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In: Statistics and Probability

Taking the family to an amusement park has become increasingly costly according to the industry publication...

Taking the family to an amusement park has become increasingly costly according to the industry publication Amusement Business, which provides figures on the cost for a family of four to spend the day at one of America’s amusement parks. A random sample of 25 families of four that attended amusement parks yielded the following costs, rounded to the nearest dollar.

122

166

171

148

135

173

137

163

119

144

164

153

162

140

142

158

130

167

173

186

92

170

126

163

172

Given the cost is normally distributed.

a) Suppose the population standard deviation is $21. Determine a 95% confidence interval for the mean cost of a family of four to spend the day at an American amusement park.

c) What is the margin of error of the 95% confidence interval obtained ?

d) Suppose we want to find a 95% confidence interval with margin of error 0.5. How many samples shall we collect?   

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