Steps in Hypothesis Testing quiz #1 Flashcards
Steps in Hypothesis Testing quiz #1
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What is defined by the significance level (alpha) in a hypothesis test? The significance level (alpha) defines the threshold for how unusual a sample must be before rejecting the null hypothesis; it is the probability of rejecting the null hypothesis when it is actually true. Which of the following is not a criterion for making a decision in a hypothesis test? Making a decision in a hypothesis test does not involve personal judgment; it is based on comparing the p-value to the significance level (alpha). What are the assumptions for conducting a significance test for a proportion? Assumptions for a significance test for a proportion include random sampling and a sufficiently large sample size so that the sampling distribution of the proportion is approximately normal. What is the general formula for the test statistic used in a test of paired samples? The test statistic for paired samples is typically t = (mean of differences) / (standard deviation of differences / sqrt(n)), where n is the number of pairs. If you conduct a hypothesis test and your p-value is 0.08, what can you conclude? If the p-value is 0.08, you fail to reject the null hypothesis at the 0.05 significance level, as the p-value is greater than alpha. What is not true when testing a claim about a proportion? It is not true that the null hypothesis for a proportion uses a 'not equal to' sign; the null hypothesis always uses an equal sign. Which of the following is not a criterion for making a decision in a hypothesis test? Decisions in hypothesis testing are not based on intuition; they are based on the comparison of the p-value to the significance level. What is not true about p-values in hypothesis testing? It is not true that a high p-value provides strong evidence against the null hypothesis; a high p-value indicates the sample is not unusual under the null hypothesis. When is it appropriate to use the paired difference t-test? The paired difference t-test is appropriate when comparing two related samples, such as measurements taken before and after a treatment on the same subjects. What is the level of significance in a hypothesis test? The level of significance (alpha) is a predetermined threshold that determines how unlikely a sample result must be before rejecting the null hypothesis. What assumptions are required to use the two-sample test of means? Assumptions for the two-sample test of means include independent random samples from each population and that the sampling distributions of the means are approximately normal. What are the two possible decisions you can make when performing a hypothesis test? The two possible decisions are to reject the null hypothesis or to fail to reject the null hypothesis. How would you accurately describe a hypothesis test? A hypothesis test is a statistical procedure used to evaluate a claim about a population parameter using sample data. Which statements about Type I error are correct? A Type I error occurs when the null hypothesis is rejected when it is actually true; its probability is equal to the significance level (alpha). What are the two types of hypotheses used in a hypothesis test and how are they related? The two types are the null hypothesis (H0), which states a claim about a population parameter, and the alternative hypothesis (Ha), which challenges that claim; they are mutually exclusive. How do you write a null hypothesis of the form μ ≤ 7 and an alternative hypothesis of μ > 7? The null hypothesis is H0: μ ≤ 7, and the alternative hypothesis is Ha: μ > 7; this setup is used for a right-tailed test. What is not true when testing a claim about a standard deviation or variance? It is not true that the null hypothesis for variance uses a 'not equal to' sign; the null hypothesis always uses an equal sign. How do you determine the direction of a hypothesis test based on the null hypothesis H0: μ ≤ 16.9? A null hypothesis of H0: μ ≤ 16.9 with an alternative of μ > 16.9 indicates a right-tailed test. What does a test statistic value of 2.23 indicate in a hypothesis test? A test statistic of 2.23 suggests the sample mean is 2.23 standard deviations above the hypothesized mean; the p-value can be calculated accordingly to determine significance. How do you determine the direction of a hypothesis test based on the null hypothesis H0: x ≤ 10.7? A null hypothesis of H0: x ≤ 10.7 with an alternative of x > 10.7 indicates a right-tailed test. What is a correct statement comparing one-tailed and two-tailed hypothesis tests? A one-tailed test evaluates deviations in one direction from the null hypothesis, while a two-tailed test evaluates deviations in both directions. Which form of alternative hypothesis makes a hypothesis test two-tailed? An alternative hypothesis of the form Ha: parameter ≠ value makes the test two-tailed. How do you write a null hypothesis p ≥ 0.44 and an alternative hypothesis p < 0.44? The null hypothesis is H0: p ≥ 0.44, and the alternative hypothesis is Ha: p < 0.44; this setup is used for a left-tailed test. Which of the following is not one of the six steps in the hypothesis testing procedure? Personal opinion is not a step in the hypothesis testing procedure; the steps are systematic and based on statistical rules. What does a test statistic value of 1.77 indicate in a hypothesis test? A test statistic of 1.77 means the sample mean is 1.77 standard deviations above the hypothesized mean; the p-value can be calculated to assess significance. How is the null hypothesis of the independent-samples t-test verbalized? The null hypothesis for the independent-samples t-test states that the means of the two populations are equal. Which statement is consistent with making a Type I error? A Type I error occurs when you reject the null hypothesis even though it is actually true. What does a test statistic value of 1.41 indicate in a hypothesis test? A test statistic of 1.41 means the sample mean is 1.41 standard deviations above the hypothesized mean; the p-value can be calculated to determine significance. Which types of hypothesis tests are considered one-tailed? Tests with alternative hypotheses of the form Ha: parameter > value or Ha: parameter < value are one-tailed. What is an accurate definition of a Type I error? A Type I error is rejecting the null hypothesis when it is actually true. What does a test statistic value of -2.12 indicate in a hypothesis test? A test statistic of -2.12 means the sample mean is 2.12 standard deviations below the hypothesized mean; the p-value can be calculated to assess significance. How do you write a null hypothesis μ ≥ 38 and an alternative hypothesis μ < 38? The null hypothesis is H0: μ ≥ 38, and the alternative hypothesis is Ha: μ < 38; this setup is used for a left-tailed test. What does a test statistic value of 1.34 indicate in a hypothesis test? A test statistic of 1.34 means the sample mean is 1.34 standard deviations above the hypothesized mean; the p-value can be calculated to determine significance. If you conduct a hypothesis test and your p-value is 0.002, what can you conclude? If the p-value is 0.002, you reject the null hypothesis at common significance levels (such as 0.05 or 0.01), as the p-value is very small. What situation involves testing a claim about a single population proportion? Testing whether the proportion of a population with a certain characteristic equals a specified value involves a single population proportion. What is a valid one-sample hypothesis test? A valid one-sample hypothesis test compares a sample statistic (such as mean or proportion) to a claimed population value using a null and alternative hypothesis. Which symbol represents a test statistic used to test a hypothesis about a population mean? The test statistic for a population mean is typically represented by z (if population standard deviation is known) or t (if it is unknown). What would be an appropriate null hypothesis in hypothesis testing? An appropriate null hypothesis states that a population parameter equals a specific value, such as H0: μ = value or H0: p = value. If testing H0: p = 0.20 vs Ha: p < 0.20 and the test statistic is -2.34, how do you find the p-value? The p-value is the probability of observing a test statistic less than -2.34 under the null hypothesis; it can be found using the standard normal distribution. Which statement is consistent with hypothesis testing? Hypothesis testing involves using sample data to evaluate a claim about a population parameter by comparing the p-value to the significance level.