Identifying Hypotheses In a randomized clinical trial of adults with an acute sore throat, 288 were treated with the drug dexamethasone and 102 of them experienced complete resolution; 277 were treated with a placebo and 75 of them experienced complete resolution (based on data from “Effect of Oral Dexamethasone Without Immediate Antibiotics vs Placebo on Acute Sore Throat in Adults,” by Hayward et al., Journal of the American Medical Association). Identify the null and alternative hypotheses corresponding to the claim that patients treated with dexamethasone and patients given a placebo have the same rate of complete resolution.
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- 1. Intro to Stats and Collecting Data1h 14m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically2h 5m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables3h 6m
- 6. Normal Distribution and Continuous Random Variables2h 11m
- 7. Sampling Distributions & Confidence Intervals: Mean3h 23m
- Sampling Distribution of the Sample Mean and Central Limit Theorem19m
- Distribution of Sample Mean - Excel23m
- Introduction to Confidence Intervals15m
- Confidence Intervals for Population Mean1h 18m
- Determining the Minimum Sample Size Required12m
- Finding Probabilities and T Critical Values - Excel28m
- Confidence Intervals for Population Means - Excel25m
- 8. Sampling Distributions & Confidence Intervals: Proportion2h 10m
- 9. Hypothesis Testing for One Sample5h 8m
- Steps in Hypothesis Testing1h 6m
- Performing Hypothesis Tests: Means1h 4m
- Hypothesis Testing: Means - Excel42m
- Performing Hypothesis Tests: Proportions37m
- Hypothesis Testing: Proportions - Excel27m
- Performing Hypothesis Tests: Variance12m
- Critical Values and Rejection Regions28m
- Link Between Confidence Intervals and Hypothesis Testing12m
- Type I & Type II Errors16m
- 10. Hypothesis Testing for Two Samples5h 37m
- Two Proportions1h 13m
- Two Proportions Hypothesis Test - Excel28m
- Two Means - Unknown, Unequal Variance1h 3m
- Two Means - Unknown Variances Hypothesis Test - Excel12m
- Two Means - Unknown, Equal Variance15m
- Two Means - Unknown, Equal Variances Hypothesis Test - Excel9m
- Two Means - Known Variance12m
- Two Means - Sigma Known Hypothesis Test - Excel21m
- Two Means - Matched Pairs (Dependent Samples)42m
- Matched Pairs Hypothesis Test - Excel12m
- Two Variances and F Distribution29m
- Two Variances - Graphing Calculator16m
- 11. Correlation1h 24m
- 12. Regression3h 33m
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- Residuals12m
- Coefficient of Determination12m
- Regression Line Equation and Coefficient of Determination - Excel8m
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- Inferences for Slope31m
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- Regression Readout of the Data Analysis Toolpak - Excel21m
- Prediction Intervals13m
- Prediction Intervals - Excel19m
- Multiple Regression - Excel29m
- Quadratic Regression15m
- Quadratic Regression - Excel10m
- 13. Chi-Square Tests & Goodness of Fit2h 21m
- 14. ANOVA2h 28m
9. Hypothesis Testing for One Sample
Steps in Hypothesis Testing
Problem 11.2.4
Textbook Question
Right-Tailed, Left-Tailed, Two-Tailed Is the hypothesis test described in Exercise 1 right-tailed, left-tailed, or two-tailed? Explain your choice.
Verified step by step guidance1
Understand the context of the hypothesis test: Determine whether the problem involves testing if a parameter is greater than, less than, or simply different from a specific value. This will guide the choice of tail direction.
Recall the definitions of the types of hypothesis tests: A right-tailed test is used when the alternative hypothesis (H₁) states that the parameter is greater than a specific value. A left-tailed test is used when H₁ states that the parameter is less than a specific value. A two-tailed test is used when H₁ states that the parameter is not equal to a specific value.
Examine the alternative hypothesis (H₁): Identify the inequality sign in H₁. If it uses '>', it is a right-tailed test. If it uses '<', it is a left-tailed test. If it uses '≠', it is a two-tailed test.
Consider the research question or claim being tested: The direction of the test depends on whether the claim is about an increase, a decrease, or simply a difference in the parameter being studied.
Conclude the type of test: Based on the inequality in H₁ and the context of the problem, classify the test as right-tailed, left-tailed, or two-tailed, and explain your reasoning clearly.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Hypothesis Testing
Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (H1), then using sample data to determine whether to reject H0 in favor of H1. The outcome helps in understanding if there is enough evidence to support a specific claim about the population.
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Step 1: Write Hypotheses
One-Tailed vs. Two-Tailed Tests
In hypothesis testing, a one-tailed test evaluates the possibility of the relationship in one direction (either greater than or less than), while a two-tailed test assesses both directions. A right-tailed test looks for evidence that a parameter is greater than a certain value, whereas a left-tailed test checks if it is less. The choice between these tests depends on the research question and the nature of the hypothesis.
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Difference in Proportions: Hypothesis Tests
Critical Region
The critical region in hypothesis testing is the set of all values of the test statistic that would lead to the rejection of the null hypothesis. For a right-tailed test, this region is located in the upper tail of the distribution, while for a left-tailed test, it is in the lower tail. In a two-tailed test, the critical regions are found in both tails, reflecting the possibility of extreme values in either direction.
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