Questions: p-value = 0.347 The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 79.1. There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 79.1. The sample data support the claim that the population mean is not equal to 79.1. There is not sufficient sample evidence to support the claim that the population mean is not equal to 79.1.

p-value = 0.347
The p-value is...
less than (or equal to) α
greater than α

This test statistic leads to a decision to...
reject the null
accept the null
fail to reject the null

As such, the final conclusion is that...
There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 79.1.
There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 79.1.
The sample data support the claim that the population mean is not equal to 79.1.
There is not sufficient sample evidence to support the claim that the population mean is not equal to 79.1.

Transcript text: $p$-value $=0.347$ The $p$-value is... less than (or equal to) $\alpha$ greater than $\alpha$ This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 79.1 . There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 79.1 . The sample data support the claim that the population mean is not equal to 79.1 . There is not sufficient sample evidence to support the claim that the population mean is not equal to 79.1 .

Solution

Solution Steps

Step 1: Determine the p-value Comparison

The calculated $ p $-value is $ 0.347 $. We compare this value to the significance level $ \alpha = 0.05 $.

Since $ 0.347 > 0.05 $, we conclude that the p-value is greater than $ \alpha $.

Step 2: Decision on the Null Hypothesis

Based on the comparison of the $ p $-value and $ \alpha $, we make a decision regarding the null hypothesis. Since the $ p $-value is greater than $ \alpha $, we fail to reject the null hypothesis.

Step 3: Final Conclusion

The conclusion drawn from the decision is that there is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to $ 79.1 $.

Final Answer

The p-value is greater than $ \alpha $. This test statistic leads to a decision to fail to reject the null. As such, the final conclusion is that there is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to $ 79.1 $.

\[ \boxed{\text{The conclusion is: There is not sufficient evidence to reject the claim that the population mean is not equal to } 79.1.} \]

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