Answer:
Check Explanation
Step-by-step explanation:
i) The manager hopes to investigate whether there's significant evidence to conclude that the mean number of defective bulbs per case is greater than 20 during the morning shift by comparing the p-value obtained with the significance level at which the hypothesis test was performed at.
ii) The null hypothesis as stated in the question is that the mean number of defective bulbs per case is less than or equal to 20.
The alternative hypothesis takes the other side of the hypothesis; that there is indeed a significant evidence to suggest that the mean number of defective bulbs per case is greater than 20.
Mathematically,
The null hypothesis
H₀: μ₀ ≤ 20
The alternative hypothesis
Hₐ: μ₀ > 20
iii) The critical value the manager should use to determine the rejection region is the significance level at which the test was carried out, that is, significance level of 0.10.
iv) Normally, if the p-value is greater than the significance level, we fail to reject the null hypothesis.
Conversely, if the p-value is less than the significance level, then, we reject the null hypothesis.
For this question,
p-value = 0.021
significance level = 0.10
0.021 < 0.1
p-value < significance level
Hence, we can reject the null hypothesis because the p-value is less than the significance level. We can conclude that there is enough evidence to suggest that the mean number of defective bulbs per case is greater than 20.
e) A type 1 error occurs when we reject the null hypothesis, when in reality, the null hypothesis is true.
Now that we have signified the existence of 3vidence to suggest that the mean number of defective bulbs per case is greater than 20, if the reality is that mean number of defective bulbs per case is less than or equal to 20. A type 1 error can then be stated to have been committed in the rejection of the true hypothesis.
Hope this Helps!!
