Questions and Answers
What is the p-value for this test?
Where is the p-value for the new diet study?
How large a sample of batteries should be taken for the engineer's study?
Find a 90% confidence interval estimate for the difference in ages of high- and low-income people at the time of HIV infection.
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What is the 99% confidence interval for μ, the mean lifetime of the new 'long-life' bulb?
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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?
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In which of the following instances would the t-distribution be used instead of the z-distribution?
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Which of the following is a 90% confidence interval for the mean number of blue candies per package?
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Which of the following is the smallest possible test statistic that would reject the null hypothesis in favor of the alternative hypothesis?
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Is a t-score of 2.79 significant at the 5% level? At the 1% level?
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Where is the P-value for the medical care deduction at a sample mean of $934?
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What conclusion is reached if the sample mean is 13.1 minutes for fire truck arrival time?
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Is there sufficient evidence to say that the average cost of angioplasty is less than that of bypass surgery?
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Where is the P-value for the auditor’s remark about accounts receivable averaging about $2000?
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In testing whether the mean time for runners in a pentathlon event is 25 seconds, which interval is the P-value located?
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What is the P-value for the farmer testing if a new fertilizer has increased mean weight?
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Which decision rule should be used for testing the price of asthma medicine?
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What is the appropriate test to determine if the clutch size of robin's eggs has changed?
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Which statement correctly describes the relationship between a t distribution and a standard normal distribution?
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What assumption is necessary for the validity of the t-test comparing two sales locations?
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What gives a 95% confidence interval for the mean lifetime of a brand of lightbulbs?
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What is the mean pain level for patients in a study on leech therapy?
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How many electronic components should be sampled to be 99% sure of knowing the mean quantity within ±0.6?
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What is the 90% confidence interval estimate for ounces of protein per pound of a fish species?
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What is a 95% confidence interval estimate for the strength gain from resistance training?
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What establishes a 90% confidence interval estimate for the ages of renal grafts that undergo late acute rejection?
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What is the critical t-value for finding a 90% confidence interval from a sample of 15 observations?
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How large a sample should be taken to estimate differences in divorce rates between Los Angeles and New York?
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Under what conditions is it meaningful to construct a confidence interval estimate when the data consist of the entire population?
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What is the criteria for choosing a t-test rather than a z-test when making an inference about the population mean?
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What is the 98% confidence interval for the mean resistance of 100 resistors?
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What is the average time required to travel from New York to Buffalo?
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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.