To determine whether the manager can conclude that there is sufficient evidence to show that the mean number of defective bulbs per case is greater than 20, we can analyze the provided information regarding the hypothesis test.
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Null Hypothesis (H0): The mean number of defective bulbs per case is less than or equal to 20.
- \( H_0: \mu \leq 20 \)
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Alternative Hypothesis (H1): The mean number of defective bulbs per case is greater than 20.
- \( H_1: \mu > 20 \)
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Test Statistic: The test statistic provided is 1.5.
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Critical Value: The critical value for a one-tailed test at a significance level of 0.10 is 1.282.
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Decision Rule: If the test statistic is greater than the critical value, we reject the null hypothesis.
Here, the test statistic (1.5) is greater than the critical value (1.282).
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Decision: Since the test statistic exceeds the critical value, we would reject the null hypothesis.
Based on this information, the conclusion is:
True: The manager can conclude that there is sufficient evidence to show that the mean number of defective bulbs per case is greater than 20 during the morning shift using a level of significance of 0.10.
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