AP Statistics Flashcards: Carrying Out Test For Population Mean

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This deck focuses on Carrying Out Test For Population Mean, giving you a quick way to review the definitions, rules, and examples that matter most for AP Statistics.

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Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What does $n$ represent in hypothesis testing?

Answer: Sample size. Number of observations in the sample.

Flashcard 2: What is the role of the alternative hypothesis ($H_a$)?

Answer: Proposes the opposite of the null hypothesis. Represents researcher's theory to be supported.

Flashcard 3: Which option is a requirement for the Central Limit Theorem?

Answer: Sample size $n$ is sufficiently large. Enables normal approximation for sampling distribution.

Flashcard 4: What is the critical value approach?

Answer: Compare test statistic to critical value to decide on $H_0$. Uses predetermined threshold to make statistical decision.

Flashcard 5: Choose the condition that must be met for a t-test.

Answer: Random sample or normal distribution. Ensures valid statistical inference assumptions.

Flashcard 6: Identify the degrees of freedom for a t-test.

Answer: $n - 1$. Sample size minus one for t-distribution.

Flashcard 7: What does a Type I error mean in hypothesis testing?

Answer: Rejecting $H_0$ when it is true. False positive error in statistical testing.

Flashcard 8: What is the relationship between confidence level and confidence interval width?

Answer: Higher confidence level results in wider interval. Trade-off between confidence and precision.

Flashcard 9: What is power in the context of hypothesis testing?

Answer: Probability of rejecting $H_0$ when it is false. Ability to detect true effects when they exist.

Flashcard 10: What is the sample mean ($\bar{x}$) used in hypothesis testing?

Answer: Average of sample data points. Central measure of sample location.

Flashcard 11: Which option is affected by the choice of $\alpha$?

Answer: Significance level and Type I error rate. Alpha determines probability thresholds for decisions.

Flashcard 12: What is the sample mean ($\bar{x}$) used in hypothesis testing?

Answer: Average of sample data points. Central measure of sample location.

Flashcard 13: What is the consequence of a Type II error?

Answer: Failing to detect a real effect. Missing a real effect that exists.

Flashcard 14: What is the impact of a small p-value?

Answer: Evidence against $H_0$. Low probability suggests null hypothesis is false.

Flashcard 15: What does a Type II error mean in hypothesis testing?

Answer: Failing to reject $H_0$ when it is false. False negative error in statistical testing.

Flashcard 16: What does $n$ represent in hypothesis testing?

Answer: Sample size. Number of observations in the sample.

Flashcard 17: What is the sample standard deviation ($s$)?

Answer: Measure of variation among sample data points. Estimates population standard deviation from sample.

Flashcard 18: What is the purpose of a hypothesis test for a population mean?

Answer: To determine if sample mean differs from population mean. Tests whether sample provides evidence of population difference.

Flashcard 19: What is the decision rule for rejecting $H_0$ using p-value?

Answer: Reject $H_0$ if p-value $< \alpha$. Standard decision criterion for hypothesis testing.

Flashcard 20: Which option is a benefit of a larger sample size?

Answer: More precise estimate of population mean. Reduced sampling error improves estimation accuracy.

Flashcard 21: What does a Type II error mean in hypothesis testing?

Answer: Failing to reject $H_0$ when it is false. False negative error in statistical testing.

Flashcard 22: What does the term 'statistically significant' imply?

Answer: Results unlikely due to chance at given $\alpha$. Unlikely to occur by random chance alone.

Flashcard 23: Calculate the test statistic: $\bar{x} = 98$, $\mu = 100$, $s = 5$, $n = 25$.

Answer: $t = -2$. Using $t = \frac{98-100}{5/\sqrt{25}} = \frac{-2}{1} = -2$.

Flashcard 24: Which option is a correct interpretation of a 95% confidence interval?

Answer: 95% of such intervals contain the population mean. Long-run interpretation of confidence level.

Flashcard 25: Identify the condition of normality for a t-test.

Answer: Population is normally distributed or $n > 30$. Ensures valid use of t-distribution for inference.

Flashcard 26: What is the consequence of a Type I error?

Answer: Falsely claiming a significant effect. Incorrectly rejecting a true null hypothesis.

Flashcard 27: What is the decision rule for rejecting $H_0$ using p-value?

Answer: Reject $H_0$ if p-value $< \alpha$. Standard decision criterion for hypothesis testing.

Flashcard 28: Identify the condition of normality for a t-test.

Answer: Population is normally distributed or $n > 30$. Ensures valid use of t-distribution for inference.

Flashcard 29: Which option defines the significance level ($\alpha$)?

Answer: Probability of rejecting $H_0$ when it is true. Controls Type I error rate in hypothesis testing.

Flashcard 30: What happens to the test statistic if the sample mean increases?

Answer: Test statistic increases. Larger difference from null increases test statistic.

Flashcard 31: Calculate the test statistic: $\bar{x} = 98$, $\mu = 100$, $s = 5$, $n = 25$.

Answer: $t = -2$. Using $t = \frac{98-100}{5/\sqrt{25}} = \frac{-2}{1} = -2$.

Flashcard 32: What is the critical region in hypothesis testing?

Answer: Range of values for which $H_0$ is rejected. Values where null hypothesis gets rejected.

Flashcard 33: What is the effect of increasing sample size on the confidence interval?

Answer: Narrower confidence interval. Larger sample reduces standard error.

Flashcard 34: What happens to the power of a test if $\alpha$ is increased?

Answer: Power increases. Higher alpha makes rejection easier.