Understanding the sampling distribution: When statistical inference is performed
ID: 3175239 • Letter: U
Question
Understanding the sampling distribution: When statistical inference is performed, the sampling distribution sometimes follows a Normal distribution and sometimes takes the form of a t distribution. When is the Normal distribution appropriate and when is the t distribution appropriate? Which distribution do you think is more realistic in practice and why? Distinguishing type I and type II errors: In each of the following scenarios, identify if a type I error, a type II error, or neither has occurred. An engineer designs an improved light bulb. The previous design had an average lifetime of 1200 hours. The mean lifetime of a random sample of 2000 new bulbs is found to have a mean lifetime of 1201 hours. Although the difference from the old mean lifetime of 1200 hours is quite small, the P-value is 0.03 and the effect is statistically significant atExplanation / Answer
2a) when sample size is large (>=30) we use normal distribution, if it is less than 30 we use t-distribtution
2b) t-distribution is realistic, because for large sample size t-distribution tends to normal
3) here alpha=level of significance is not given. let it is alpha=0.05, since P-value is 0.03 is less than alpha, so it is statistically significant and conclude that at 5% level of significance mean life is differe from 1200.
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