Asian economies impact some of the world's largest populations. The growth of an economy has a big influence on the everyday lives of ordinary people. Are Asian economies changing? A random sample of 15 Asian economies gave the following information about annual percentage growth rate. Region 1 2 3 4 5 6 7 8 Modern Growth Rate % 4.6 2.9 7.6 2.4 0.3 5.5 2.7 4.8 Historic Growth Rate 3.5 1.3 7.1 5.3 3.5 6.4 3.6 8.4 Region 9 10 11 12 13 14 15 Modern Growth Rate % 4.1 5.6 6.5 3.8 3.4 0.6 7.9 Historic Growth Rate 6.8 7.8 6.1 1.3 1.2 2.7 5.7 Does this information indicate a change (either way) in the growth rate of Asian economies? Use a 10% level of significance. (a) What is the level of significance? (b) Compute the sample test statistic. (Round your answer to two decidmal places. (c) Find the P-value of the sample of the test statistic. (Round your answer to four decimal places)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Asian economies impact some of the world's largest populations. The growth of an economy has a big influence on the everyday lives of ordinary people. Are Asian economies changing? A random sample of 15 Asian economies gave the following information about annual percentage growth rate.
| Region | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Modern Growth Rate % | 4.6 | 2.9 | 7.6 | 2.4 | 0.3 | 5.5 | 2.7 | 4.8 |
| Historic Growth Rate | 3.5 | 1.3 | 7.1 | 5.3 | 3.5 | 6.4 | 3.6 | 8.4 |
| Region | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|---|---|
| Modern Growth Rate % | 4.1 | 5.6 | 6.5 | 3.8 | 3.4 | 0.6 | 7.9 |
| Historic Growth Rate | 6.8 | 7.8 | 6.1 | 1.3 | 1.2 | 2.7 | 5.7 |
Does this information indicate a change (either way) in the growth rate of Asian economies? Use a 10% level of significance.
(a) What is the level of significance?
(b) Compute the sample test statistic. (Round your answer to two decidmal places.
(c) Find the P-value of the sample of the test statistic. (Round your answer to four decimal places)
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