The sample mean has been calculated

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Unformatted text preview: 8 When the t ­distribution is used in constructing a confidence interval based on a sample size of less than 30, what assumption must be made about the shape of the underlying population? 2 PROBLEM # 7.9 In using the t distribution table, what value of t would correspond to an upper ­tail area of 0.025 for 19 degrees of freedom? PROBLEM # 7.10 A consumer magazine has contacted a simple random sample of 33 owners of a certain model of automobile and asked each owner how many defects has to be corrected within the first 2 months of ownership. The average number of defects was ! =3.7, with a standard deviation of 1.8 defects. a. Use the t distribution to construct a 95% confidence interval for ! = the average number of defects for this model. b. Use the z distribution to construct a 95% confidence interval for ! = the average number of defects for this model. c. Given that the population standard deviation is not known, which of these two confidence intervals should be used as the interval estimate for ! ? PROBLEM # 7.11 For df=25, determine the value of A that corresponds to each of the following probabilities: a. P(t >=A)= 0.025 b. P(t=<A) = 0.10 c. P( ­A =< t <= A) = 0.98 3 PROBLEM # 7.12 From past experience, a package ­filling machine has been found to have a process standard deviation of 0.65 ounces of product weight. A simple random simple is to be selected from the machine’s output for the purpose of determining the average weight of product being packed by the machine. For 95% confidence that the sample mean will not differ from the actual population mean by more than 0.1 ounces, what sample size is required? PROBLEM # 7.13 Under what conditions is it appropriate to use the normal approximation to the binomial distribution in constructing the confidence interval for the population proportion? PROBLEM # 7.14 It has been estimated that 48% of U.S. households headed by persons in the 35 ­44 age group own mutual funds. Assuming this finding to be based on a simple random sample of 1000 households headed by persons in this age group, construct a 95% confidence interval for p= the population proportion of such households that own mutual funds. Source: Investment Company Institute, Investment Company Fact Book 2008, p.72. 1 2 3 4 5 6 A B z-Es tim ate of a Proportion S ample proportion S ample size Confidence le vel 0.48 1000 0.95 C Confidence Interval E stimate 0.48 0 Lower confidence limit Upper confidence limit D E ± 0.0 31 0.4 49 0.5 11 PROBLEM # 7.15 The Chevrolet...
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