Carrying Out Test for Population Mean - AP Statistics
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What is the consequence of a Type II error?
What is the consequence of a Type II error?
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Failing to detect a real effect. Missing a real effect that exists.
Failing to detect a real effect. Missing a real effect that exists.
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What is the impact of a small p-value?
What is the impact of a small p-value?
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Evidence against $H_0$. Low probability suggests null hypothesis is false.
Evidence against $H_0$. Low probability suggests null hypothesis is false.
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What happens to the power of a test if $\alpha$ is increased?
What happens to the power of a test if $\alpha$ is increased?
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Power increases. Higher alpha makes rejection easier.
Power increases. Higher alpha makes rejection easier.
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What is the effect of increasing sample size on the confidence interval?
What is the effect of increasing sample size on the confidence interval?
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Narrower confidence interval. Larger sample reduces standard error.
Narrower confidence interval. Larger sample reduces standard error.
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Choose the condition that must be met for a t-test.
Choose the condition that must be met for a t-test.
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Random sample or normal distribution. Ensures valid statistical inference assumptions.
Random sample or normal distribution. Ensures valid statistical inference assumptions.
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Calculate the test statistic: $\bar{x} = 98$, $\mu = 100$, $s = 5$, $n = 25$.
Calculate the test statistic: $\bar{x} = 98$, $\mu = 100$, $s = 5$, $n = 25$.
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$t = -2$. Using $t = \frac{98-100}{5/\sqrt{25}} = \frac{-2}{1} = -2$.
$t = -2$. Using $t = \frac{98-100}{5/\sqrt{25}} = \frac{-2}{1} = -2$.
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What does $n$ represent in hypothesis testing?
What does $n$ represent in hypothesis testing?
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Sample size. Number of observations in the sample.
Sample size. Number of observations in the sample.
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Which option is a correct interpretation of a 95% confidence interval?
Which option is a correct interpretation of a 95% confidence interval?
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95% of such intervals contain the population mean. Long-run interpretation of confidence level.
95% of such intervals contain the population mean. Long-run interpretation of confidence level.
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What is power in the context of hypothesis testing?
What is power in the context of hypothesis testing?
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Probability of rejecting $H_0$ when it is false. Ability to detect true effects when they exist.
Probability of rejecting $H_0$ when it is false. Ability to detect true effects when they exist.
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What does a Type II error mean in hypothesis testing?
What does a Type II error mean in hypothesis testing?
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Failing to reject $H_0$ when it is false. False negative error in statistical testing.
Failing to reject $H_0$ when it is false. False negative error in statistical testing.
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What does a Type I error mean in hypothesis testing?
What does a Type I error mean in hypothesis testing?
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Rejecting $H_0$ when it is true. False positive error in statistical testing.
Rejecting $H_0$ when it is true. False positive error in statistical testing.
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What is the sample standard deviation ($s$)?
What is the sample standard deviation ($s$)?
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Measure of variation among sample data points. Estimates population standard deviation from sample.
Measure of variation among sample data points. Estimates population standard deviation from sample.
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What is the sample mean ($\bar{x}$) used in hypothesis testing?
What is the sample mean ($\bar{x}$) used in hypothesis testing?
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Average of sample data points. Central measure of sample location.
Average of sample data points. Central measure of sample location.
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Identify the condition of normality for a t-test.
Identify the condition of normality for a t-test.
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Population is normally distributed or $n > 30$. Ensures valid use of t-distribution for inference.
Population is normally distributed or $n > 30$. Ensures valid use of t-distribution for inference.
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What is the decision rule for rejecting $H_0$ using p-value?
What is the decision rule for rejecting $H_0$ using p-value?
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Reject $H_0$ if p-value $< \alpha$. Standard decision criterion for hypothesis testing.
Reject $H_0$ if p-value $< \alpha$. Standard decision criterion for hypothesis testing.
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Which option defines the significance level ($\alpha$)?
Which option defines the significance level ($\alpha$)?
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Probability of rejecting $H_0$ when it is true. Controls Type I error rate in hypothesis testing.
Probability of rejecting $H_0$ when it is true. Controls Type I error rate in hypothesis testing.
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What is the critical value approach?
What is the critical value approach?
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Compare test statistic to critical value to decide on $H_0$. Uses predetermined threshold to make statistical decision.
Compare test statistic to critical value to decide on $H_0$. Uses predetermined threshold to make statistical decision.
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What is the consequence of a Type I error?
What is the consequence of a Type I error?
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Falsely claiming a significant effect. Incorrectly rejecting a true null hypothesis.
Falsely claiming a significant effect. Incorrectly rejecting a true null hypothesis.
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Which option is affected by the choice of $\alpha$?
Which option is affected by the choice of $\alpha$?
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Significance level and Type I error rate. Alpha determines probability thresholds for decisions.
Significance level and Type I error rate. Alpha determines probability thresholds for decisions.
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Which option is a requirement for the Central Limit Theorem?
Which option is a requirement for the Central Limit Theorem?
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Sample size $n$ is sufficiently large. Enables normal approximation for sampling distribution.
Sample size $n$ is sufficiently large. Enables normal approximation for sampling distribution.
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What is the critical region in hypothesis testing?
What is the critical region in hypothesis testing?
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Range of values for which $H_0$ is rejected. Values where null hypothesis gets rejected.
Range of values for which $H_0$ is rejected. Values where null hypothesis gets rejected.
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What is the relationship between confidence level and confidence interval width?
What is the relationship between confidence level and confidence interval width?
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Higher confidence level results in wider interval. Trade-off between confidence and precision.
Higher confidence level results in wider interval. Trade-off between confidence and precision.
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What is the role of the alternative hypothesis ($H_a$)?
What is the role of the alternative hypothesis ($H_a$)?
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Proposes the opposite of the null hypothesis. Represents researcher's theory to be supported.
Proposes the opposite of the null hypothesis. Represents researcher's theory to be supported.
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Identify the degrees of freedom for a t-test.
Identify the degrees of freedom for a t-test.
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$n - 1$. Sample size minus one for t-distribution.
$n - 1$. Sample size minus one for t-distribution.
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What does the term 'statistically significant' imply?
What does the term 'statistically significant' imply?
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Results unlikely due to chance at given $\alpha$. Unlikely to occur by random chance alone.
Results unlikely due to chance at given $\alpha$. Unlikely to occur by random chance alone.
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What happens to the test statistic if the sample mean increases?
What happens to the test statistic if the sample mean increases?
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Test statistic increases. Larger difference from null increases test statistic.
Test statistic increases. Larger difference from null increases test statistic.
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Which option is a benefit of a larger sample size?
Which option is a benefit of a larger sample size?
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More precise estimate of population mean. Reduced sampling error improves estimation accuracy.
More precise estimate of population mean. Reduced sampling error improves estimation accuracy.
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What is the decision rule for rejecting $H_0$ using p-value?
What is the decision rule for rejecting $H_0$ using p-value?
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Reject $H_0$ if p-value $< \alpha$. Standard decision criterion for hypothesis testing.
Reject $H_0$ if p-value $< \alpha$. Standard decision criterion for hypothesis testing.
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Calculate the test statistic: $\bar{x} = 98$, $\mu = 100$, $s = 5$, $n = 25$.
Calculate the test statistic: $\bar{x} = 98$, $\mu = 100$, $s = 5$, $n = 25$.
Tap to reveal answer
$t = -2$. Using $t = \frac{98-100}{5/\sqrt{25}} = \frac{-2}{1} = -2$.
$t = -2$. Using $t = \frac{98-100}{5/\sqrt{25}} = \frac{-2}{1} = -2$.
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What is the sample mean ($\bar{x}$) used in hypothesis testing?
What is the sample mean ($\bar{x}$) used in hypothesis testing?
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Average of sample data points. Central measure of sample location.
Average of sample data points. Central measure of sample location.
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