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Answer :
Final answer:
In the scenario provided, where a lathe is assumed to be cutting bars of steel at an average length of exactly 6 cm, the null hypothesis would be that the population mean length of the steel bars does not differ from 6 cm. This is formally expressed as H0: μ = 6 cm. Any observed difference is tested for statistical significance to see if it's beyond what would be expected due to simple variability.
Explanation:
In the context of this question, we have a situation where a lathe is cutting bars of steel. We want to test the hypothesis that the average length of the bars it cuts is exactly 6 centimeters. This leads us to a null hypothesis, which is a statistical hypothesis in which no significant difference is expected. Thus, the null hypothesis would be: H0: μ = 6 cm where μ stands for the population mean length of the bars of steel.
The observed difference (0.08 cm) is used to conduct a statistical analysis in which we test if this difference is statistically significant or due to random chance(variability).
Remember that this null hypothesis assumes that the population mean does not differ from the 6 cm length specified. In other words, we assume that the lathe is in perfect adjustment based on this hypothesis.
Learn more about Null Hypothesis here:
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Rewritten by : Barada
The hypothesis testing for this problem is:
a. The hypothesis for this problem are:
Null: H0: μ=6
Alternative: Ha: μ≠6
b. Test
T-statistics = (6.08 - 6) / 0.44* √(121) = 2
c. P value = 0.047759
Since our p-value is smaller than the significant level of 0.05, we can say that we reject the null hypothesis.
Conclusion: there is enough evidence to say lathe is not in perfect adjustment.
a. The hypothesis for this problem are:
Null: H0: μ=6
Alternative: Ha: μ≠6
b. Test
T-statistics = (6.08 - 6) / 0.44* √(121) = 2
c. P value = 0.047759
Since our p-value is smaller than the significant level of 0.05, we can say that we reject the null hypothesis.
Conclusion: there is enough evidence to say lathe is not in perfect adjustment.
