sure you follow the steps as outlined in class and the readings.

__Round standard deviations and percentages to 1 DP. Remember to round at the end.__

**Follow this format for all hypothesis testing questions: **

**State your Null Hypothesis – use words, not just a percentag****Calculate the Standard Deviation.****Draw by hand a normal distribution curve of the with the mean AND two standard deviations identified.****Calculate (if necessary) the observed percentage.****Construct the proper sentence either rejecting or not rejecting the Null Hypothesis. Use the proper statistical language.****Give an informal conclusion (write in your own words).**

**Questions 7 – 12 **

The Beautiful Body Cosmetics Company claims that its new wart cream dissolves 54% of all warts with one application. A scientist from a competing company is given the job of disproving this claim. She purchases a few jars of the product and does her own tests. This scientist tries the cream on several randomly selected people (and randomly selected warts!) and finds that after applying the cream to 300 warts, 158 of unattractive warts disappeared with one application. Perform a hypothesis test and determine what the scientist would conclude about Beautiful Body’s product.

**Question 7****2 pts**

State your Null Hypothesis – use words, not just a percentage.

12pt

Paragraph

0 words

**Question 8****3 pts**

Find the standard deviation using claim percentage as *p *and the survey size as* n*.

0.028% | |

2.8% |

2.9% | |

3.0% |

0.029% |

**Question 9****3 pts**

Draw by hand a normal distribution curve of the with the mean AND two standard deviations identified. Upload your diagram.

Upload

Choose a File

**Question 10****3 pts**

Calculate the observed percentage and enter your answer. Round your answer to one decimal place.

**Question 11****2 pts**

Compare your observed percentage to the interval of p± 2σ. Construct the proper sentence either rejecting or not rejecting the null hypothesis.

12pt

Paragraph

0 words

**Question 12****2 pts**

Write your conclusion in your words.

12pt

Paragraph

0 words

Questions 13 -18

Senator Lott claims that 50% of Americans want federal funding for PBS**cut. **You, a devout fan of “Barney” and “Lamb Chop” (sadly, Shari Lewis passed away in 1998), are deeply suspicious of this claim. So, you decide to take your own *unbiased *poll.** **You sample 250 people and find that 46% want to see the cuts in funding. Perform a hypothesis test, and give your conclusions. **(The question below was an issue a few years ago when Trent Lott was in the Senate)**

**Question 13****2 pts**

State your Null Hypothesis – use words, not just a percentage.

12pt

Paragraph

0 words

**Question 14****3 pts**

Find the standard deviation using claim percentage as *p *and the survey size as* n*.

3.0% | |

0.032% |

0.031% | |

3.2% |

3.1% |

**Question 15****3 pts**

Draw by hand a normal distribution curve of the with the mean AND two standard deviations identified. Upload your diagram.

Upload

Choose a File

**Question 16****3 pts**

What is the observed percentage? Enter your answer.

**Question 17****2 pts**

Compare your observed percentage to the interval of p± 2σ. Construct the proper sentence either rejecting or not rejecting the null hypothesis.

12pt

Paragraph

0 words

**Question 18****2 pts**

Write your conclusion in your words.

12pt

Paragraph

0 words

Questions 19 – 25

You decide to take another sample of people to find out for sure about the public’s opinion on cuts to PBS, this time of 1,500 people. From this sample, 700 folks favor the cuts. Perform another hypothesis test.

**Question 19****2 pts**

State your Null Hypothesis – use words, not just a percentage.

12pt

Paragraph

0 words

**Question 20****3 pts**

Find the standard deviation using claim percentage as *p *and the survey size as* n*.

1.2% | |

1.0% |

1.3% | |

0.03% |

0.029% |

**Question 21****3 pts**

Draw by hand a normal distribution curve of the with the mean AND two standard deviations identified. Upload your diagram.

Upload

Choose a File

**Question 22****3 pts**

Calculate the observed percentage and enter your answer. Round your answer to one decimal place.

**Question 23****2 pts**

Compare your observed percentage to the interval of p± 2σ. Construct the proper sentence either rejecting or not rejecting the null hypothesis.

12pt

Paragraph

0 words

**Question 24****2 pts**

Write a short concluding statement in your own words.

12pt

Paragraph

0 words

**Question 25****1 pts**

Now that you have taken another sample of people to find out for sure about the public’s opinion on cuts to PBS explain *why *there is a difference.

12pt

Paragraph

0 words

Questions 26 – 32

The Mars Company, the maker of M&M’s, recently claimed that M&M’s were so much fun because they were a perfect rainbow, that is, each bag they made contained equal numbers of each of the five colors.

An enterprising student decided to test this and bought one small bag, chosen at random.

The number of M&M’s found for each color was:

Brown: 19

Blue: 5

Green: 5

Orange: 9

Yellow: 10

Perform a hypothesis test and state your conclusions about Mars’ claim.

**Question 26****2 pts**

State your Null Hypothesis – use words, not just a percentage.

12pt

Paragraph

0 words

**Question 27****3 pts**

Find the standard deviation using claim percentage as *p *and the survey size as* n*.

6.0% | |

0.058% |

5.8% | |

5.7% |

0.057% |

**Question 28****3 pts**

Upload

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**Question 29****3 pts**

Calculate the observed percentage for **each color **and enter your answers. Round your answers to one decimal place.

12pt

Paragraph

0 words

**Question 30****2 pts**

Compare all your observed percentages to the interval of p± 2σ. Construct the proper sentence either rejecting or not rejecting the null hypothesis.

12pt

Paragraph

0 words

**Question 31****2 pts**

Write a short concluding statement in your own words.

12pt

Paragraph

0 words

**Question 32****0 pts**

**EXTRA CREDIT QUESTION – If correct, your grader will add 4 points to your final grade on this assignment. **

If the colors were in equal proportions, what would be the probability(in percent form) that a random sample of 48 M&M’s will have the above proportion of brown ones? (Hint: Go back to the Normal Distribution Curve and look at the probabilities under the curve.)

No need to perform another hypothesis test here.

Questions 33 – 38

Dr. Joseph claims that very young children are **equally** attracted to different colored balls. There are three balls to choose from, all identical in size:

- 1 is black and white striped
- 1 is two shades of pastel
- 1 is brightly colored

His colleague, Dr. Smith, wants to test if this is true. She places her young subjects in a playroom with the three different balls above. The balls are shuffled between trials so that it will not influence the results. From her observations, Dr. Smith found that of the 80 toddlers she tested, 42 went for the brightly colored ball.

Formulate an appropriate null hypothesis as if you were the researcher, and perform a hypothesis test. In the end, state your conclusion explicitly, i.e. do children tend to show a preference for bright colors?

**Question 33****2 pts**

State your Null Hypothesis – use words, not just a percentage.

12pt

Paragraph

0 words

**Question 34****2 pts**

Find the standard deviation using claim percentage as *p *and the survey size as* n*.

5.2% | |

0.052% |

5.0% | |

0.053% |

5.3% |

**Question 35****3 pts**

Upload

Choose a File

**Question 36****3 pts**

Calculate the observed percentage and enter your answer. Round your answer to one decimal place.

**Question 37****2 pts**

12pt

Paragraph

0 words

**Question 38****2 pts**

Write a short concluding statement in your own words.

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