A. Simple random sample
B. Stratified sample
C. Cluster sample
D. Systematic sample
2. A factory produces light bulb for which the population proportion of light bulb with defective threads is 0.05 . A new technology has become available recently and the developer claims that the population proportion of light bulb with defective threads will be less than 0.05 . To test the validity of this claim, 400 light bulbs produced by the new technology are selected at random and the sample proportion of defective is computed. This result will be used to make decision as to whether or not the factory should invest in the new technology. The factory wants a significant level of 0.05 in their decision.
If a type I error is made in carrying out this test, what is the consequence to the factory?
A. They will invest in the new technology while it is no better than the current process being used.
B. They will not invest in the new technology while it is no better than the current process being used.
C. They will invest in the new technology while it is an improvement over the process currently being used.
D. They will not invest in the new technology while it is an improvement over the process currently being used.
3. Suppose we wish to test $H_{0}: \mu \leq 47$ versus $H_{a}: \mu47$. What will result if we

Question

A. Simple random sample
B. Stratified sample
C. Cluster sample
D. Systematic sample
2. A factory produces light bulb for which the population proportion of light bulb with defective threads is 0.05 . A new technology has become available recently and the developer claims that the population proportion of light bulb with defective threads will be less than 0.05 . To test the validity of this claim, 400 light bulbs produced by the new technology are selected at random and the sample proportion of defective is computed. This result will be used to make decision as to whether or not the factory should invest in the new technology. The factory wants a significant level of 0.05 in their decision.
If a type I error is made in carrying out this test, what is the consequence to the factory?
A. They will invest in the new technology while it is no better than the current process being used.
B. They will not invest in the new technology while it is no better than the current process being used.
C. They will invest in the new technology while it is an improvement over the process currently being used.
D. They will not invest in the new technology while it is an improvement over the process currently being used.
3. Suppose we wish to test $H_{0}: \mu \leq 47$ versus $H_{a}: \mu>47$. What will result if we

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ A Type I error occurs when we reject the null hypothesis $ H_0 $ when it is actually true. In this case, the null hypothesis is that the population proportion of defective light bulbs is $ \mu \leq 0.05 $. ‖ ‖ step 2 ⋮ If a Type I error is made, the factory will conclude that the new technology is better (i.e., that the proportion of defective bulbs is less than 0.05) when, in fact, it is not. This means they will invest in the new technology unnecessarily. ‖ ‖ step 3 ⋮ Therefore, the consequence of making a Type I error is that they will invest in the new technology while it is no better than the current process being used. ‖ ∻Answer∻ ***A*** ∻Key Concept∻ ⚹Type I error in hypothesis testing⚹ ∻Explanation∻ ⚹A Type I error occurs when the null hypothesis is incorrectly rejected, leading to a false conclusion that a treatment or technology is effective when it is not.◊What is the definition of a Type I error in hypothesis testing?⍭ Generate me a similar question◊⚹

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