The article "Effects of Bottle Closure Type on Consumer Perception of Wine Quality"+ reported that in a sample of 106 wine consumers, 22 thought that screw tops were an acceptable substitute for natural corks. Suppose a particular winery decided to use screw tops for one of its wines unless there was strong evidence to suggest that fewer than 23% of wine consumers found this acceptable. LAUSE SALT (a) Using a significance level of 0.10, what would you recommend to the winery? State the appropriate null and alternative hypotheses. Ho: P < 0.23 H: P = 0.23 Ho: P = 0.23 H: P = 0.23 Ho:p> 0.23 H: P = 0.23 O Ho: P = 0.23 H₂: P < 0.23 Ho: P = 0.23 H:p> 0.23 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) x X Z= P-value = State the conclusion in the problem context. Reject the null hypothesis. There is not sufficient evidence to suggest that less than 23% of all customers find screw tops acceptable. Reject the null hypothesis. There is sufficient evidence to suggest that less than 23% of all customers find screw tops acceptable. Do not reject the null hypothesis. There is sufficient evidence to suggest that less than 23% of all customers find screw tops acceptable. O Do not reject the null hypothesis. There is not sufficient evidence to suggest that less than 23% of all customers find screw tops acceptable.
The article "Effects of Bottle Closure Type on Consumer Perception of Wine Quality"+ reported that in a sample of 106 wine consumers, 22 thought that screw tops were an acceptable substitute for natural corks. Suppose a particular winery decided to use screw tops for one of its wines unless there was strong evidence to suggest that fewer than 23% of wine consumers found this acceptable. LAUSE SALT (a) Using a significance level of 0.10, what would you recommend to the winery? State the appropriate null and alternative hypotheses. Ho: P < 0.23 H: P = 0.23 Ho: P = 0.23 H: P = 0.23 Ho:p> 0.23 H: P = 0.23 O Ho: P = 0.23 H₂: P < 0.23 Ho: P = 0.23 H:p> 0.23 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) x X Z= P-value = State the conclusion in the problem context. Reject the null hypothesis. There is not sufficient evidence to suggest that less than 23% of all customers find screw tops acceptable. Reject the null hypothesis. There is sufficient evidence to suggest that less than 23% of all customers find screw tops acceptable. Do not reject the null hypothesis. There is sufficient evidence to suggest that less than 23% of all customers find screw tops acceptable. O Do not reject the null hypothesis. There is not sufficient evidence to suggest that less than 23% of all customers find screw tops acceptable.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text:**Title: Statistical Analysis on Consumer Acceptance of Screw Tops for Wine Bottles**
**Introduction:**
The study examines the consumer perception of screw tops as wine bottle closures. Based on a sample of 106 wine consumers, 22 accepted screw tops as a suitable alternative to natural corks. The winery is considering using screw tops if fewer than 23% find them unacceptable, using a significance level of 0.10.
**Hypothesis Testing:**
- **Null Hypothesis (\(H_0\))**: \(p = 0.23\) (23% of consumers accept screw tops)
- **Alternative Hypothesis (\(H_a\))**: \(p < 0.23\) (Fewer than 23% accept screw tops)
**Calculations:**
- Calculate the test statistic \(z\) and determine the \(P\)-value (round \(z\) to two decimal places and \(P\)-value to four decimal places). The calculation attempts here are incorrect, as indicated.
**Conclusion:**
- **Decision**: Do not reject the null hypothesis.
- **Reasoning**: There isn't sufficient evidence to suggest fewer than 23% of customers find screw tops acceptable.
This analysis suggests the winery should not conclude that fewer than 23% of customers find screw tops acceptable based on the data provided. Further research and data gathering may be necessary for a conclusive decision.
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