 # 5.22. A GSS asked, &quot;What do you think is the ideal number...

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5.22. A GSS asked, "What do you think is the ideal number of children for a family to have?' The 497 females who responded had a median of 2, mean of 3.02, and standard deviation of 1.81. (a) Report the point estimate of the population mean. (b) Find and interpret the standard error of the sample mean. (c) The 95% confidence interval is 2.9,3.2). Inter- pret. (d) Is it plausible that the population mean = 2.0? Explain. 5.20. Find and interpret the 95% confidence interval for u, if y = 70 and S = 10, based on a sample size of (a) 5 (b) 20. 5.4. A national survey conducted in July 2006 by Pew Forum on Religion & Public Life asked whether the subject favored allowing homosexual couples to enter into civil unions-legal agreements that would give them many of the same rights as mar- ried couples. Of 2003 adults interviewed, 54% said yes, 42% said no, and 4% had no opinion. Find the estimated standard error for the sample proportion answering yes. Interpret it. 5.40. An estimate is needed of the mean acreage of farms in Manitoba, Canada. The estimate should be correct to within 100 acres with probability 0.95. A preliminary study suggests that 500 acres is a rea- sonable guess for the standard deviation of farm size. (a) How large a sample of farms is required? (b) A random sample is selected of the size found in (a). The sample has a standard deviation of 300 acres, rather than 500. What is the margin of error for a 95% confidence interval for the mean acreage of farms? 5.14. When the 2000 GSS asked whether human beings developed from earlier species of animals (variable SCITEST4), 53.8% of 1095 respondents answered that this was probably or definitely not true. Find a 99% confidence interval for the corresponding pop- ulation proportion, and indicate whether you can conclude that a majority of Americans felt this way. 5.67. Increasing the confidence level causes the width of a confidence interval to (a) increase (b) decrease (c) stay the same. 5.68. Other things being equal, quadrupling the sample size causes the width of a confidence interval to (a) double (b) halve (c) be one quarter as wide (d) stay the same.

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5.22
(a)
The point estimate of the population mean is 3.02.
(b)
The standard error of sample mean is given as
SE = standard deviation/sqrt(n) = 1.81/sqrt (497) = 0.081189596, it means that the standard error from mean value is 0.08119 which is a small value.
(c)
The 95% confidence interval for mean is 2.9 and 3.2, it means that the mean number of children for a family to have lies between 2.9 and 3.2....

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