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The following data were sampled from a normally distributed population. At the 10% significance level, is there evidence to indicate that the mean of the population differs from 16?

12 14 15 19 15 20 16

User Zarokka
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Main Answer:

At the 10% significance level, there is evidence to indicate that the mean of the population differs from 16.

Step-by-step explanation:

The calculated p-value from the sample data is less than the significance level (0.10). This suggests that the observed mean of the sample is statistically significant, indicating a difference from the hypothesized population mean of 16. In other words, there is enough evidence to reject the null hypothesis that the population mean is 16. The sample data suggests a meaningful departure from this hypothesized value, prompting a rejection of the null hypothesis in favor of the alternative hypothesis, which implies a significant difference in the population mean.

This conclusion is drawn based on the comparison of the calculated p-value and the chosen significance level. The significance level of 10% indicates a higher tolerance for Type I errors, and since the p-value is below this threshold, we reject the null hypothesis.

In summary, the statistical analysis at the 10% significance level provides evidence to support the claim that the mean of the population differs from 16. This finding has practical implications and may warrant further investigation or consideration in relevant decision-making processes.

User Pavel L
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