## All Weeks Inferential Statistical Analysis with Python Quiz Answers

In this course, we will explore the basic principles behind using data for estimation and for assessing theories. We will analyze both categorical data and quantitative data, starting with one population technique and expanding to handle comparisons of two populations. We will learn how to construct confidence intervals. We will also use sample data to assess whether or not a theory about the value of a parameter is consistent with the data. A major focus will be on interpreting inferential results appropriately.

### Inferential Statistical Analysis with Python Week 01 Quiz Answers

#### Week 1: Python Basics Assessment

Q1. Using either the help function or online documentation, find the default for axis in the Pandas drop function (pandas.DataFrame.drop). Enter your answer below.

Answers:

Q2. Using either the help function or online documentation as a resource, select the default option for the kind input parameter for the Numpy sort function (np.sort). (https://docs.scipy.org/doc/numpy-1.15.1/reference/generated/numpy.sort.html)

The kind parameter indicates the sorting algorithm used.

- heapsort
- quicksort
- stable
- mergesort

Q3. What does the following function get_element return when the input is lst = [1, 7, 3, 5]?

`1.def get_element(lst):`

2.new_lst = []

3.for i in lst:

4.new_lst.append(i**2)

5.return lst[1]

- 1
- 3
- 9
- 7
- 25
- 49

Q4. What is the output of the following code?

`1.my_dict = {'peaches':'cream', 'cat':'dog', 'this one':'that one'}`

2.my_dict['this one']

- {‘peaches’:’cream’, ‘cat’:’dog’, ‘this one’:’that one’}
- ‘dog’
- {‘that one’}
- ‘that one’
- ‘peaches’

Q5. What are the keys in my_dict?

`1.my_dict = {'peaches':'cream', 'cat':'dog', 'this one':'that one'}`

2.my_dict['this one']

- ‘peaches’, ‘cat’, ‘this one’
- peaches, cat, this one
- ‘cream’, ‘dog’, ‘that one’
- cream, dog, that one

Q6. What are the values in my_dict? Select all that apply.

`1.my_dict = {'peaches':'cream', 'cat':'dog', 'this one':'that one'}`

- ‘cream’, ‘dog’, ‘that one’
- ‘peaches’, ‘that one’, ‘cat’
- ‘cream’, ‘dog’, ‘cat’
- ‘cream’, ‘dog’, ‘this one’

Q7. What happens when the function save_plot is called?

import matplotlib.pyplot as plt

`1.def save_plot(x, y):`

2.plt.plot(x, y)

3.plt.savefig('new_plot')

- A plot is outputted and saved as ‘new_plot’.
- The function returns a plot.
- nothing
- y

### Inferential Statistical Analysis with Python Week 02 Quiz Answers

#### Quiz 1: All About Confidence Intervals

Q1. Use the following background to answer the corresponding questions.

Background: Information devices, such as smartphones, tablets, laptops, and E-readers, are widely used by Americans today. A survey conducted by Pew Research Center in January of 2018, asked a random sample of Americans to report which of these specific information devices they own. The study revealed that 53% of the Americans who were surveyed own a tablet (based on a random sample of 526 Americans). From these results, the 90% confidence interval for the population proportion of Americans who own a tablet was reported to be (0.4942, 0.5658).

Which of the following corresponds to the value of 53%?

- Sample proportion
- Population proportion
**Statistic**- Parameter
- Estimate of the population proportion
- Test Statistic

Q2. Use the following background to answer the corresponding questions.

Background: Information devices, such as smartphones, tablets, laptops, and E-readers, are widely used by Americans today. A survey conducted by Pew Research Center in January of 2018, asked a random sample of Americans to report which of these specific information devices they own. The study revealed that 53% of the Americans who were surveyed own a tablet (based on a random sample of 526 Americans). From these results, the 90% confidence interval for the population proportion of Americans who own a tablet was reported to be (0.4942, 0.5658).

Which of the following would be considered an appropriate interpretation of the given 90% confidence interval?

- We are certain that the population proportion of Americans who own a tablet lies within the interval (0.4942, 0.5658).
- There is a 90% chance that the population proportion of Americans who own a tablet lies 49.42% and 56.58%.
- We estimate, with 90% confidence, that the sample proportion of Americans who own a tablet lies within the interval (0.4942, 0.5658).
**With 90% confidence, we estimate that the population proportion of Americans who own a tablet is between 49.42% and 56.58%.**

Q3. Use the following background to answer the corresponding questions.

Background: Information devices, such as smartphones, tablets, laptops, and E-readers, are widely used by Americans today. A survey conducted by Pew Research Center in January of 2018, asked a random sample of Americans to report which of these specific information devices they own. The study revealed that 53% of the Americans who were surveyed own a tablet (based on a random sample of 526 Americans). From these results, the 90% confidence interval for the population proportion of Americans who own a tablet was reported to be (0.4942, 0.5658).

How would the width of a 95% confidence interval compare to that of the 90% interval given?

- Stays the same
**Wider**- Narrower
- Unable to tell

Q4. Use the following background to answer the corresponding questions.

Which of the following best describes a confidence level in the context of the problem?

- If we

repeated this study many times, each time producing a new sample (of the same

size) from which a 90% confidence interval is computed, then 90% of the

resulting confidence intervals would be expected to contain the sample

proportion of all Americans who own a tablet. - If we repeated this study many times, each time producing a new sample (of the same size) from which a 90% confidence interval is computed, then we would expect the population proportion of all Americans who own a tablet to be contained within the (0.4942, 0.5658) interval 90% of the time.
**If we**

repeated this study many times, each time producing a new sample (of the same

size) from which a 90% confidence interval is computed, then 90% of the

resulting confidence intervals would be expected to contain the population

proportion of all Americans who own a tablet.

Q5. Use the following background to answer the corresponding questions.

Based on the reported 90% confidence interval (and no additional calculations), does it appear that a majority of Americans own a tablet? Select the answer with the appropriate explanation.

- Yes, because 53% is above 50%
- Yes, because 90% is above 50%
**No, because the entire interval of reasonable values for p is not above 50%**- Yes, because most of the interval is above 50%

Q6. Use the following background to answer the corresponding questions.

Another researcher is looking to conduct a similar survey to find out the proportion of all Michigan residents own a tablet. What minimum sample size does the researcher need in order to create a 95% conservative confidence interval with a margin of error of no more than 3%? (Do not use the approximate value for “a few” – use the more precise standard value.)

- The researcher would need a sample of at least 33 Michigan residents
- The researcher

would need a sample of at least 267 Michigan residents - The researcher

would need a sample of at least 752 Michigan residents - The researcher would need a sample of at least 1067.11 Michigan residents
**The researcher would need a sample of at least 1068 Michigan residents**- The researcher

would need a sample of at least 1503 Michigan residents

Q7. Use the following background to answer the corresponding questions.

Is the following an appropriate statement about the given 90% confidence interval? “We estimate that 53% of all Americans own a tablet with a 90% margin of error of 3.58%.”

**Appropriate**- Not appropriate

#### Quiz 2: Sample Size & Assumptions

Q1. A poll was done at a public University asking undergraduate students whether they are an in state student or out of state student. A sample of 232 undergraduate students at the University were asked and it was revealed that 43% of students were from out of state. From the results, a 95% confidence interval was calculated to be (0.3663, 0.4937).

Which of the following corresponds to the value of 43%? (Select all that apply)

- Statistic
- Parameter
- Sample proportion
- Population proportion
- Estimate of the population proportion
- Test statistic

Q2. In order to make the above confidence interval researchers first had to check their assumptions. Select all the appropriate assumptions that are needed to create a one population proportion confidence interval.

- The population proportion comes from data that is considered a simple random sample
- The sample proportion comes from data that is considered a simple random sample
- The number of respondents who replied “out of state” must be at least 10
- The number of respondents who replied “in state” must be at least 10
- The distribution of our population proportion must be normally distributed

Q3. What is the margin of error for the given 95% confidence interval above?

- 1.96
- 0.00106
- 0.0325
- 0.0637
- 0.1274

Q4. A larger sample was taken and the same sample proportion was found. How would the width of the 95% confidence interval change from our initial interval?

- Widen
- Shorten
- Stay the same
- Unable to tell

Q5. If the researcher would like to have their confidence interval be narrower, more precise, which of the following would achieve this?

- Change the confidence level to 90%
- Change the confidence level to 99%
- Calculate a conservative 95% confidence interval

Q6. What minimum sample size does the researcher need in order to create a 95% conservative confidence interval with a margin of error of no more than 4%?

- 24.5
- 25
- 600
- 600.25
- 601

Q7. What minimum sample size does the researcher need in order to create a 98% conservative confidence interval with a margin of error of no more than 3%?

- 1067.11
- 1068
- 1502.85
- 1503

Q8. Which of the following would be considered an appropriate interpretation of the given 95% confidence interval?

- We estimate, with 95% confidence that the sample proportion of out of state undergraduate students at this University is between (0.3663, 0.4937)
- We are 95% confident that the population proportion of out of state undergraduate students at this University is between 36.63% and 49.37%
- There is a 95% chance that the population proportion of out of state undergraduate students at this University is between 36.63% and 49.37%
- If we repeated this study many times we would expect to obtain the true population proportion of out of state undergraduate students at this University 95% of the time in the resulting confidence interval of (0.3663, 0.4937)

Q9. Which of the following best describes the confidence level in the context of the problem?

- If we repeated this study many times, each time producing a new sample (of the same size) from which a 95% confidence interval is computed, then we would expect the population proportion of out of state undergraduate students at this University to be contained within the (0.3663, 0.4937) interval 95% of the time.
- If we repeated a similar study many times, each time producing a new sample (of various sizes) from which a 95% confidence interval is computed, then 95% of the resulting confidence intervals would be expected to contain the population proportion of out of state undergraduate students at this University.
- If we repeated this study many times, each time producing a new sample (of the same size) from which a 95% confidence interval is computed, then 95% of the resulting confidence intervals would be expected to contain the sample proportion of out of state undergraduate students at this University.
- If we repeated this study many times, each time producing a new sample (of the same size) from which a 95% confidence interval is computed, then 95% of the resulting confidence intervals would be expected to contain the population proportion of out of state undergraduate students at this University.

Q10. Based on the reported 95% confidence interval (and no additional calculations), does it appear there is a minority of undergraduate students at the University that are from out of state?

- Yes, because 43% is below 50%
- No, because our sample size is not large enough
- No, because the entire interval is below 50%
- Yes, because the entire interval is below 50%
- Unable to tell

#### Confidence Intervals Assessment Answers

Q1. What variable is used in the column ‘napping’ to indicate a toddler takes a nap?

**Comment if you know the answers**

Q2. What is the sample size **𝑛**?

**Comment if you know the answers**

Q3. What is the sample size for toddlers who nap, 𝑛1?

**Comment if you know the answers**

Q4. What is the sample size for toddler who do not nap, 𝑛2?

**Comment if you know the answers**

Q5. Given our sample sizes of n1 and n2 for napping and non-napping toddlers respectively, how many degrees of freedom (**𝑑𝑓**) are there for the associated 𝑡distributions?

*Note your answer in the following format: x, y*

- 14, 4
- 26, 12
- 4, 14
- 15, 3
- 12, 26

Q6. What is 𝑡* for nap and no nap?

*(Note your answer in the following format truncated after the third decimal place: #.###, #.###)*

- 1.986, 2.149
- 2.144, 2.776
- 4.446, 5.237
- 2.255, 3.125

Q7. What is the 95% confidence interval for the average bedtime for **toddlers who nap**?

*(Note your answer rounded to four decimal places)*

- (19.9210, 20.6870)
- (18.9597, 20.2203)
- (20.0352, 20.5728)
- (19.9767, 20.6313)

Q8. What is the 95% confidence interval for the average bedtime for **toddlers who do not nap**?

*Note your answer rounded to four decimal places)*

- (18.7965, 20.3835)
- (18.9597, 20.2203)
- (19.9767, 20.6313)
- (19.1061, 20.0739)

#### Inferential Statistical Analysis with Python Week 03 Quiz Answers

Q1. For each question, identify the appropriate statistical scenario described in the problem background.

Background: In a blind taste test to compare two new juice flavors, grape and apple, consumers were given a sample of each flavor and the results will be used to estimate the percentage of all such consumers who prefer the grape flavor to the apple flavor.

- Single population proportion
- Difference in two population proportions
- Single population mean
- Population mean difference for paired data
- Difference in two population means

Q2. For each question, identify the appropriate statistical scenario described in the problem background.

Background: A company has recently started an exercise program for its workers to assess if it will improve job satisfaction on average, as measured by a questionnaire (with higher scores indicating more satisfied employees). Scores for 30 randomly selected workers were recorded both before the start of program and after the exercise program’s implementation.

- Single population proportion
- Difference in two population proportions
- Single population mean
- Population mean difference for paired data
- Difference in two population means

Q3. For each question, identify the appropriate statistical scenario described in the problem background.

Background: Over the last ten years, a local college has improved their athletic facilities, implemented online player registration, and offered new payment plans for intramural sports. They wish to evaluate if the participation rate in intramural sports is higher today than it was ten years ago. They poll a large random sample of alumni that graduated ten years ago and a large random sample of currently enrolled students.

- Single population proportion
- Difference in two population proportions
- Single population mean
- Population mean difference for paired data
- Difference in two population means

Q4. For each question, identify the appropriate statistical scenario described in the problem background.

Background: A local blood drive urges donors to set up an appointment for their donation. They give donors with an appointment priority over those who come in without one. The coordinators would like to estimate the difference in average wait times for donors with an appointment and donors without an appointment.

- Single population proportion
- Difference in two population proportions
- Single population mean
- Population mean difference for paired data
- Difference in two population means

Q5. For each question, identify the appropriate statistical scenario described in the problem background.

Background: The Safety Patrol for a ski resort conducts a survey of skiers and snowboarders to assess if there is a significant difference in the rate of skiers and the rate of snowboarders that are able to state the Mountain’s Responsibility Code. A large sample of skiers and snowboarders are polled randomly throughout the day.

- Single population proportion
- Difference in two population proportions
- Single population mean
- Population mean difference for paired data
- Difference in two population means

Q6. For each question, identify the appropriate statistical scenario described in the problem background.

Background: Police set up a vehicle checkpoint at which drivers are stopped at random and their cars are inspected for safety problems. Police look to estimate the percentage of all cars on the road that may be unsafe.

- Single population proportion
- Difference in two population proportions
- Single population mean
- Population mean difference for paired data
- Difference in two population means

Q7. For each question, identify the appropriate statistical scenario described in the problem background.

Background: Electric scooters from a new startup company have recently been deployed in major cities across the nation as a cheap form of transportation. The company finds that the average scooter trip lasts 12.8 minutes. Looking to expand to smaller towns, the company deploys a small group of scooters to Ann Arbor. The company would like to evaluate if the average trip time is less for the scooters in the town of Ann Arbor.

- Single population proportion
- Difference in two population proportions
- Single population mean
- Population mean difference for paired data
- Difference in two population means

Q8. For each question, identify the appropriate statistical scenario described in the problem background.

Background: Two methods of treatment, A and B, for a particular disease were investigated. Out of 257 patients treated with method A, 41 were cured of the disease. Out of 244 patients treated with method B, 64 were cured of the disease. Does either treatment have a higher healing rate?

- Single population proportion
- Difference in two population proportions
- Single population mean
- Population mean difference for paired data
- Difference in two population means

Q9. For each question, identify the appropriate statistical scenario described in the problem background.

Background: A local gym offers a variety of fitness classes, one of these being Cardio Crash – a class designed to get participants’ heart rates up. Workout instructors would like to learn more about the average difference in heart rate during the class. They record each participant’s heart rate before the class begins and midway through the workout routine.

- Single population proportion
- Difference in two population proportions
- Single population mean
- Population mean difference for paired data
- Difference in two population means

Q10. For each question, identify the appropriate statistical scenario described in the problem background.

Background: A local grocery store recently installed new scanning machines at the self-service checkout kiosks to improve checkout speeds. On average, it used to take customers 6 minutes to checkout at the self-service kiosks. The store records the checkout times of 35 randomly selected customers using the newly updated self-service kiosks.

- Single population proportion
- Difference in two population proportions
- Single population mean
- Population mean difference for paired data
- Difference in two population means

#### Quiz 2: Hypothesis Testing in Python Assessment

Q1. What is the difference of sample mean bedtimes for toddlers who nap and toddlers who don’t nap? (Rounded to three decimal places.)

- 0.714
- 0.5355
- 20.126
- 0.1785

Q2. Given our sample size of 𝑛, how many degrees of freedom (𝑑𝑓) are there for the associated 𝑡 distribution? (again, assume that the two sample variances are equal)

Answers :

Q3. What is the 𝑡-test statistic for the first hypothesis test? (rounded to two decimal places)

- 2.41
- 4.41
- 3.61
- 2.61

Q4. What is the p-value for the first hypothesis test? (rounded to four decimal places)

- 0.0134
- 0.0080
- 0.9866
- 0.0147

Q5. For the second hypothesis test, do you reject or fail to reject the null hypothesis, given α = 0.05?

- Reject
- Fail to reject

#### Inferential Statistical Analysis with Python Week 04 Quiz Answers

Q1. A simple random sample of 500 undergraduates at a large university self-administered a political knowledge test, where the maximum score is 100 and the minimum score is 0. The mean score was 62.5, and the standard deviation of the scores was 10. What is a 95% confidence interval for the overall undergraduate mean at the university?

- (62.46, 62.54)
- (61.62, 63.38)
- (42.90, 82.10)
- (62.05, 62.95)

Q2. Given the result in Problem 1, what would we conclude about a hypothesized mean of 63?

- We have evidence in support of this hypothesized mean.
- We have evidence against this hypothesized mean.

Q3. How do we interpret the confidence interval in Problem 1?

- There is a 95% chance that the true undergraduate mean lies in this interval.
- 5% of all potential values for the true mean lie outside of this interval.
- The p-value for testing a null hypothesis that the mean is 63 is 0.05.
- 95% of all confidence intervals computed this way will cover the true population mean (in expectation).

Q4. We perform a two-tailed, one-sample t-test of the null hypothesis that the true population mean is 63, versus the alternative hypothesis that the mean is different from 63. We find a test statistic of t = -1.12 (df = 499), with a p-value of 0.264. What is our decision about the null hypothesis at an alpha=0.05?

- We reject it; the mean is significantly lower than this hypothesized mean.
- We reject it; the mean is significantly different from this hypothesized mean.
- We fail to reject it; the mean is not significantly different from this hypothesized mean.
- We do not have enough information to make a decision.

Q5. A new experimental drug for reducing the pain due to migraine headaches is being tested in a randomized controlled trial. A total of 100 participants with a history of migraine headaches are given the drug, and 100 participants with the same history are given a placebo pill. Each participant is asked about their pain one hour after taking the medication, and whether it has been reduced (yes or no). A biostatistician computes an exact 95% confidence interval for the difference in the proportions of people experiencing pain relief within one hour (treatment minus control). The 95% confidence interval for the difference in proportions is (-0.05, 0.09). What should the biostatistician conclude?

- The sample sizes are too small to make any meaningful inference about the difference in proportions.
- There is no evidence at all of the experimental pill being effective; the proportions are statistically identical.
- The experimental pill produced a significant improvement in the proportion experiencing pain relief within one hour.
- We need to know the proportions to make a decision.

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