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A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The image shows an educational question about hypothesis testing in statistics, focusing on a golf analyst's claim regarding the standard deviation of 18-hole scores for a golfer. The task is to state the null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_a\)) in words and symbols, and to determine the type of hypothesis test (left-tailed, right-tailed, or two-tailed). Options for the null hypothesis (\(H_0\)): - **A.** "The standard deviation of the 18-hole scores for a golfer is at most 3.6 strokes." Symbolically: \(H_0: \sigma \leq 3.6\) - **B.** "The standard deviation of the 18-hole scores for a golfer is at least 3.6 strokes." Symbolically: \(H_0: \sigma \geq 3.6\) - **C.** "The standard deviation of the 18-hole scores for a golfer is not 3.6 strokes." Symbolically: \(H_0: \sigma \neq 3.6\) - **D.** "The standard deviation of the 18-hole scores for a golfer is less than 3.6 strokes." Symbolically: \(H_0: \sigma < 3.6\) Options for the alternative hypothesis (\(H_a\)): - **A.** "The standard deviation of the 18-hole scores for a golfer is 3.6 strokes." (Note: The remaining text is not visible in the image, but the choice implies something contrary to the null hypotheses stated.) The task involves selecting the correct hypotheses and explaining the reasoning, including whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
Transcribed Image Text:The image shows an educational question about hypothesis testing in statistics, focusing on a golf analyst's claim regarding the standard deviation of 18-hole scores for a golfer. The task is to state the null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_a\)) in words and symbols, and to determine the type of hypothesis test (left-tailed, right-tailed, or two-tailed). Options for the null hypothesis (\(H_0\)): - **A.** "The standard deviation of the 18-hole scores for a golfer is at most 3.6 strokes." Symbolically: \(H_0: \sigma \leq 3.6\) - **B.** "The standard deviation of the 18-hole scores for a golfer is at least 3.6 strokes." Symbolically: \(H_0: \sigma \geq 3.6\) - **C.** "The standard deviation of the 18-hole scores for a golfer is not 3.6 strokes." Symbolically: \(H_0: \sigma \neq 3.6\) - **D.** "The standard deviation of the 18-hole scores for a golfer is less than 3.6 strokes." Symbolically: \(H_0: \sigma < 3.6\) Options for the alternative hypothesis (\(H_a\)): - **A.** "The standard deviation of the 18-hole scores for a golfer is 3.6 strokes." (Note: The remaining text is not visible in the image, but the choice implies something contrary to the null hypotheses stated.) The task involves selecting the correct hypotheses and explaining the reasoning, including whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
A golf analyst claims that the standard deviation of the 18-hole scores for a golfer is less than 3.6 strokes. State \( H_0 \) and \( H_a \) in words and in symbols. Then determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed. Explain your reasoning. **Null Hypothesis (\( H_0 \)):** - **In words:** The standard deviation of the 18-hole scores for a golfer is 3.6 strokes. - **In symbols:** \( H_0: \sigma = 3.6 \) **Alternative Hypothesis (\( H_a \)):** - **Option A:** - **In words:** The standard deviation of the 18-hole scores for a golfer is 3.6 strokes. - **In symbols:** \( H_a: \sigma = 3.6 \) - **Option B:** - **In words:** The standard deviation of the 18-hole scores for a golfer is more than 3.6 strokes. - **In symbols:** \( H_a: \sigma > 3.6 \) - **Option C:** - **In words:** The standard deviation of the 18-hole scores for a golfer is not 3.6 strokes. - **In symbols:** \( H_a: \sigma \neq 3.6 \) - **Option D:** - **In words:** The standard deviation of the 18-hole scores for a golfer is less than 3.6 strokes. - **In symbols:** \( H_a: \sigma < 3.6 \) **Conclusion:** The hypothesis test is **left-tailed** because the **alternative hypothesis** contains \( < \). This setup helps determine if the standard deviation of golfers' scores is statistically significantly less than 3.6 strokes, indicating that scores are more consistent than previously thought.
Transcribed Image Text:A golf analyst claims that the standard deviation of the 18-hole scores for a golfer is less than 3.6 strokes. State \( H_0 \) and \( H_a \) in words and in symbols. Then determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed. Explain your reasoning. **Null Hypothesis (\( H_0 \)):** - **In words:** The standard deviation of the 18-hole scores for a golfer is 3.6 strokes. - **In symbols:** \( H_0: \sigma = 3.6 \) **Alternative Hypothesis (\( H_a \)):** - **Option A:** - **In words:** The standard deviation of the 18-hole scores for a golfer is 3.6 strokes. - **In symbols:** \( H_a: \sigma = 3.6 \) - **Option B:** - **In words:** The standard deviation of the 18-hole scores for a golfer is more than 3.6 strokes. - **In symbols:** \( H_a: \sigma > 3.6 \) - **Option C:** - **In words:** The standard deviation of the 18-hole scores for a golfer is not 3.6 strokes. - **In symbols:** \( H_a: \sigma \neq 3.6 \) - **Option D:** - **In words:** The standard deviation of the 18-hole scores for a golfer is less than 3.6 strokes. - **In symbols:** \( H_a: \sigma < 3.6 \) **Conclusion:** The hypothesis test is **left-tailed** because the **alternative hypothesis** contains \( < \). This setup helps determine if the standard deviation of golfers' scores is statistically significantly less than 3.6 strokes, indicating that scores are more consistent than previously thought.
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