AP Statistics Chapter 11 Quiz

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?

156

110 (correct)

202

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

4.4 +/- 1.26 Signup and view all the answers

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

1450 ± 2.756(150/√30) 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?

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

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

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

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

7 ± 1.708 (1/√26) 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?

2.301 Signup and view all the answers

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

Significant at the 5% level but not at the 1% level. Signup and view all the answers

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

Between 0.05 and 0.10 Signup and view all the answers

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

The P-value is 0.07, indicating some evidence against the 12-minute claim. 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 < 0.001, so this is very strong evidence that angioplasty costs less. Signup and view all the answers

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

Between 0.05 and 0.10 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?

0.005 Signup and view all the answers

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

P (t > 2) with 15 degrees of freedom Signup and view all the answers

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

Reject the null hypothesis if p-value > 0.025. Signup and view all the answers

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

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

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

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

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

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

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

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

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

μx < 8, σx = 4.8 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?

107 Signup and view all the answers

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

3.2 ± 0.202 Signup and view all the answers

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

11.61 ± 3.69 Signup and view all the answers

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

4.048 ± 0.799 Signup and view all the answers

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

1.341 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?

722 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?

Never 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?

The standard deviation of the population is unknown. Signup and view all the answers

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

201.5 ± 0.093 Signup and view all the answers

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

188 minutes 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.