Questions: Statistic: What is the statistic in this study?

Statistic: What is the statistic in this study?
Transcript text: Home Content/MTH/2 zy Section 2.6 - MTH learn.zybooks.com/zybook/MTH_217_58672503/chapter/2/section/6 zyBooks Feedback? 3S Strategy We will call the process of simulating could-have-been statistics under a specific chance model the 3S strategy. After forming our research conjecture and collecting the sample data, we will use the 35 strategy to weigh the evidence against the chance model. This $3 S$ strategy will serve as the foundation for addressing the question of statistical significance in Step 4 of the statistical investigation method. 3S Strategy for measuring strength of evidence. 1. Statistic: Compute the statistic from the observed sample data. 2. Simulate: Identify a "by-chance-alone" explanation for the data. Repeatedly simulate values of the statistic that could have happened when the chance model is true. 3. Strength of evidence: Consider whether the value of the observed statistic from the research study is unlikely to occur if the chance model is true. If we decide the observed statistic is unlikely to occur by chance alone, then we can conclude that the observed data provide strong evidence against the plausibility of the chance model. If not, then we consider the chance model to be a plausible (believable) explanation for the observed data; in other words what we observed could plausibly have happened just by random chance. Feedback? Let's review how we have already applied the $3 S$ strategy to this study. PARTICIPATION ACTIVITY 2.6.20: Question 19 Statistic: What is the statistic in this study?
failed

Solution

failed
failed

Solution Steps

Step 1: Calculate the Sample Mean

The sample mean \( \bar{x} \) is calculated using the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} = \frac{65}{10} = 6.5 \]

Thus, the sample mean is:

\[ \text{Sample Mean: } \bar{x} = 6.5 \]

Step 2: Calculate the Standard Error

The standard error \( SE \) is calculated using the formula:

\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{1.5}{\sqrt{10}} \approx 0.4743 \]

Step 3: Calculate the Test Statistic

The test statistic \( t \) is calculated using the formula:

\[ t = \frac{\bar{x} - \mu_0}{SE} = \frac{6.5 - 6.5}{0.4743} = 0.0 \]

Step 4: Calculate the P-value

For a two-tailed test, the P-value is calculated as:

\[ P = 2 \times (1 - T(|z|)) = 1.0 \]

Step 5: Conclusion

Since the P-value \( P = 1.0 \) is greater than the significance level \( \alpha = 0.05 \), we conclude that the observed data do not provide strong evidence against the chance model.

Final Answer

The observed data do not provide strong evidence against the chance model.

\(\boxed{\text{No strong evidence against the chance model}}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful