# Formula 84 single population mean unknown standard

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Chapter 4 / Exercise 4
Single Variable Essential Calculus
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Formula 8.4:Single Population Mean, Unknown Standard Deviation, Student’s-t DistributionUse the Student’s-t Distribution with degrees of freedom df=n-1. EBM=tα2·snFormula 8.5:Single Population Proportion, Normal DistributionUse the Normal Distribution for a single population proportionp=xnEBP=zα2·qp·qnp+q=1The confidence interval has the format(p-EBP,p+EBP).Formula 8.6:Point Estimatesxis a point estimate forμp’ is a point estimate forρsis a point estimate forσ1This content is available online at <>.2"Central Limit Theorem: Central Limit Theorem for Sample Means" <>Available for free at Connexions <>
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Chapter 4 / Exercise 4
Single Variable Essential Calculus
Stewart Expert Verified
1358.2 Homework3NOTE: If you are using a student’s-t distribution for a homework problem below, you may assumethat the underlying population is normally distributed.(In general, you must first prove thatassumption, though.)Exercise 8.2.1(Solution on p. 148.)Among various ethnic groups, the standard deviation of heights is known to be approximately 3inches. We wish to construct a 95% confidence interval for the mean height of male Swedes. 48male Swedes are surveyed. The sample mean is 71 inches. The sample standard deviation is 2.8inches.a. i.x=________ii.σ=________iii.sx=________iv.n=________v.n-1=________b.Define the Random VariablesXandX, in words.c.Which distribution should you use for this problem? Explain your choice.d.Construct a 95% confidence interval for the population mean height of male Swedes.i.State the confidence interval.ii.Sketch the graph.iii.Calculate the error bound.e.What will happen to the level of confidence obtained if 1000 male Swedes are surveyed insteadof 48? Why?Exercise 8.2.2In six packages of “The Flintstones® Real Fruit Snacks” there were 5 Bam-Bam snack pieces. Thetotal number of snack pieces in the six bags was 68. We wish to calculate a 96% confidence intervalfor the population proportion of Bam-Bam snack pieces.a.Define the Random VariablesXandP’, in words.b.Which distribution should you use for this problem? Explain your choicec.Calculatep’.d.Construct a 96% confidence interval for the population proportion of Bam-Bam snack piecesper bag.i.State the confidence interval.ii.Sketch the graph.iii.Calculate the error bound.e.Do you think that six packages of fruit snacks yield enough data to give accurate results? Whyor why not?Exercise 8.2.3(Solution on p. 148.)A random survey of enrollment at 35 community colleges across the United States yielded thefollowing figures (source:Microsoft Bookshelf): 6414; 1550; 2109; 9350; 21828; 4300; 5944; 5722;2825; 2044; 5481; 5200; 5853; 2750; 10012; 6357; 27000; 9414; 7681; 3200; 17500; 9200; 7380; 18314;6557; 13713; 17768; 7493; 2771; 2861; 1263; 7285; 28165; 5080; 11622.Assume the underlyingpopulation is normal.a. i.x=3This content is available online at <>.
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