MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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16. 

### Watch Corporation of Switzerland: Time Accuracy Analysis **Question:** Watch Corporation of Switzerland claims that its watches on average will neither gain nor lose time during a week. A sample of 18 watches provided the following gains (+) or losses (−) in seconds per week. **Data:** A downloadable Excel file is available [here](#) for detailed analysis. **Sample Gains or Losses (in seconds per week):** ``` -0.44, -0.24, -0.32, -0.30, +0.41, -0.28, +0.48, +0.24, -0.13, -0.28, -0.62, -0.45, -0.49, -0.57, -0.07, -0.20, -0.53, +0.06 ``` **Hypothesis Testing:** (a) **State the null hypothesis and the alternate hypothesis.** | Hypothesis | Symbolic Representation | |------------|-------------------------| | H0: | μ = 0 | | H1: | μ ≠ 0 | (b) **State the decision rule for 0.01 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)** ``` At a level of 0.01 significance, we reject H0: μ = 0 if t < _____ or t > _____ . ``` (Note: The specific critical values need to be calculated based on the t-distribution table for the given sample size and significance level.) In summary, this analysis involves testing the claim by calculating the sample mean and standard deviation, followed by performing a t-test and comparing the results against the critical values determined for a 1% significance level. This enables us to statistically verify if the watches on average indeed have no significant gain or loss in time as claimed by the Watch Corporation of Switzerland.
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Transcribed Image Text:### Watch Corporation of Switzerland: Time Accuracy Analysis **Question:** Watch Corporation of Switzerland claims that its watches on average will neither gain nor lose time during a week. A sample of 18 watches provided the following gains (+) or losses (−) in seconds per week. **Data:** A downloadable Excel file is available [here](#) for detailed analysis. **Sample Gains or Losses (in seconds per week):** ``` -0.44, -0.24, -0.32, -0.30, +0.41, -0.28, +0.48, +0.24, -0.13, -0.28, -0.62, -0.45, -0.49, -0.57, -0.07, -0.20, -0.53, +0.06 ``` **Hypothesis Testing:** (a) **State the null hypothesis and the alternate hypothesis.** | Hypothesis | Symbolic Representation | |------------|-------------------------| | H0: | μ = 0 | | H1: | μ ≠ 0 | (b) **State the decision rule for 0.01 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)** ``` At a level of 0.01 significance, we reject H0: μ = 0 if t < _____ or t > _____ . ``` (Note: The specific critical values need to be calculated based on the t-distribution table for the given sample size and significance level.) In summary, this analysis involves testing the claim by calculating the sample mean and standard deviation, followed by performing a t-test and comparing the results against the critical values determined for a 1% significance level. This enables us to statistically verify if the watches on average indeed have no significant gain or loss in time as claimed by the Watch Corporation of Switzerland.
### Hypothesis Testing: Mean Gain or Loss in Time for Watches #### Step 1: Calculate the Value of the Test Statistic *Input the computed value based on your sample data into the space provided.* ``` Value of the test statistic: [________] ``` #### Step 2: Interpret the Null Hypothesis The null hypothesis (\(H_0\)) for this test is that there is no mean gain or loss in time for the watches, meaning the mean gain or loss is equal to zero. - The question: "Is it reasonable to conclude that the mean gain or loss in time for the watches is 0? Use the 0.01 significance level." ``` Ho. It [________] reasonable to conclude that the mean gain or loss in time for the watches is 0. ``` Options could be 'is' or 'is not' reasonable based on the test statistic and p-value. #### Step 3: Estimate the p-Value *Estimate the p-value based on the test statistic and determine whether it is significant at the 0.01 significance level.* ``` Estimate the p-value. ``` ### Explanation of Graphs or Diagrams There are no graphs or diagrams in this segment of text. The focus is on inputting numerical values and interpreting the hypothesis test results. Additional steps typically involve calculating the test statistic, comparing it to critical values from a statistical table, and estimating the p-value to reach a conclusion about the null hypothesis.
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Transcribed Image Text:### Hypothesis Testing: Mean Gain or Loss in Time for Watches #### Step 1: Calculate the Value of the Test Statistic *Input the computed value based on your sample data into the space provided.* ``` Value of the test statistic: [________] ``` #### Step 2: Interpret the Null Hypothesis The null hypothesis (\(H_0\)) for this test is that there is no mean gain or loss in time for the watches, meaning the mean gain or loss is equal to zero. - The question: "Is it reasonable to conclude that the mean gain or loss in time for the watches is 0? Use the 0.01 significance level." ``` Ho. It [________] reasonable to conclude that the mean gain or loss in time for the watches is 0. ``` Options could be 'is' or 'is not' reasonable based on the test statistic and p-value. #### Step 3: Estimate the p-Value *Estimate the p-value based on the test statistic and determine whether it is significant at the 0.01 significance level.* ``` Estimate the p-value. ``` ### Explanation of Graphs or Diagrams There are no graphs or diagrams in this segment of text. The focus is on inputting numerical values and interpreting the hypothesis test results. Additional steps typically involve calculating the test statistic, comparing it to critical values from a statistical table, and estimating the p-value to reach a conclusion about the null hypothesis.
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