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0/22 Questions Answered

Assignment 6

Q1 Social Media 16 Points

In the fall of 2016, 13% of US teens reported using Facebook as

their primary form of social media. A recent online survey found

that 16 of 526 US teens claim that they use Facebook as their

primary form of social media. Is there evidence that this proportion

is less than it was in 2016?

Q1.1 Graph 1 Point

What type graph could be used to display the data?

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Q1.2 Sample Proportion 1 Point

Calculate the proportion of US teens in the sample who use

Bar Chart!

Boxplot!

Segmented Bar Chart!

Scatterplot!

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Calculate the proportion of US teens in the sample who use

Facebook as their primary form of social media. Round your

answer to three decimal places.

Enter your answer here

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Q1.3 Notation 1 Point

What notation should be used for the value calculated in Q1.2?

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Q1.4 Parameter of Interest 2 Points

Write out the parameter of interest for this study. What does

represent in this context?

Enter your answer here

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! x̄

! µ

! π

! p̂

π

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Q1.5 Null Hypothesis 1 Point

What is the null hypothesis for this study?

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Q1.6 Direction of Alternative Hypothesis 1 Point

Based on the research question, what is the direction of the

alternative hypothesis?

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Q1.7 Null Distribution 3 Points

To use the one proportion test in the catstats package in R, what

values do we need to enter to create a null distribution which is

The true proportion of US teens who use Facebook as their

primary form of social media is 0.13.

!

The true proportion of US teens who use Facebook as their

primary form of social media is less than 0.13.

!

The true proportion of US teens who use Facebook as their

primary form of social media is 0.03.

!

The sample proportion of US teens who use Facebook as their

primary form of social media is 0.03.

!

Greater than!

Less than!

Not equal to!

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values do we need to enter to create a null distribution which is

plotting the proportion of successes from each simulation?

probability_success

Enter your answer here

sample_size

Enter your answer here

as_extreme_as

Enter your answer here

Save Answer

Q1.8 R Simulation 1 Point

Download the A6_SocialMedia.R file from D2L under Content --> Unit 2 --> Assignment R Files. Fill in the blanks in the code for

probability_success, sample_size, and as_extreme_as using the

values from Q1.7. Export the simulation created as a PNG and

upload the image here.

Please select file(s) Select file(s)

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Q1.9 Strength of evidence 1 Point

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Based on the p-value found in Q1.8, how strong is the evidence

against the null hypothesis?

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Q1.10 Bootstrap Distribution 1 Point

Use the following Bootstrap Distribution to answer the following

questions.

What is the level of confidence used to create this interval?

Little to no evidence!

Very strong!

Moderate!

99%!

95%!

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Save Answer

Q1.11 Interpret CI 3 Points

Interpret the confidence interval in context of the problem.

Enter your answer here

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Q2 Breastfeeding 18 Points

The Center for Disease Control reported in 2011 that 41% of all

mothers of three month old infants in the United States were

exclusively breastfeeding. In Montana, a random sample of 75

mothers surveyed resulted in 36 who stated they exclusively breast

fed their infant at three months old. Do these data provide

evidence the Montana rate of exclusive breastfeeding at 3 months

old is different than the national average in 2011?

Q2.1 2 Points

Fill in the blank with the appropriate letter to match each

component of this study to its appropriate statistical term.

95%!

5%!

1%!

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component of this study to its appropriate statistical term.

A. Population

B. Parameter

C. Sample

D. Statistic

E. Sample size

The proportion of all Montana mothers who breast feed exclusively

at 3 months

Enter your answer here

All Montana mothers

Enter your answer here

The proportion of women in our sample that breast feed exclusively

at 3 months

Enter your answer here

The 75 Montana mothers surveyed

Enter your answer here

Save Answer

Q2.2 Hypotheses 1 Point

Choose the appropriate hypotheses to test the research question.

, ! H :0 µ = 0.41 H :A µ = 0.41

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Save Answer

Q2.3 Normal Distribution Conditions 2 Points

Show your work to verify that the success-failure condition is

satisfied to use the normal approximation.

Enter your answer here

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Q2.4 Normal Distribution Conditions 1 Point

Is the Independence condition met for these data?

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, ! H :0 π = 0.41 H :A π = 0.41

, ! H :0 =p̂ 0.41 H :A =p̂  0.41

, ! H :0 π = 0.41 H :A π > 0.41

Yes, because the sample size is large enough.!

No, because only Montana mothers are surveyed.!

Yes, because a random sample was taken of Montana mothers.!

No, because the sample size is not large enough.!

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Q2.5 Null Standard Error 4 Points

a) Calculate the null standard error of the sample proportion. Show

your work and round your answer to three decimal places.

Enter your answer here

b) Using your answer to part (a) of this question, calculate the

standardized statistic for the sample proportion. Show your work

and round your answer to three decimal places.

Enter your answer here

Save Answer

Q2.6 Interpret p-value 1 Point

The p-value found under a standard normal distribution at or more

extreme than our observed Z value in Q2.5 was 0.1324. Interpret

this value in context of the problem.

The true proportion of Montana mother's who exclusively breast

fed their infant at three months old is 0.1324.

!

If the true proportion of Montana mother's who exclusively

breast fed their infant at three months old is 0.48, in 13.24% of

simulated samples we would observe a proportion of Montana

mother's who exclusively breast fed their infant at three months

old of 0.41 or more extreme.

!

13.24% of simulated samples will give an observed sample

proportion of Montana mother's who exclusively breast fed their

infant at three months old of 0.48.

!

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Save Answer

Q2.7 Standard Error of phat 1 Point

Which of the following shows the correct calculation of the standard

error of if we do not assume the null hypothesis is true.

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Q2.8 Confidence Interval 3 Points

Calculate the 95% confidence interval using a multiplier of 1.96.

Show your work and round your answer to three decimal places.

Report in interval notation.

Enter your answer here

infant at three months old of 0.48.

If the true proportion of Montana mother's who exclusively

breast fed their infant at three months old is 0.41, in 13.24% of

simulated samples we would observe 36 out of 75 Montana

mother's who exclusively breast fed their infant at three months

old or more extreme.

!

p̂

! =75 0.41(1−0.41) 0.057

! =75 0.48(1−0.48) 0.058

! =75 0.41(1−0.41)

0.057

! =75 0.48(1−0.48)

0.058

z⋆

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Q2.9 Conclusion 3 Points

Based on the p-value and the 95% confidence interval, choose the

correct conclusion to the research question in context of the

problem.

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Q3 Cite your sources 1 Point

Cite any sources you referenced to complete this assignment. That

should include R and your course textbook. Also include the

names of all people you worked.

There is very strong evidence that the true proportion of

Montana mother's who exclusively breast fed their infant at three

months old is 0.48.

!

There is little to no evidence that the true proportion of Montana

mother's who exclusively breast fed their infant at three months

old is 0.48.

!

There is very strong evidence that the true proportion of

Montana mother's who exclusively breast fed their infant at three

months old differs from 0.41.

!

There is little to no evidence that the true proportion of Montana

mother's who exclusively breast fed their infant at three months

old differs from 0.41.

!

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Enter your answer here

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Q4 Extra Credit 0 Points

[+2] Use R to get a p-value and a 95% confidence interval for question 2 (Montana mothers) using the prop.test function. Use section 5.3 of your textbook and the video covering section 5.3 for

help with the arguments in the function.

[+1] Use the qnorm() function to determine the multiplier for a 80% confidence level. Section 5.3 in your textbook and videos for

sections 5.2 and 5.3 may help with this.

Take a screenshot of your R code and output and provide it here for up to 3 points extra credit.

Please select file(s) Select file(s)

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z⋆

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