To determine the correct conclusion for this hypothesis test, let's walk through the steps involved:
1. Hypotheses Setting:
- Null Hypothesis [tex]\( H_0 \)[/tex]: [tex]\( p_A - p_B = 0 \)[/tex], meaning there is no difference in the proportions of defective computer chips between plant [tex]\( A \)[/tex] and plant [tex]\( B \)[/tex].
- Alternative Hypothesis [tex]\( H_1 \)[/tex]: [tex]\( p_A - p_B > 0 \)[/tex], meaning the proportion of defective computer chips at plant [tex]\( A \)[/tex] is greater than at plant [tex]\( B \)[/tex].
2. Level of Significance ([tex]\(\alpha\)[/tex]):
- The significance level [tex]\(\alpha\)[/tex] is given as 0.05.
3. P-value:
- The p-value from the test is given as 0.225.
4. Decision Rule:
- To decide whether to reject the null hypothesis, we compare the p-value to the level of significance.
- If the p-value is less than [tex]\(\alpha\)[/tex] ([tex]\( p \leq \alpha \)[/tex]), we reject the null hypothesis.
- If the p-value is greater than [tex]\(\alpha\)[/tex] ([tex]\( p > \alpha \)[/tex]), we fail to reject the null hypothesis.
5. Comparison:
- Here, the p-value is 0.225.
- The level of significance [tex]\(\alpha\)[/tex] is 0.05.
- Since the p-value (0.225) is greater than [tex]\(\alpha\)[/tex] (0.05), we fail to reject the null hypothesis.
6. Conclusion:
- By failing to reject the null hypothesis, it means there is insufficient evidence to support the claim that the proportion of defective computer chips is significantly greater at plant [tex]\( A \)[/tex].
Therefore, the correct conclusion is:
The owner should fail to reject the null hypothesis since [tex]\( 0.225 > 0.05 \)[/tex]. There is insufficient evidence that the proportion of defective computer chips is significantly greater at plant [tex]\( A \)[/tex].
Hence, the correct option is:
The owner should fail to reject the null hypothesis since [tex]\( 0.225 > 0.05 \)[/tex]. There is insufficient evidence that the proportion of defective computer chips is significantly greater at plant [tex]\( A \)[/tex].
