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Class Assignment Two Elementary Statistics: Picturing the World MTH 233 Raj Kayathi Chapter 6 The following data set represents the repair cost (in dollars) for a random sample of 30 dishwashers (adapted from Consumer Reports) 41.82 90.07 100.05 118.77 52.81 90.35 101.32 119.01 57.80 91.68 103.59 120.70 68.16 91.72 104.19 140.52 73.48 93.01 105.62 141.84 78.88 95.21 111.32 147.06 88.13 95.34 117.14 88.79 96.50 118.42 (a) Find the point estimate of the population mean. (b) Find the margin of error for a 95% level of confidence. (c) Construct a 95% confidence interval for the population mean and interpret the results. {draw:rect} Solution: The point estimate of the population mean is computed as: {draw:frame} {draw:frame} (b) By definition, the margin of error is computed as: {draw:frame} {draw:frame} {draw:frame} {draw:frame} {draw:frame} {draw:frame} {draw:frame} {draw:frame} {draw:frame} {draw:frame} Also, standard deviation {draw:frame} {draw:frame} {draw:frame} {draw:frame} {draw:frame} This means that: Margin of error = 2.0395*(24.72242/√30) = 9.205709 (c) The 95% confidence interval is computed as: {draw:frame} {draw:frame} {draw:frame} {draw:frame} {draw:frame} = (88.90429, 107.3157) {draw:frame} {draw:frame} This means that there's a 95% chance that the interval (88.90429, 107.3157) contains the actual population mean {draw:frame} {draw:frame} {draw:frame} {draw:frame} {draw:frame} . {draw:rect} In a survey of 1037 adults from the United States age 65 and over, 643 were concerned about getting the flu. (Source: Harvard School for Public Health) Find a point estimate for the population proportion p of those concerned about getting the flu. Construct a 90% confidence interval for the population proportion.

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