AP Statistics Chapter 11 Quiz
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Questions and Answers

What is the p-value for this test?

  • .1294
  • .0099 (correct)
  • .2881
  • .0355
  • .1167

    • Where is the p-value for the new diet study?

  • Between .05 and .10
  • Over .10
  • Between .025 and .05
  • Between .01 and .025
  • Below .01 (correct)

    • How large a sample of batteries should be taken for the engineer's study?

  • 55
  • 156
  • 110 (correct)
  • 10
  • 202

    • Find a 90% confidence interval estimate for the difference in ages of high- and low-income people at the time of HIV infection.

    <p>4.4 +/- 1.26</p> Signup and view all the answers

    What is the 99% confidence interval for μ, the mean lifetime of the new 'long-life' bulb?

    <p>1450 ± 2.756(150/√30)</p> Signup and view all the answers

    Which of the following is the correct formula for a 90% confidence interval for the mean number of pages printed with the new type of cartridge?

    <p>3,875 ± 1.714 × (170/√24)</p> Signup and view all the answers

    In which of the following instances would the t-distribution be used instead of the z-distribution?

    <p>Constructing a confidence interval for the difference between two population means; the population standard deviations, σ1 and σ2, are unknown.</p> Signup and view all the answers

    Which of the following is a 90% confidence interval for the mean number of blue candies per package?

    <p>7 ± 1.708 (1/√26)</p> Signup and view all the answers

    Which of the following is the smallest possible test statistic that would reject the null hypothesis in favor of the alternative hypothesis?

    <p>2.301</p> Signup and view all the answers

    Is a t-score of 2.79 significant at the 5% level? At the 1% level?

    <p>Significant at the 5% level but not at the 1% level.</p> Signup and view all the answers

    Where is the P-value for the medical care deduction at a sample mean of $934?

    <p>Between 0.05 and 0.10</p> Signup and view all the answers

    What conclusion is reached if the sample mean is 13.1 minutes for fire truck arrival time?

    <p>The P-value is 0.07, indicating some evidence against the 12-minute claim.</p> Signup and view all the answers

    Is there sufficient evidence to say that the average cost of angioplasty is less than that of bypass surgery?

    <p>P &lt; 0.001, so this is very strong evidence that angioplasty costs less.</p> Signup and view all the answers

    Where is the P-value for the auditor’s remark about accounts receivable averaging about $2000?

    <p>Between 0.05 and 0.10</p> Signup and view all the answers

    In testing whether the mean time for runners in a pentathlon event is 25 seconds, which interval is the P-value located?

    <p>0.005 &lt; P &lt; 0.01</p> Signup and view all the answers

    What is the P-value for the farmer testing if a new fertilizer has increased mean weight?

    <p>P (t &gt; 2) with 15 degrees of freedom</p> Signup and view all the answers

    Which decision rule should be used for testing the price of asthma medicine?

    <p>Reject the null hypothesis if p-value &gt; 0.025.</p> Signup and view all the answers

    What is the appropriate test to determine if the clutch size of robin's eggs has changed?

    <p>A one-tailed t-test on one population mean.</p> Signup and view all the answers

    Which statement correctly describes the relationship between a t distribution and a standard normal distribution?

    <p>The t-distribution has a larger standard deviation than the standard normal distribution.</p> Signup and view all the answers

    What assumption is necessary for the validity of the t-test comparing two sales locations?

    <p>The population of the sales records at each location is normally distributed.</p> Signup and view all the answers

    What gives a 95% confidence interval for the mean lifetime of a brand of lightbulbs?

    <p>1,025 ± 2.13 (130/√16)</p> Signup and view all the answers

    What is the mean pain level for patients in a study on leech therapy?

    <p>μx &lt; 8, σx = 4.8</p> Signup and view all the answers

    How many electronic components should be sampled to be 99% sure of knowing the mean quantity within ±0.6?

    <p>107</p> Signup and view all the answers

    What is the 90% confidence interval estimate for ounces of protein per pound of a fish species?

    <p>3.2 ± 0.202</p> Signup and view all the answers

    What is a 95% confidence interval estimate for the strength gain from resistance training?

    <p>11.61 ± 3.69</p> Signup and view all the answers

    What establishes a 90% confidence interval estimate for the ages of renal grafts that undergo late acute rejection?

    <p>4.048 ± 0.799</p> Signup and view all the answers

    What is the critical t-value for finding a 90% confidence interval from a sample of 15 observations?

    <p>1.341</p> Signup and view all the answers

    How large a sample should be taken to estimate differences in divorce rates between Los Angeles and New York?

    <p>722</p> Signup and view all the answers

    Under what conditions is it meaningful to construct a confidence interval estimate when the data consist of the entire population?

    <p>Never</p> Signup and view all the answers

    What is the criteria for choosing a t-test rather than a z-test when making an inference about the population mean?

    <p>The standard deviation of the population is unknown.</p> Signup and view all the answers

    What is the 98% confidence interval for the mean resistance of 100 resistors?

    <p>201.5 ± 0.093</p> Signup and view all the answers

    What is the average time required to travel from New York to Buffalo?

    <p>188 minutes</p> Signup and view all the answers

    Study Notes

    Confidence Intervals and Hypothesis Testing

    • The mean lifetime of a new light bulb is estimated using a sample of 30 tested bulbs, yielding a mean of 1,450 hours and a standard deviation of 150 hours. A 99% confidence interval is determined.
    • A printer cartridge study with 24 printers showed a mean of 3,875 sheets printed and a standard deviation of 170 sheets. The correct formula for a 90% confidence interval is calculated.
    • The t-distribution models the sampling distribution for constructing confidence intervals for unknown population means when population standard deviations are unknown.

    Statistical Tests and P-values

    • A sample of 26 candy packages gave a mean of 7 blue candies with a standard deviation of 1, leading to the determination of a 90% confidence interval.
    • A two-sided test on caloric intake for 28 lab rats identifies the smallest test statistic required to reject the null hypothesis at a significance level of α = 0.05.
    • A hypothesis test with a random sample of size 10 yields a t-score of 2.79. The significance of this score is evaluated at both the 5% and 1% levels.

    Claim Evaluations and Evidence

    • An IRS representative's claim of an average medical deduction of $1,250 is evaluated against a sampled mean of $934 from 12 families with a standard deviation of $616. The P-value indicates moderate evidence against the claim.
    • A city spokesperson's assertion of a 12-minute fire truck response time is tested with records from 64 emergencies, revealing a sample mean of 13.1 minutes. The resulting P-value indicates some evidence against the spokesperson's claim.
    • A medical study comparing costs for angioplasty and bypass surgery reveals average costs and standard deviations, leading to an evaluation of evidence for cost differences.

    Critical Values and Sample Sizes

    • A study of 5 fish yields protein data to calculate a 90% confidence interval for protein per pound.
    • The determination of the critical t-value for a 90% confidence interval with a sample size of 15 helps guide decision-making in statistics.
    • A farmer's hypothesis test regarding the mean weight of apples utilizes a one-tailed test with a focus on necessary assumptions for validity.

    Test Statistics Assumptions

    • The t-test is appropriate when the standard deviation of the population is unknown, while the z-test is used when the population standard deviation is known.
    • A factory manager's pollution claim is evaluated through statistical analysis to assess the risk of making Type II errors in hypothesis testing.
    • Sample sizes for estimating differences in means, notably for different socio-economic groups, must meet specific criteria to ensure accurate results.

    Impacts of Confidence Intervals

    • A consumer awareness group analyzes the price of asthma medicine over time, utilizing hypothesis testing to determine if the price has significantly increased.
    • A comparison of performance before and after a training program for elderly individuals calculates the strength gain confidence interval.
    • Various factors influence the construction of confidence intervals, including sample size and data distribution characteristics.

    Population Considerations

    • Evaluations of public health data, such as birth weights and their effects on intelligence, inform confidence interval estimates for differences in population means.
    • The impact of socioeconomic status on health outcomes, like age at HIV infection, is assessed using confidence intervals to explore potential disparities.

    Additional Statistical Learning

    • Understanding the relationship between sample distributions and methods for comparing means enhances knowledge on hypothesis testing and confidence estimation.
    • Familiarity with calculating confidence intervals and P-values equips researchers to better analyze their experimental results and claims effectively.

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    Description

    Test your knowledge on confidence intervals and mean lifetime estimations with these multiple-choice questions from Chapter 11 of AP Statistics. This quiz will challenge your understanding of statistical concepts and calculations related to real-world applications.

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