Review - Statistics - Fall 2020(1)

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University of Minnesota, Duluth *

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100

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Statistics

Date

Feb 20, 2024

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docx

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3

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Uploaded by BarristerGalaxyChimpanzee34

1. Weight of new sugar packet is normally distributed with mean 90 grams and standard deviation 10grams. Calculate the probability: P(85 < x < 95) 2. You took a sample of 25 packets from the population in 1 above. What is the following probability: P(85 < x̅ < 95), where x̅ is the sample mean. Read this section and answer the question that follows: You were told that the average weight in a sugar packet is 550 grams. Your friend started making these packets from bulk sugar. You took a sample of 24 such packets and the mean for these packets is 500 grams and the standard deviation is 22 grams. You want to test the hypothesis that the average for this sample is different from the national average. Use α=.05. Question: 3. What is the alternative hypothesis for this situation? 4. What is the value of the test statistic in this situation? 5. Should the t-test be used in this situation? 6. What is the rejection region in this situation? 7. The decision is made that the average for this sample is different from the national average. Knowing this, do you accept or reject the null hypothesis? Read this section and answer the question that follows: You were told that the average weight in a sugar packet is 550 grams. Your friend started making these packets from bulk sugar. You took a sample of 24 such packets and the mean for these packets is 500 grams and the standard deviation is 22 grams. But now, your friend told you that she is sure that your packets have fewer grams of sugar. You do the test again. Use α=.05. 8. What is the alternative hypothesis for this situation? 9. What is the rejection region for this situation? 10. Should you reject the null hypothesis in this situation? 11. What is the 95% confidence interval for the population mean in this situation? Read this section and answer the question that follows: Suppose the average amount of sugar in a packet is 600 with a standard deviation of 100 grams. Your friend sells these packets at her store. You believe that, in fact, the average amount of sugar in these packets is different from 600 grams. To test the hypothesis, you took a sample of 16 packets from your friend. The average for this group is 650 calories. Question: 12.What is the value of the test statistic in this situation?
13. Should the t-test be used in this situation? 14. What is the rejection region for this situation? 15. Should you accept or reject the null hypothesis in this situation? 16. What is the 95% confidence interval for the population mean? Look at the regression output below: SUMMARY OUTPUT Regression Statistics Multiple R 0.89377 4 R Square 0.79883 2 Adjusted R Square 0.78446 3 Standard Error 1.38158 4 Observation s 31 ANOVA df SS MS F Significan ce F Regression 2 212.231 7 106.11 59 55.593 72 1.77751E -10 Residual 28 53.4456 8 1.9087 74 Total 30 265.677 4 Coefficie nts Standar d Error t Stat P- value Lower 95% Upper 95% Intercept 1.16416 2 0.65490 2 1.7776 13 0.0863 32 - 0.177343 6 2.5056 68 X1 0.09133 5 0.18049 0.5060 4 0.6167 9 - 0.278382 53 0.4610 53 X2 0.78190 3 0.18889 1 4.1394 46 0.0002 89 0.394977 851 1.1688 28 Now answer the question that follows: 17.What is the interpretation of Significance F, 1.77751E-10 ? 18. An interpretation of the p-value . 0.61679 is...
19. An interpretation of the p-value 0.000289 is... 20.Now answer the question that follows: For X1= 7 and x2=9, what is the forecasted value of Y?
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