AP Stat CWC Final Review Flashcards
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Questions and Answers

What is the alternative hypothesis in the context provided?

Ha: μ > 24.5

Based on a sample producing a mean of 13.4 with a z-score of 2.12, what can be concluded?

  • There is reason to conclude that μ = 10
  • No conclusion can be drawn
  • There is reason to conclude that μ < 10
  • There is reason to conclude that μ > 10 (correct)

    • What is the approximate p-value for the test on the average amount of active ingredient per tablet?

    0.012

    Which test should be conducted to determine if Brand A batteries last longer than Brand B?

    <p>One-sided, two-sample t-test</p> Signup and view all the answers

    What is the most reasonable distribution of the differences when rolling two dice?

    <p>Normal looking distribution with both negative and positive numbers</p> Signup and view all the answers

    Given damage during delivery, what is the probability that a new microwave oven stops working in less than 2 years?

    <p>0.40</p> Signup and view all the answers

    What is the probability that the device will not fail in one year given component failure probabilities?

    <p>0.922</p> Signup and view all the answers

    What profit does XYZ Office Supplies Company expect to make for the next year?

    <p>$220,700</p> Signup and view all the answers

    What does the expected value of -$0.95 per ticket mean for the raffle?

    <p>The ticket owners lose an average of $0.95 per raffle ticket.</p> Signup and view all the answers

    What is the standard deviation of Y for the profit equation Y = 75X - 100?

    <p>$432.00</p> Signup and view all the answers

    What is the probability that a group of four adult male passengers will exceed the weight limit?

    <p>0.023</p> Signup and view all the answers

    Which sample statistics change when values are multiplied by a constant greater than 1?

    <p>Mean, median, and standard deviation</p> Signup and view all the answers

    Which value of n maximizes the probability of winning a prize?

    <p>n=10 only</p> Signup and view all the answers

    What is the least probable value of X when sampling chips?

    <p>0</p> Signup and view all the answers

    Do the data support the use of a normal model based on given sample statistics?

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

    What is the probability that N, a normally distributed variable, equals 8?

    <p>0</p> Signup and view all the answers

    What gives the margin of error for the confidence interval in Amber's regression analysis?

    <p>(2.228) (0.745)</p> Signup and view all the answers

    Which conditions appear to be met based on the residual plot?

    <p>II and III only</p> Signup and view all the answers

    Which residual plot provides the strongest evidence for an appropriate regression model?

    <p>Very randomly scattered graph with no sort of pattern</p> Signup and view all the answers

    Which statement is true about the claims made regarding the confidence interval width and sample size?

    <p>Quincy's claim is correct.</p> Signup and view all the answers

    What conclusion can be drawn from the agronomist’s test with a p-value of 0.25?

    <p>The null hypothesis is not rejected because 0.25 &gt; 0.05. There is not sufficient evidence to suggest a linear relationship.</p> Signup and view all the answers

    Which of the following questions about cars in a school parking lot will allow for the collection of a set of categorical data?

    <p>What are the colors of the cars in the lot?</p> Signup and view all the answers

    Which of the following statements is not supported by the frequency table of ice cream flavors?

    <p>One-half of the students chose vanilla or chocolate.</p> Signup and view all the answers

    Which of the following statements is not supported by the color design preference table?

    <p>For men, the number who chose a design with black was greater than the number who chose a design with blue.</p> Signup and view all the answers

    Which of the following statements is supported by the relative frequency bar chart?

    <p>Grade 12 had the least relative frequency of participating students.</p> Signup and view all the answers

    What is the sum of the squared deviations of the golf scores from the mean?

    <p>∑(x−x¯)^2=(86−84)²+(81−84)²+(87−84)²+(82−84)²</p> Signup and view all the answers

    Which of the following must be true about the data sets summarized by boxplots A and B?

    <p>The data in Set A have a larger range than the data in Set B.</p> Signup and view all the answers

    What represents the parameters of the distribution for the ATM transactions?

    <p>μ=80;σ=10</p> Signup and view all the answers

    What is closest to the proportion of orders processed in less than 240 seconds at the coffee shop?

    <p>0.17</p> Signup and view all the answers

    Is it appropriate to assume the sampling distribution of subway riders is approximately normal given the sample?

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

    Which of the following conditions verify that inference procedures are appropriate for testing a population proportion?

    <p>All of the above.</p> Signup and view all the answers

    What is a correct interpretation of the 95 percent confidence interval for climate change opinion?

    <p>We are 95 percent confident that the proportion of all people in the country who think climate change is a problem is between 0.146 and 0.214.</p> Signup and view all the answers

    What is the correct test statistic for the proportion of bats with a wingspan greater than 10 inches?

    <p>z=(0.25−0.30)/√((0.30*0.70)/80)</p> Signup and view all the answers

    What should researchers do to avoid a Type II error when testing machine precision?

    <p>Increase the significance level to increase the probability of a Type II error.</p> Signup and view all the answers

    What is closest to the confidence interval for the difference in blemished apples at a 98 percent level?

    <p>(−105, 265)</p> Signup and view all the answers

    What is the interpretation of the confidence interval for voter spending opinion?

    <p>We are 95% confident that the difference in the proportions of all voters in districts C and M who favor an increase in state spending for the arts is between −0.16 and 0.08.</p> Signup and view all the answers

    How many dogs are expected to be treated if the clinic sees 230 animals in a month?

    <p>140.3</p> Signup and view all the answers

    What is the correct interpretation of the p-value from the auditing employee sample?

    <p>If the null hypothesis were true, there would be a 68 percent chance of obtaining a chi-square value of at least 0.771.</p> Signup and view all the answers

    Which statement is true about the random assignment in a study on acupuncture?

    <p>The independence condition has been met.</p> Signup and view all the answers

    Which is the appropriate test for the association between cell phone brand and age-group?

    <p>A chi-square test of independence.</p> Signup and view all the answers

    What is the correct interpretation of the p-value in the chi-square test for high school absentee rates?

    <p>Assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic of 19.02 or larger.</p> Signup and view all the answers

    What is true about the car ownership results from the company survey?

    <p>If the person owns a car, he or she is more likely to live elsewhere in the city than to live in the downtown area.</p> Signup and view all the answers

    What does the relationship between employment status and class suggest?

    <p>There appears to be an association, since the proportion of juniors having jobs is much larger than the proportion of seniors having jobs.</p> Signup and view all the answers

    What is the estimated increase in temperature for a 5 chirp increase?

    <p>16.5 °F</p> Signup and view all the answers

    Which of the following could be the least squares regression line?

    <p>ŷ = 8.5 + 0.3x</p> Signup and view all the answers

    When is it preferable to use stratified random sampling?

    <p>When the population can be divided into strata.</p> Signup and view all the answers

    The bank needs to use an inference procedure for employees' volunteer activities.

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

    How can a simple random sample be obtained in a student survey?

    <p>Choose students from a roster randomly.</p> Signup and view all the answers

    Which concern is NOT legitimate about using automated phone surveys?

    <p>Registered voters with unlisted telephone numbers may be underrepresented.</p> Signup and view all the answers

    How can response bias in surveys be minimized?

    <p>Carefully word and field-test survey questions.</p> Signup and view all the answers

    Is the experimental design good if cold temperature is confounded with brand?

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

    What best describes the manager's study comparing two detergents?

    <p>A completely randomized design.</p> Signup and view all the answers

    Which method shows a cause-and-effect relationship?

    <p>A controlled experiment.</p> Signup and view all the answers

    Which statements explain why aspirin recommendations from a study may not be generalized?

    <p>All of the above.</p> Signup and view all the answers

    What is the approximate 90 percent confidence interval for average repair costs?

    <p>$127.95 ± $6.25</p> Signup and view all the answers

    Why must the population size be at least 10 times the sample size?

    <p>To ensure independence among observations.</p> Signup and view all the answers

    Will a 95% confidence interval include μ = 8 if the p-value is 0.034?

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

    Which is the appropriate alternative hypothesis regarding perchlorate levels?

    <p>The average level of perchlorate is greater than 24.5 parts per billion.</p> Signup and view all the answers

    Study Notes

    Categorical Data

    • Collecting data on car colors in a school parking lot results in categorical data.

    Frequency Tables

    • A frequency table showing ice cream flavor preferences indicates that the statement "One-half of the students chose vanilla or chocolate" is unsupported.

    Market Research

    • A study on color design preferences reveals that men's choices for black designs were not greater than for blue designs.

    Relative Frequencies

    • A bar chart illustrates that 12th grade students had the least participation in community service.

    Golf Scores

    • The sum of the squared deviations from the mean score of a golfer is derived from the individual scores.

    Boxplots

    • Only one conclusion about the size and range of two data sets represented in boxplots can be drawn.

    Normal Distribution Parameters

    • An ATM's transaction count is normally distributed with a mean of 80 and a standard deviation of 10.

    Processing Times

    • The proportion of coffee shop orders processed in under 240 seconds is estimated at 0.17.

    Proportion Estimation

    • Sampling distribution normality cannot be assumed with only 30 residents, where 28 commute by subway.

    Conditions for Inference

    • Valid statistical inferences regarding a sample proportion require conditions related to sampling methods and sample sizes.

    Confidence Intervals

    • A 95% confidence interval suggests a proportion of a population thinking climate change is a problem lies between 0.146 and 0.214.

    One-Sample Z-Test

    • The correct test statistic for investigating differences in bat wingspans is calculated using specified population and sample proportions.

    Statistical Errors

    • To mitigate Type II errors in hypothesis testing, a significance level increase is advisable.

    Interval Estimates

    • A 98% confidence interval for blemished apples ranges approximately between -105 and 265.

    Confidence Interval Interpretation

    • A confidence interval for differences in proportions favors an increase in arts spending among a specific district's voters.

    Expected Values

    • In a study of animal types at a vet clinic, expected distributions based on historical percentages are calculated for 230 animals treated.

    Chi-Square Test

    • A sample chi-square test determines the appropriateness of auditing based on job levels, with interpretation centered on p-values.

    Experimental Design

    • Random assignment in a medical study supports independence, crucial for chi-square tests of homogeneity.

    Chi-Square Test of Independence

    • Investigating the relationship between age groups and cell phone brand preference uses a chi-square test of independence.

    Linear Regression

    • The equation for chirp count and temperature models an increase in temperature correlated with increased chirp frequency.

    Least Squares Regression Line

    • Regression statistics provide potential least squares regression line based on given means and standard deviations for variables.

    Stratified Sampling

    • Stratified random sampling is preferable when subgroups exhibit considerable similarity within strata.

    Census Surveys

    • Census data collected from all bank employees negates the need for inference procedures about volunteer participation.

    Sampling Methods

    • True simple random samples can be achieved by random number selection methods.

    Sampling Procedure Concerns

    • A sampling method may overlook underrepresented groups such as registered voters with unlisted numbers.

    Minimizing Response Bias

    • Response bias can be minimized through meticulous question design and pre-testing.

    Confounding Variables

    • An experiment on rubber band elasticity risks confounding effects between temperature and brand.

    Experimental Design

    • A coin-flip method for detergent testing exemplifies a completely randomized design for effectiveness comparison.

    Cause-and-Effect Relationships

    • Controlled experiments are necessary for establishing cause-and-effect links between variables.

    Medical Study Caution

    • Results from a physician study caution against blanket recommendations, owing to gender and occupation limitations.

    Confidence Interval Calculation

    • A repair cost sample leads to a specific confidence interval around the average cost based on calculated mean and deviation.

    Independence Among Observations

    • A finite population must be significantly larger than the sample size to ensure negligible observational dependence.

    Null Hypothesis Testing

    • A low p-value indicates rejection of the null hypothesis in favor of indicating that mean differences exist.

    Alternative Hypothesis

    • Concerns about perchlorate levels in drinking water establish a test for mean values exceeding safety thresholds.

    Sample Mean Analysis

    • A mean comparison test yields indications of significant difference in active ingredient content across sampled tablets.

    Independent T-Test

    • A one-sided two-sample t-test is suitable for assessing whether Brand A batteries outlast Brand B based on life duration trials.

    Difference Distribution

    • Rolling two dice and computing their outcome differences results in a normal distribution appearance in graphical representation.

    Microwave Oven Durability

    • The probability analysis surrounding microwave failure rates highlights potential concerns with both damage and operational lifetime.### Microwave Oven Delivery
    • Probability of a damaged microwave oven failing in less than 2 years is 0.40.

    Electronic Device Components

    • Components A, B, and C have failure probabilities of 0.01, 0.03, and 0.04, respectively.
    • Independent failures lead to a device failure probability of 0.922 in one year.

    XYZ Office Supplies Company

    • Expected profit for next year from calculators is $220,700.
    • Profit from wholesale calculators is $20 each; retail is $30 each.

    Raffle Fundraising

    • 1,000 raffle tickets sold for $1 each with a $50 prize.
    • Expected net gain for ticket holders is -$0.95, indicating an average loss per ticket.

    Concrete Delivery Profit

    • Probability distribution for cubic yards of concrete sold results in an expected value of 19.25.
    • Profit equation is Y = 75X - 100; standard deviation of profit Y is $432.00.

    Rowboat Weight Limit

    • Normal distribution of adult male weights: mean = 190 lbs, standard deviation = 10 lbs.
    • Probability of a group of four exceeding the 800 lb weight limit is 0.023.

    Sample Statistics and Constants

    • Multiplying each value in a data set by a constant greater than 1 affects the mean, median, and standard deviation.

    Prize Winning Probability

    • To maximize the probability of winning a prize, choose n = 10 games.

    Acceptable Chips in Circuit Boards

    • Out of 4 randomly selected computer chips, the least probable number of acceptable chips (X) is 0.

    Normality in Sampling Distribution

    • Sales prices of homes were right-skewed; sample means from random samples of size 100 will yield an approximately normal distribution with a mean of $206,274 and standard deviation of $3,788.

    Properties of Normal Random Variables

    • Probability of a continuous random variable equating to a specific value (e.g., P(N=8)) is 0.

    Confidence Interval on Regression

    • For a sample of 12 students, the margin of error is calculated as (2.228)(0.745).

    Conditions for Residual Plots

    • Conditions checked in residual plots include linear relationship and constant standard deviation of y; confirmed by II only.

    Evidence for Regression Model Fit

    • A residual plot with a random scatter and no patterns indicates a strong evidence for the appropriateness of the regression line.

    Confidence Interval Width and Sample Size

    • Increasing sample size to 30 decreases the width of the confidence interval; claim made by Quincy is correct.

    Agronomist's Hypothesis Testing

    • Testing for a linear relationship between wheat stalk height and yield yielded a p-value of 0.25; null hypothesis is not rejected, showing insufficient evidence for a relationship.

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    Description

    Prepare for your AP Statistics exam with this set of flashcards focused on categorical data and frequency tables. Each card poses important questions and presents relevant examples, ensuring you grasp key statistical concepts. Perfect for a final review before the exam!

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