the power of statistics coursera weekly challenge 4 answers

Test your knowledge: Introduction to confidence Intervals

1. Which of the following statements describes an interval estimate?

  • An interval estimate uses a single value to estimate a population parameter.
  • An interval estimate uses a range of values to estimate a sample statistic.
  • An interval estimate uses a range of values to estimate a population parameter.
  • An interval estimate uses a single value to estimate a sample statistic.

2. What is the maximum expected difference between a population parameter and a sample estimate?

  • Margin of error 
  • Standard deviation
  • Confidence level
  • Range 

3. A 95% confidence interval means that 95% of all the data values in the dataset fall within the interval.

  • True
  • False

Test your knowledge: Construct confidence intervals

4. After identifying a sample statistic, what is the proper order of the next three steps of constructing a confidence interval?

  • Choose a confidence level, find the margin of error, and calculate the interval
  • Find the margin of error, choose a confidence level, and calculate the interval 
  • Choose a confidence level, calculate the interval, and find the margin of error.
  • Find the margin of error, calculate the interval, and choose a confidence level

5. A data professional is working for an online retail company. Their manager asks them to estimate the mean time customers spend on the company’s website. They construct a confidence interval based on a sample mean of 50 seconds and a margin of error of 4 seconds. What is the interval?

  • [54, 46]
  • [50, 54]
  • [46, 50]
  • [46, 54]

6. What happens as a sample size gets larger? Select all that apply.

  • The confidence interval narrows. 
  • The margin of error decreases.
  • The margin of error increases.
  • The confidence interval widens.

Test your knowledge: Work with confidence intervals in Python

7. What Python function enables a data professional to compute the standard deviation term in the sample standard error of a mean?

  • pandas.DataFrame.mode()
  • pandas.DataFrame.median()
  • pandas.DataFrame.std()
  • pandas.DataFrame.hist()

8. A data professional is constructing a confidence interval of the sample mean using the function scipy.stats.norm.interval(). What arguments should they specify? Select all that apply.

  • Scale, which they set to the sample standard error
  • Loc, which they set to the sample mean
  • Iqr, which they set to the interquartile range
  • Alpha, which they set to the confidence level

Weekly challenge 4

9. What is a key difference between a point estimate and an interval estimate?

  • A point estimate uses a range of values to estimate a population parameter; an interval estimate uses a single value to estimate a population parameter.
  • A point estimate uses a single value to estimate a population parameter; an interval estimate uses a range of values to estimate a population parameter.
  • A point estimate uses a single value to estimate a sample statistic; an interval estimate uses a range of values to estimate a sample statistic. 
  • A point estimate uses a range of values to estimate a sample statistic; an interval estimate uses a single value to estimate a sample statistic.

10. Fill in the blank: The _____ represents the maximum expected difference between a population parameter and a sample estimate.

  • margin of error
  • sampling distribution
  • sample statistic
  • confidence level

11. A data professional working for a moving company is estimating the average time it takes to complete a move. Based on a sample mean of 3 hours, they construct the following 95% confidence interval: [2.5 , 3.5]. What does 95% refer to?

  • The percentage of all possible sample means that fall within the range of the interval
  • The margin of error
  • The percentage of data values in the dataset
  • The success rate of the estimation process

12. A data professional working for a restaurant chain is constructing a confidence interval to help estimate annual sales. To start, they identify the sample statistic they are working with. According to the four steps that detail how to construct a confidence interval for a proportion, what should they do next?

  • Plot a histogram.
  • Choose a confidence level.
  • Calculate the interval.
  • Find the margin of error.

13. What happens as sample size gets smaller? Select all that apply.

  • The confidence interval gets wider.
  • The margin of error increases.
  • The margin of error decreases.
  • The confidence interval gets narrower.

14. What argument of the scipy.stats.norm.interval() function can be used to choose the confidence level?

  • std
  • alpha
  • scale
  • loc

15. Fill in the blank: For small sample sizes, data professionals use the _____ to make calculations with the data.

  • z-distribution
  • s-distribution
  • t-distribution
  • normal distribution

16. Which of the following statements accurately describe the graph of the t-distribution? Select all that apply.

  • When the sample size reaches 30, the normal distribution can be used for calculations.
  • As the sample size increases, the t-distribution approaches the normal distribution.
  • The graph of the t-distribution has an arc shape.
  • It has a higher frequency of outliers due to the smaller dataset.

17. What would a data professional use to estimate a population parameter using a range of values?

  • Point estimate
  • Interval estimate
  • Sampling frame
  • Z-score

18. A data professional working for a theme park is estimating the mean time visitors spend in the park. They construct the following 95% confidence interval based on a sample mean of 3.5 hours: [2.5, 4.5]. What is the margin of error?

  • +/- 2.5 hours
  • +/- 1 hour
  • +/- 4.5 hours
  • +/- 2 hours

19. Fill in the blank: According to the four steps that detail how to construct a confidence interval for a proportion, finding the margin of error is the _____ step in this process.

  • third
  • fourth
  • first
  • second

20. Which of the following statements accurately describes the relationship between confidence level and confidence interval?

  • As the confidence level gets lower, the confidence interval remains the same.
  • As the confidence level gets lower, the confidence interval gets wider.
  • As the confidence level gets higher, the confidence interval gets wider.
  • As the confidence level gets higher, the confidence interval gets narrower.

21. A data professional is using scipy.stats.norm.interval() in Python to construct a confidence interval. Which of the following pieces of code can they use to choose a confidence level of 99%?

  • alpha = 0.99
  • scale = 0.99
  • loc = 0.99
  • std = 0.99

22. Which of the following statements accurately describe the graph of the t-distribution? Select all that apply.

  • It has smaller tails than the standard normal distribution due to the larger dataset.
  • As the sample size increases, the t-distribution approaches the normal distribution.
  • It has a bell shape.
  • It has a higher frequency of outliers due to the smaller dataset.

23. What concept describes the likelihood that a particular sampling method will produce a confidence interval that includes the population parameter?

  • Sample statistic
  • Point estimate
  • Confidence level
  • Margin of error

24. In the context of constructing a confidence interval of a population mean, what does the loc argument of the scipy.stats.norm.interval() function refer to?

  • Interquartile range 
  • Sample standard error
  • Confidence level
  • Sample mean

25. Which of the following statements accurately describe a point estimate? Select all that apply.

  • A point estimate estimates a sample statistic.
  • A point estimate uses a range of values. 
  • A point estimate estimates a population parameter. 
  • A point estimate uses a single value.

26. Fill in the blank: Because there is more uncertainty involved in estimating the standard error, data professionals use the _____ when working with a small sample size.

  • t-distribution
  • z-distribution
  • s-distribution
  • normal distribution

Leave a Reply