Inferential Statistics Week 4 Quiz Answer

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Week 4 Quiz

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Question 1)

Which of the following is not required for the distribution of the sample proportion to be nearly normal?

Sample size should be at least 30 and the population distribution should not be extremely skewed.

There should be at least 10 failures.

There should be at least 10 successes.

observations should be independent.

Question 2)

When checking conditions for calculating a confidence interval for a proportion, you should use which number of successes and failures?

Observed

Expected (based on the null value)

Depends on the context

Not applicable. The number of successes and failures (observed or otherwise) is not part of the conditions required for calculating a confidence interval for a proportion.

Question 3)

You are tasked with conducting a hypothesis test evaluating whether a majority or minority of Americans think it was a bad decision to hold the 2014 winter games in Russia. You're going to use data from a 2014 Pew Research poll asked 1,003 Americans this question, and 44% responded yes. Which of the following is the correct set of hypotheses?

H₀ : p = 0.50; H_A:p ≠ 0.44

H₀ : p = 0.44; H_A:p ≠ 0.44

H₀ : p = 0.5; H_A:p ≠ 0.5

H₀ : p = 0.5; H_A:p <0.5

Question 4)

You and a friend are about to visit the aviary at the local zoo for the first time. A trustworthy zookeeper says the aviary holds about 3,000 birds. Your friend read somewhere that 10% of those birds are cardinals, but he thinks there are really more cardinals than that. You're both great at identifying cardinals so you decide to test this claim with a hypothesis test on the true proportion pof cardinals in the aviary. You walk around the aviary together and get a simple random sample by spotting 250 birds. Of these, 35 were cardinals and 215 were not cardinals. The p-value is 0.0175. Which of the following is false?

The success-failure condition is met

if in fact 10% of the birds in the aviary are cardinals, the probability of obtaining a random sample of 250 birds where exactly 14% are cardinals is 0.0175.

H₀ : p = 0.10

p = 0.14

Question 5)

Gallup conducts an annual poll of U.S. residents. Approximately 1,000 residents across all 50 states and Washington D.C. are asked "Do you believe the use of marijuana should be made legal?" The distribution of responses by date of survey is shown in the table below. Imagine a hypothesis test evaluating whether there is a difference from 2012 to 2013 between proportions of "yes" responses. Using the information in the table below, calculate the standard error for this hypothesis test. Choose the closest answer.

0.022

0.5798

0.4754

0.5274

0.00048

Question 6)

"In statistical inference for proportions, standard error (SE) is calculated differently for hypothesis tests and confidence intervals." Which of the following is the best justification for this statement?

Because in hypothesis testing we're interested in the variability of the true population distribution, and in confidence intervals we're interested in the variability of the sampling distribution.

Because in hypothesis testing, we assume the null hypothesis is true, hence we calculate SE using the null value of the parameter. In confidence intervals, there is no null value, hence we use the sample proportion(s).

Because if we used the same method for hypothesis tests as we did for confidence intervals, the calculation would he impossible.

Because statistics is full of arbitrary formulas.

Question 7)

An introductory stats professor hypothesizes that 50% of students learn best by watching the videos, 10% by reading the book, 20% by solving questions, and the rest from the discussion forums. She surveys a random sample of a large sample of students asking them how they learn best, and wants to use these data to evaluate her hypothesis. Which method should she use?

Z-test

X² test of goodness of fit

hypothesis test for a single mean

X² test of independence

ANOVA

F-test

t-test

Question 8)

A variety of studies suggest that 10% of the world population is left-handed. It is also claimed that artists are more likely to be left-handed. In order to test this claim we take a random sample of 40 art students at a college and find that 6 of them (1596) are left handed. Which of the following is the correct set-up for calculating the p-value for this test?

Roll a 10-sided die 40 times and record the proportion of times you get a 1. Repeat this many times, and calculate the proportion of simulations where the sample proportion is 10% or more.

Randomly sample 40 non-art students, and record the number of left-handed students in the sample. Repeat this many times and calculate the proportion of samples where at least 15% of the students are left-handed.

In a bag place 40 chips, 6 red and 34 blue. Randomly sample 40 chips, with replacement, and record the proportion of red chips in the sample. Repeat this many times, and calculate the proportion of samples where at least 10% of the chips are red.

Roll a 10-sided die 40 times and record the proportion of times you get a 1. Repeat this many times, and calculate the proportion of simulations where the sample proportion is 15% or more.

Question 9)

True or false: The x statistic is always non-negative.

True

False

Question 10)

Suppose in a population 20% of people wear contact lenses. What is the expected shape of the sampling distribution of proportion of contact lens wearers in random samples of 30 people from this population?

right-skewed

left-skewed

uniform

nearly normal

Question 11)

At a stop sign, some drivers come to a full stop, some come to a 'rolling stop' (not a full stop, but slow down), and some do not stop at all. We would like to test if there is an association between gender and type of stop (full, rolling, or no stop). We collect data by standing a few feet from a stop sign and taking note of type of stop and the gender of the driver. Below is a contingency table summarizing the data we collected. If gender is not associated with type of stop, how many males would we expect to not stop at all? Choose the closest answer.