**7.144 Sample size calculation.**Example 7.13 (page 449) tells us that the mean height of 10-year-old girls is $N(56.4, 2.7)$ and for boys it is $N(55.7, 3.8)$. The null hypothesis that the mean heights of 10-year-old boys and girls are equal is clearly false. The difference in mean heights is $56.4 - 55.7 = 0.7$ inch. Small differences such as this can require large sample sizes to detect. To simplify our calculations, let’s assume that the standard deviations are the same, say $\sigma = 3.2$, and that we will measure the heights of an equal number of girls and boys. How many would we need to measure to have a 90% chance of detecting the (true) alternative hypothesis?

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Answered: 7.144 Sample size calculation. Example…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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3. A principal wishes to estimate the average number ofhours students spend dolngbomework per week. The standard deviaton from a prevlous study is 4.5 hours. How large a sample must be selected if he wants to be 95% confident of finding whether the true mean differes from the sample mean by 2.1 hours?
5.28 Risks and insurance. The idea of insurance is that we all face risks that are unlikely but carry high cost. Think of a fire destroying your home. So we form a group to share the risk: we all pay a small amount, and the insurance policy pays a large amount to those few of us whose homes burn down. An insurance company looks at the records for millions of homeowners and sees that the mean loss from fire in a year is μ = $250 per house and that the standard deviation of the loss is σ = $1000. (The distribution of losses is extremely right-skewed: most people have $0 loss, but a few have large losses.) The company plans to sell fire insurance for $250 plus enough to cover its costs and profit. If the company sells 25,000 policies, what is the approximate probability that the average loss in a year will be greater than $270?
1.18 Cats on YouTube. Suppose you want to estimate the percentage of videos on YouTube that are cat videos. It is impossible for you to watch all videos on YouTube so you use a random video picker to select 1000 videos for you. You find that 2% of these videos are cat videos. Determine which of the following is an observation, a variable, a sample statistic (value calculated based on the observed sample), or a population parameter
3. A researcher samples 5 colony of Species of K and 5 colonies of Species L, measures their sizes as: Species K Species L 4.7 5.3 5.2 4.6 6.1 4.1 5.8 4.8 5.2 4.2 а. Test if mean colony size of Species K and Species L are different from each other? Report a p-value. (You mav need to do an additional test to decide which test to apply for comparing the means) b. What is the power of the test in part a? С. The researcher would like to design a new experiment which will allow a two tailed hypothesis test with significance 0.05 and power 0.90. What should be the sample sizes nk and ni for Species K and Species L (use k = 1). %3D
7. With a previous contractor, the mean time to replace a streetlight was 3.2 days. A city councilwoman thinks that the new contractor is not getting the streetlights replaced as quickly. She selects a random sample of 12 streetlight service calls for the new contractor, and obtains the following times to replacement (days). 6.2 7.1 5.4 5.5 7.5 2.6 4.3 2.9 3.7 0.7 5.6 1.7 Using a significance level of 0.01, test the councilwoman's claim. You may assume that all conditions are satisfied.
7.2.4
5.35 Cyberbullying, continued. Refer to Exercise 5.33. a. What is the expected number of undergraduates in your sample who say that they have received hurtful comments online in the past 30 days? What is the expected number of undergraduates who say that they have not received hurtful comments online in the past 30 days? What do the two means add up to?
8.4.1 Approximately 91% of all adults in South Korea have a cell phone. In a simple random sample of 200 adults in the United States, 171 owned cell phones. Is there convincing evidence to suggest the proportion of adults who own cell phones in the U.S. is lower than the proportion of adults who own cell phones in South Korea? Conduct a significance test using the 4-step process.
6. In December 2001, 38% of adults with children under the age of 18 reported that their family ate dinner together 7 nights a week. In a recent poll, 403 out of 1122 randomly selected adults with children under the age of 18 reported that their family ate dinner together 7 nights a week. Has the proportion of families with children under the age of 18 who eat dinner together 7 nights a week decreased? Use a 0.05 level of significance.
4. 0 There is some indication that as countries' levels of literacy increases, authoritarian tendencies decline among the population. The following data show literacy (measured in number of literate people per 10 people) and authoritarian scores on a standard authoritarinaism- measuring scale from 8 countries. The data are: Xiiteracy : 9.2, 7.5, 8.8, 6.5, 4.3, 5.9, 9.7, 8.5 XAuth: 2.1, 3.4, 2.5, 7.3, 8.9, 5.7, 1.3, 2.5 Is there a reliable relationship between the two variables? If yes, what would the predicted authoritarian score of a country where only quarter of the country is literate? What about for a country where the literacy rate is %100? Use alpha = .05.
Examine whether the following sample could have come from a population with mean 15(assume normality): 16, 18, 13, 11, 20, 22, 11, 19, 18, 15. Use 95% level of significance.(Given: t0.05,10 = 1.812, t0.05,9=1.833, t0.01, 9=2.821, t0.01,10=2.764)

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