should be used Determine the critical value(s) for this hypothesis test. Round the solution(s) to two decimal places. If more than one critical value exists, enter the solutions using a comma-separated list. Determine the test statistic. Round the solution to two decimal places. Determine the appropriate conclusion for this hypothesis test. O The sample data do not provide sufficient evidence to reject the null hypothesis that the propor of all dentists that recommend this brand of toothpaste is 0.9 and thus we conclude that the proportion of dentists that recommend this brand of toothpaste is likely equal to 0.9. O The sample data do not provide sufficient evidence to reject the alternative hypothesis that the proportion of dentists who recommend this brand of toothpaste is significantly different than 0. thus we conclude that the proportion of all dentists that recommend this brand of toothpaste is likely different than 0.9. O The sample data provide sufficient evidence to reject the null hypothesis that the proportion o dentists that recommend this brand of toothpaste is 0.9 and thus we conclude that the proporti dentists that recommend this brand of toothpaste is not equal to 0.9. O The sample data provide sufficient evidence to reject the alternative hypothesis that the propo of dentists who recommend this brand of toothpaste is significantly different than 0.9 and thus conclude that the proportion of all dentists that recommend this brand of toothpaste is likely e to 0.9. 74°F O

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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Transcribed Image Text:### Hypothesis Testing Steps #### Step 1: Identify the Distribution The student's t-distribution should be used. #### Step 2: Determine the Critical Value(s) Determine the critical value(s) for this hypothesis test. Round the solution(s) to two decimal places. If more than one critical value exists, enter the solutions using a comma-separated list. ``` [Text box for critical values] ``` #### Step 3: Calculate the Test Statistic Determine the test statistic. Round the solution to two decimal places. ``` [Text box for test statistic] ``` #### Step 4: Conclusion Determine the appropriate conclusion for this hypothesis test. Four options are presented: 1. **Option 1:** - The sample data do not provide sufficient evidence to reject the null hypothesis that the proportion of all dentists that recommend this brand of toothpaste is 0.9 and thus we conclude that the proportion of dentists that recommend this brand of toothpaste is likely equal to 0.9. 2. **Option 2:** - The sample data do not provide sufficient evidence to reject the alternative hypothesis that the proportion of dentists who recommend this brand of toothpaste is significantly different than 0.9 and thus we conclude that the proportion of all dentists that recommend this brand of toothpaste is likely different than 0.9. 3. **Option 3:** - The sample data provide sufficient evidence to reject the null hypothesis that the proportion of all dentists that recommend this brand of toothpaste is 0.9 and thus we conclude that the proportion of dentists that recommend this brand of toothpaste is not equal to 0.9. 4. **Option 4:** - The sample data provide sufficient evidence to reject the alternative hypothesis that the proportion of dentists who recommend this brand of toothpaste is significantly different than 0.9 and thus we conclude that the proportion of all dentists that recommend this brand of toothpaste is likely equal to 0.9. ### Example Graph or Diagram Explanation There are no graphs or diagrams present in the image. The content consists entirely of textual information for a statistical hypothesis testing problem. ### Additional Notes Please make sure to input your computed values in the provided text boxes for critical values and test statistic. Choose the correct conclusion based on your hypothesis test results by selecting one of the provided options.

$### Nine out of Ten Dentists Recommend This Toothpaste! You have certainly heard the above claim before. Advertisers frequently claim that some percentage of doctors or dentists recommend a given health product. It's best to take such claims with a large grain of salt. Suppose a recent advertisement claims that 9 out of 10 dentists (90%) recommend a certain brand of toothpaste. A consumer advocacy group is highly suspicious of this claim and randomly surveys 224 dentists. They find that 95.1% of the sample recommends the given brand of toothpaste. Using a significance level of 2.5%, test the hypothesis that the proportion of all dentists who recommend this brand of toothpaste is different than 90%. State the null and alternative hypotheses for this test. **Null Hypothesis (H₀):** \[ H_0: \] **Alternative Hypothesis (H₁):** \[ H_1: \] Determine if this test is left-tailed, right-tailed, or two-tailed. - left-tailed - right-tailed - two-tailed Should the standard normal (z) distribution or Student's (t) distribution be used for this test? - The standard normal (z) distribution should be used - The Student's t distribution should be used Determine the critical value(s) for this hypothesis test. Round the solution(s) to two decimal places. If more than one critical value exists, enter the solutions using a comma-separated list. (Inputs for critical values)$

Transcribed Image Text:### Nine out of Ten Dentists Recommend This Toothpaste! You have certainly heard the above claim before. Advertisers frequently claim that some percentage of doctors or dentists recommend a given health product. It's best to take such claims with a large grain of salt. Suppose a recent advertisement claims that 9 out of 10 dentists (90%) recommend a certain brand of toothpaste. A consumer advocacy group is highly suspicious of this claim and randomly surveys 224 dentists. They find that 95.1% of the sample recommends the given brand of toothpaste. Using a significance level of 2.5%, test the hypothesis that the proportion of all dentists who recommend this brand of toothpaste is different than 90%. State the null and alternative hypotheses for this test. **Null Hypothesis (H₀):** \[ H_0: \] **Alternative Hypothesis (H₁):** \[ H_1: \] Determine if this test is left-tailed, right-tailed, or two-tailed. - left-tailed - right-tailed - two-tailed Should the standard normal (z) distribution or Student's (t) distribution be used for this test? - The standard normal (z) distribution should be used - The Student's t distribution should be used Determine the critical value(s) for this hypothesis test. Round the solution(s) to two decimal places. If more than one critical value exists, enter the solutions using a comma-separated list. (Inputs for critical values)

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