Statistical Concepts and Hypothesis Testing

These flashcards cover key concepts related to statistical hypothesis testing, confidence intervals, and probability distributions based on recent lecture notes.

According to a 2011 Rasmussen poll, what percentage of adults opposed having students attend school year-round?

C) 53%

A) 47%
B) 50%
C) 53%
D) 55%

When testing whether more than 50% of adults oppose year-round school, what are the correct null (H0) and alternative (Ha) hypotheses?

B) H0: p \le 0.50, Ha: p > 0.50

A) H0: p = 0.50, Ha: p \ne 0.50
B) H0: p \le 0.50, Ha: p > 0.50
C) H0: p > 0.50, Ha: p \le 0.50
D) H0: p \ge 0.50, Ha: p < 0.50

What is the established graduation rate for young Americans, as per common statistical data?

C) 87%

A) 75%
B) 80%
C) 87%
D) 90%

In a study referenced to estimate the proportion of young Americans earning a high school diploma, what was the sample size used?

C) 1600

A) 800
B) 1200
C) 1600
D) 2000

Given a sample of 1600 young Americans and a known population graduation rate, what is the probability that at least 88% of them have earned their high school diploma?

C) 0.8830

A) 0.1170
B) 0.5000
C) 0.8830
D) 0.9500

If the calculated test statistic for a hypothesis test is 2.09, what is the correct p-value associated with this statistic?

B) 0.0183

A) 0.0083
B) 0.0183
C) 0.0283
D) 0.0383

In a statistical study involving monkey weight using binomial distribution, for what reason would it be inappropriate to use the normal approximation to the binomial distribution?

B) np < 10

A) n(1-p) < 10
B) np < 10
C) The sample size is too large
D) The success probability p is too high

In the context of a lab technician checking medical equipment, if the null hypothesis is that the equipment is functioning properly, which statement accurately describes a Type I error?

B) The technician concludes the equipment is not functioning properly when it is actually functioning properly.

A) The technician concludes the equipment is functioning properly when it is indeed functioning properly.
B) The technician concludes the equipment is not functioning properly when it is actually functioning properly.
C) The technician concludes the equipment is functioning properly when it is actually not functioning properly.
D) The technician concludes the equipment is not functioning properly when it is indeed not functioning properly.

In the context of hypothesis testing, if the calculated p-value is less than the predetermined significance level (alpha), what is the appropriate statistical decision?

B) Reject the null hypothesis.

A) Fail to reject the null hypothesis.
B) Reject the null hypothesis.
C) Accept the null hypothesis.
D) Increase the sample size.

If we want to estimate the percentage of voters in favor of extending tax cuts to within 2 percentage points with 95% confidence, and no prior estimate of the proportion is available, what is the minimum required sample size?

C) 2401

A) 601
B) 961
C) 2401
D) 3845

Which of the following describes two methods to achieve a narrower (more precise) confidence interval for a population proportion?

C) Increase the sample size and decrease the confidence level.

A) Decrease the sample size and decrease the confidence level.
B) Increase the sample size and increase the confidence level.
C) Increase the sample size and decrease the confidence level.
D) Decrease the sample size and increase the confidence level.

Given a 95% confidence interval for a population proportion is (0.459, 0.521), what is the point estimate of the true proportion?

B) 0.490

A) 0.459
B) 0.490
C) 0.521
D) 0.062

For a confidence interval of (0.459, 0.521) for a population proportion, what is the margin of error (E)?

A) 0.031

A) 0.031
B) 0.062
C) 0.459
D) 0.521

In a hypothesis test where the calculated p-value is 0.042 and the significance level (alpha) is 0.05, what is the appropriate conclusion?

B) Reject the null hypothesis because the p-value is smaller than the significance level.

A) Fail to reject the null hypothesis because the p-value is greater than the significance level.
B) Reject the null hypothesis because the p-value is smaller than the significance level.
C) There is insufficient evidence to make a conclusion.
D) The results are statistically inconclusive.

Which statement accurately describes the relationship between a p-value and the null hypothesis in statistical testing?

B) A small p-value implies strong evidence against the null hypothesis.

A) A large p-value implies strong evidence against the null hypothesis.
B) A small p-value implies strong evidence against the null hypothesis.
C) The p-value has no direct relationship with the null hypothesis.
D) A small p-value always proves the null hypothesis is false.

When a medical researcher states a margin of error of about 3% regarding lead-based paint exposure, what does this margin of error signify?

B) It means the true proportion of exposure may vary by approximately this percentage from the sample proportion.

A) It indicates the probability of making a Type I error.
B) It means the true proportion of exposure may vary by approximately this percentage from the sample proportion.
C) It represents the confidence level of the study.
D) It is the p-value obtained from the hypothesis test.

A random sample of 495 adults found that 59 have diabetes. What is the constructed 98% confidence interval for the population proportion of adults with diabetes?

B) (0.0853, 0.1531)

A) (0.0901, 0.1483)
B) (0.0853, 0.1531)
C) (0.1009, 0.1375)
D) (0.0789, 0.1595)

If a survey about Internet orders yields a 95% confidence interval of (0.82, 0.94) for the proportion of orders that arrive on time, what is the most accurate interpretation of this interval?

C) We are 95% confident that the population proportion of orders that arrive on time is between 0.82 and 0.94.

A) There is a 95% chance that the sample proportion is between 0.82 and 0.94.
B) 95% of all Internet orders arrive on time.
C) We are 95% confident that the population proportion of orders that arrive on time is between 0.82 and 0.94.
D) In 95% of future samples, the sample proportion will fall between 0.82 and 0.94.

If a calculated confidence interval for a population proportion does not contain a specific value (e.g., 0.96) claimed by a representative, what conclusion can be drawn?

C) Evidence indicates the representative's claim is incorrect at the given confidence level.

A) The representative's claim is definitely correct.
B) The confidence interval is invalid.
C) Evidence indicates the representative's claim is incorrect at the given confidence level.
D) More data is needed to make a conclusion.

What is the sample size needed to estimate the proportion of adults confident in the U.S. banking system to within 5% with 95% confidence?

C) 384

A) 100
B) 250
C) 384
D) 500

If, in a hypothesis test where the null hypothesis states the true proportion is 0.49 and the alternative is that it's greater than 0.49, the p-value for a sample proportion of 0.52 is calculated as 0.0712, what does this p-value represent?

B) The probability of observing a sample proportion larger than 0.52 if the true population proportion is actually 0.49.

A) The probability that the true proportion is 0.49.
B) The probability of observing a sample proportion larger than 0.52 if the true population proportion is actually 0.49.
C) The probability of making a Type I error.
D) The probability that the sample proportion is exactly 0.52.

If a claim is made that 44% of workers invest in individual retirement accounts, what are the appropriate null (H0) and alternative (Ha) hypotheses for testing this claim?

C) H0: p = 0.44, Ha: p \ne 0.44

A) H0: p < 0.44, Ha: p \ge 0.44 B) H0: p \le 0.44, Ha: p > 0.44
C) H0: p = 0.44, Ha: p \ne 0.44
D) H0: p \ne 0.44, Ha: p = 0.44

In a hypothesis test about the mean calorie content of frozen dinners, where the null hypothesis states the mean is 240 calories, what constitutes a Type I error?

B) Concluding the mean calorie content is not 240 when it actually is 240.

A) Concluding the mean calorie content is 240 when it is indeed 240.
B) Concluding the mean calorie content is not 240 when it actually is 240.
C) Concluding the mean calorie content is 240 when it is actually not 240.
D) Concluding the mean calorie content is not 240 when it is indeed not 240.

In a hypothesis test where the null hypothesis is H0: p = 0.32 and the test statistic is calculated as Z = 2.10, what is the one-tailed p-value (e.g., for Ha: p > 0.32)?

B) 0.0179

A) 0.00895
B) 0.0179
C) 0.0358
D) 0.0716

In a sample of 180 adults, 53% say they never wear a helmet. Which expression best describes the approximate normal distribution for this observed sample proportion (p̂)?

B) p̂ \sim AN(0.53, 0.0372)

A) p̂ \sim N(0.59, 0.0367)
B) p̂ \sim AN(0.53, 0.0372)
C) p̂ \sim B(180, 0.53)
D) p̂ \sim t_{179}(0.53)

If the true population proportion of adults who never wear a helmet is known to be 59%, and a sample of 180 adults is taken, which formula describes the expected approximate probability distribution for the proportion of adults in the sample who never wear a helmet?

C) p̂ \sim AN(0.59, 0.0367)

A) p̂ \sim AN(0.53, 0.0372)
B) p̂ \sim B(180, 0.59)
C) p̂ \sim AN(0.59, 0.0367)
D) p̂ \sim t_{179}(0.59)

Given a large university's known freshmen retention rate of 72%, what is the probability that the retention rate in a random sample of 220 freshmen is less than 68%?

C) 0.0934

A) 0.0215
B) 0.0456
C) 0.0934
D) 0.1587

If a calculated confidence interval for a population proportion does not include a hypothesized or claimed specific value, what general conclusion can be drawn?

C) The evidence indicates that the claim is likely incorrect at the given confidence level.

A) The claim is definitively correct within the interval.
B) There is insufficient evidence to dispute the claim.
C) The evidence indicates that the claim is likely incorrect at the given confidence level.
D) The sample size was too small to