AP Statistics Chapter 6 Quiz
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Questions and Answers

What does the standardized test statistic rely on when comparing a statistic to a parameter?

  • Standard deviation of the parameter
  • Standard error of the statistic (correct)
  • Mean of the statistic
  • Critical value of the parameter

    • Which formula correctly represents the confidence interval calculation?

  • Statistic × (critical value) × standard error of the statistic
  • Statistic ± (critical value) × standard error of the statistic (correct)
  • Statistic + (critical value) × standard error of the statistic
  • Statistic ± (critical value) / standard error of the statistic

    • In a Chi-square statistic calculation, what does the symbol χ² represent?

  • The ratio of observed to expected frequencies
  • The average of expected frequencies
  • The difference between observed and expected frequencies (correct)
  • The sum of squared differences between expected frequencies

    • What is the primary purpose of calculating a confidence interval?

    <p>To estimate the range within which the population parameter lies</p> Signup and view all the answers

    What relationship does the standard error of the statistic have with sample size?

    <p>It decreases as the sample size increases</p> Signup and view all the answers

    What is the probability that a randomly selected household in Tower Hill has at least two cell phones?

    <p>0.70</p> Signup and view all the answers

    Which statement is true about binomial and geometric random variables?

    <p>A geometric setting allows for more than two outcomes for each trial.</p> Signup and view all the answers

    What is the probability that the basketball player makes at least two of her three free throws if she makes 80% of her shots?

    <p>0.896</p> Signup and view all the answers

    In the distribution of household cell phones, what is the probability of a household having zero cell phones?

    <p>0.1</p> Signup and view all the answers

    If a geometric random variable has a success probability of 0.85, how is its distribution characterized?

    <p>It is skewed to the left.</p> Signup and view all the answers

    How many total households' phone data are provided in the probability distribution for Tower Hill?

    <p>6</p> Signup and view all the answers

    What does the geometric setting assume about the trials?

    <p>Each trial must be independent.</p> Signup and view all the answers

    For the basketball player, what is the probability of making exactly one free throw out of three attempts?

    <p>0.192</p> Signup and view all the answers

    What type of statistical setting is being described when selecting individuals until finding an HIV-positive person?

    <p>Geometric setting</p> Signup and view all the answers

    In the context of selecting policewomen and policemen, what does the height probability distribution indicate?

    <p>Heights are normally distributed with different means and standard deviations.</p> Signup and view all the answers

    How many individuals would you expect to select to find the first HIV-positive person if the prevalence is 1%?

    <p>100</p> Signup and view all the answers

    What is the primary reason the selection of height measurements does not form a geometric or binomial setting?

    <p>Each trial has a different probability of success.</p> Signup and view all the answers

    What percentage of respondents in an online poll subscribe to the 'five-second rule'?

    <p>20%</p> Signup and view all the answers

    What assumption can be made about the population when conducting the selection of individuals in a geometric setting with a 1 in 100 prevalence?

    <p>The population is larger than 1000.</p> Signup and view all the answers

    If the mean height of policewomen is 65 inches and the mean height of policemen is 70 inches, what concept does this illustrate?

    <p>A normal distribution with different means</p> Signup and view all the answers

    Why is it important to indicate the methods used in selecting individuals for a study?

    <p>To verify the randomness of the selection process.</p> Signup and view all the answers

    What is the expected value of the daily profit X for Jocelyn's babysitting business?

    <p>$13.5</p> Signup and view all the answers

    If a bottling machine improperly caps 5% of bottles, what is the probability of exactly 2 improperly capped bottles in a sample of 20?

    <p>0.19</p> Signup and view all the answers

    What is the probability of rolling exactly 3 sevens in 10 rolls of an 8-sided die?

    <p>0.0439</p> Signup and view all the answers

    Sharon has mp3 files with a mean size of 4.0 MB and standard deviation of 1.8 MB. What is likely to be the mean size of 10 randomly selected songs?

    <p>40 MB</p> Signup and view all the answers

    To fit a geometric distribution, what must the random variable X ensure?

    <p>The probability of success is constant.</p> Signup and view all the answers

    Which of these values indicates a correct application of the probability mass function to find the probability of exactly 2 successes?

    <p>0.19</p> Signup and view all the answers

    In creating a mixtape, how are the songs' lengths typically estimated from their file sizes?

    <p>Length = 1.07(file size) - 0.02</p> Signup and view all the answers

    What is the correct interpretation of a probability of 0.19 when dealing with the scenario of improperly capped bottles?

    <p>19% chance exactly 2 bottles will be improperly capped.</p> Signup and view all the answers

    What is the formula for the mean of a discrete random variable X?

    <p>$ ext{E}(X) = ext{µ}_X = ext{Σ} x_i ⋅ P(x_i)$</p> Signup and view all the answers

    For a binomial distribution, which of the following statements is true about the parameters identified as n and p?

    <p>n represents the number of trials and p represents the probability of success.</p> Signup and view all the answers

    What does the standard deviation σX express in a probability distribution?

    <p>The dispersion of the random variable around the mean.</p> Signup and view all the answers

    Which formula correctly represents the probability of a specific outcome x in a binomial distribution?

    <p>$P(X = x) = \frac{n!}{x!(n-x)!} p^x (1-p)^{n-x}$</p> Signup and view all the answers

    How is the mean for a geometric distribution defined?

    <p>$ ext{µ}_X = \frac{1}{p}$</p> Signup and view all the answers

    Which of the following is NOT a characteristic of the binomial distribution?

    <p>The trials are dependent on each other.</p> Signup and view all the answers

    What does the notation $P(X = x)$ imply in probability distributions?

    <p>The probability that variable X takes on the value exactly equal to x.</p> Signup and view all the answers

    In a discrete probability distribution, how is the variance calculated?

    <p>$ ext{Var}(X) = Σ P(x_i)(x_i - µ_X)^2$</p> Signup and view all the answers

    What is the mean of the sampling distribution for a single population proportion, p̂?

    <p>$p$</p> Signup and view all the answers

    In the context of two populations, what does the symbol p̂c represent?

    <p>The combined sample proportion</p> Signup and view all the answers

    What is the standard error for the difference in sample proportions, p̂1 - p̂2?

    <p>$ rac{p̂_1(1 - p̂_1)}{n_1} + rac{p̂_2(1 - p̂_2)}{n_2}$</p> Signup and view all the answers

    What does the symbol μX indicate in sampling distributions for means?

    <p>The mean of the sampling distribution</p> Signup and view all the answers

    For two populations, what is the formula for the standard error of X1 and X2?

    <p>$ rac{s_{12}}{n_1} + rac{s_{22}}{n_2}$</p> Signup and view all the answers

    Which equation represents the standard error of the sample mean for one population?

    <p>$ rac{s}{n}$</p> Signup and view all the answers

    What does the symbol μb represent in the context of simple linear regression?

    <p>The expected value of the slope</p> Signup and view all the answers

    What is the formula used to calculate the standard error of the slope in simple linear regression?

    <p>$ rac{s_{y}}{s_{x} imes n }$</p> Signup and view all the answers

    In sampling distributions, which term describes the measure of variability from the theoretical population?

    <p>Standard deviation</p> Signup and view all the answers

    Which of the following statements is true regarding standard error?

    <p>It decreases as the sample size increases.</p> Signup and view all the answers

    What is the formula for the variance of the difference in sample means for two populations?

    <p>$ rac{s_1^2}{n_1} + rac{s_2^2}{n_2}$</p> Signup and view all the answers

    When assuming both population proportions are equal, which of the following formulas is correct for the standard error of p̂1 - p̂2?

    <p>$p̂_c (1 - p̂_c) rac{1}{n_1} + rac{1}{n_2}$</p> Signup and view all the answers

    Study Notes

    AP Statistics Chapter 6 Test Notes

    • Question 1: Probability of at least two cell phones. The probability distribution for the number of cell phones in a household is given. To find the probability of at least two cell phones, sum the probabilities for 2, 3, 4, and 5 cell phones.

    • Question 2: True statements about binomial and geometric settings. A binomial setting has a fixed number of trials, and the probability of success remains constant for each trial. A geometric setting counts the number of trials until a success.

    • Question 3: Probability of making at least two free throws. A basketball player makes 80% of her free throws. The problem asks for the probability she makes at least two of three free throws, given independent attempts. Use the binomial probability formula.

    • Question 4: Expected value of daily profit. A babysitting business has a probability distribution for daily profit. To find the expected value, multiply each daily profit by its corresponding probability and sum the results.

    • Question 5: Probability of exactly 2 improperly capped bottles. A bottling machine improperly applies caps to 5% of bottles. Find the approximate probability that exactly 2 caps are improperly applied when selecting 20 bottles randomly. (Use the binomial probability formula).

    • Question 6: Probability of getting exactly 3 sevens in 10 rolls. Calculate the probability of rolling exactly 3 sevens in 10 rolls of an 8-sided die. (Use the binomial probability formula).

    • Question 7: Mean and standard deviation of total megabytes. The mean size of an MP3 song file is 4.0 megabytes, and the standard deviation is 1.8 megabytes. Find the mean and standard deviation of the total size (in megabytes) of 10 randomly selected songs.

    • Question 8: Condition for a geometric distribution. A geometric distribution requires the probability of success to be the same for each trial. The number of trials is not fixed.

    • Question 9: Mean and standard deviation of commute time. Find the mean and standard deviation of a commute that involves the Blue line (mean=18 min, SD=2 min), Red Line (mean=12 min, SD=1 min) and a waiting time (mean=10 min, SD=5 min), assuming independence.

    • Question 10: Probability of needing a tow truck. The probability of drivers carrying jumper cables is 16%. Find the probability of needing to call a tow truck after asking 10 people without success. (Use the geometric probability formula).

    • Question 11: Probability of a report weighing less than 45 grams. The weight of reports in a department follows a normal distribution. Mean = 60 grams, SD =12 grams. Find the probability that the next report weighs less than 45 grams.

    • Question 12: Finding the Expected Number of People to Interview. Find the number of people the reporter needs to interview to find their first Democrat if 60% of adults are registered Democrats.

    • Question 13: Binomial, Geometric, or Neither. Determine whether the random variable described satisfies the conditions for a binomial setting, geometric setting or neither.

    • Question 14: Probability of a policewoman being taller. Suppose height of policemen is normally distributed with mean 70 in and SD 3 in. Policewomen have mean height 65 in. and SD 2.5 inches. Find the probability of a randomly selected policewoman being taller than a randomly selected policeman.

    • Question 15: Probability of subscribing to "five-second rule" . 20% of people subscribe to the 'five-second rule'. Determine the probability that exactly 3 people subscribe in a sample of 15. Find the expected value of this sample. Find the standard deviation of this sample.

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    AP Stats Chapter 6 Test PDF

    Description

    Test your knowledge on probability concepts covered in AP Statistics Chapter 6. This quiz includes questions about binomial and geometric settings, calculating specific probabilities, and expected value analysis for real-life scenarios like a babysitting business.

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