The iron rod is supposed to have conductivity 10.1.
Do the measurements give good evidence that the true conductivity is not 10.1?
To determine if the measurements provide good evidence that the true conductivity of the iron rod is not 10.1, we need to perform a statistical analysis on the data.
Here's a step-by-step guide on how to assess the evidence using hypothesis testing:
1. Define the hypothesis:
- Null Hypothesis (H0): The true conductivity of the iron rod is 10.1.
- Alternative Hypothesis (Ha): The true conductivity of the iron rod is not 10.1.
2. Gather the data: Collect all the measurements of the iron rod's conductivity.
3. Calculate sample statistics: Compute the mean and standard deviation of the measurements.
4. Choose a significance level: Select a significance level (alpha) that represents the level of certainty required to reject the null hypothesis. Common values are 0.05 (5%) or 0.01 (1%).
5. Perform hypothesis testing: Use a statistical test, such as a one-sample t-test, to compare the sample mean with the hypothesized value of 10.1. The test will provide a p-value, which represents the probability of obtaining the observed data if the null hypothesis is true.
6. Interpret the p-value: If the p-value is less than the chosen significance level (alpha), it indicates strong evidence against the null hypothesis. In this case, it suggests that the true conductivity of the iron rod is unlikely to be 10.1. On the other hand, if the p-value is greater than alpha, there is insufficient evidence to reject the null hypothesis, implying that the true conductivity could potentially be 10.1.
7. Consider effect size and practical significance: While hypothesis testing provides information on statistical significance, it is also important to evaluate the effect size and practical significance of any differences observed.
By following these steps, you can assess whether the measurements provide good evidence to reject the hypothesis that the true conductivity of the iron rod is 10.1.