Can you please explain this problem to me? Also, I do not know what formula to use. Thank you

A market research consultant hired by a leading softdrink company wants to determine the proportion of consumers who favor its low-calorie drink over the leading competitor's low-calorie drink in a particular urban location. A random sample of 250 consumers from the market under investigation is provided below

a. Find a 95% confidence interval for the proportion of all consumers in this market who prefer this company's drink over the competitor's. What does this confidence interval tell us?

b. Does the confidence interval in part a support the claim made by one of the company's marketing managers that more than half of the consumers in this urban location favor its drink over the competitor's? Explain your answer.

c. Comment on the sample size used in this study. Specifically, is the sample unnecessarily large? Is it too small? Explain your reasoning.

Consumer Gender Age Preference

1 F Over 60 Our brand

2 F Between 40 and 60 Our brand

3 M Between 40 and 60 Our brand

4 F Over 60 Competing brand

5 M Between 20 and 40 Our brand

6 F Between 20 and 40 Competing brand

7 F Between 20 and 40 Our brand

8 F Between 40 and 60 Competing brand

9 F Between 20 and 40 Competing brand

10 F Between 40 and 60 Competing brand

11 F Over 60 Competing brand

12 F Between 20 and 40 Our brand

13 F Over 60 Competing brand

14 F Between 40 and 60 Competing brand

15 F Between 40 and 60 Competing brand

16 F Between 20 and 40 Our brand

17 F Between 20 and 40 Competing brand

18 F Between 40 and 60 Competing brand

19 F Over 60 Our brand

20 F Between 20 and 40 Our brand

21 M Over 60 Our brand

22 F Between 40 and 60 Competing brand

23 F Between 40 and 60 Competing brand

24 F Between 40 and 60 Our brand

25 F Between 20 and 40 Our brand

26 M Between 20 and 40 Our brand

27 M Between 20 and 40 Our brand

28 F Over 60 Competing brand

29 F Between 20 and 40 Competing brand

30 F Between 40 and 60 Competing brand

31 F Between 20 and 40 Our brand

32 F Between 20 and 40 Our brand

33 F Between 20 and 40 Competing brand

34 F Between 40 and 60 Competing brand

35 F Between 20 and 40 Competing brand

36 F Between 40 and 60 Our brand

37 F Between 40 and 60 Our brand

38 M Between 20 and 40 Our brand

39 F Between 20 and 40 Competing brand

40 F Between 40 and 60 Competing brand

41 M Less than 20 Our brand

42 M Less than 20 Our brand

43 F Between 40 and 60 Our brand

44 F Over 60 Competing brand

45 M Less than 20 Competing brand

46 F Between 20 and 40 Competing brand

47 M Between 20 and 40 Our brand

48 F Over 60 Our brand

49 F Between 20 and 40 Competing brand

50 F Between 20 and 40 Our brand

51 F Between 40 and 60 Our brand

52 F Between 20 and 40 Our brand

53 F Over 60 Competing brand

54 F Between 40 and 60 Competing brand

55 F Between 20 and 40 Competing brand

56 F Over 60 Competing brand

57 F Between 40 and 60 Competing brand

58 M Between 40 and 60 Our brand

59 F Between 20 and 40 Competing brand

60 M Over 60 Our brand

61 F Between 20 and 40 Our brand

62 M Between 20 and 40 Competing brand

63 F Over 60 Competing brand

64 M Between 40 and 60 Our brand

65 M Between 40 and 60 Our brand

66 F Between 20 and 40 Competing brand

67 F Between 40 and 60 Our brand

68 M Over 60 Competing brand

69 F Between 20 and 40 Our brand

70 M Between 20 and 40 Competing brand

71 F Over 60 Competing brand

72 M Over 60 Competing brand

73 F Between 40 and 60 Competing brand

74 F Between 20 and 40 Our brand

75 F Between 40 and 60 Our brand

76 M Between 40 and 60 Competing brand

77 F Between 40 and 60 Our brand

78 M Between 20 and 40 Our brand

79 F Between 40 and 60 Our brand

80 F Between 20 and 40 Competing brand

81 M Over 60 Our brand

82 M Between 40 and 60 Competing brand

83 F Between 40 and 60 Our brand

84 F Between 20 and 40 Our brand

85 M Less than 20 Our brand

86 F Between 40 and 60 Our brand

87 M Between 40 and 60 Our brand

88 M Between 20 and 40 Our brand

89 F Between 40 and 60 Our brand

90 M Between 40 and 60 Competing brand

91 M Between 40 and 60 Competing brand

92 M Between 20 and 40 Our brand

93 F Between 20 and 40 Competing brand

94 F Over 60 Competing brand

95 F Between 20 and 40 Competing brand

96 F Between 20 and 40 Our brand

97 F Between 20 and 40 Competing brand

98 F Over 60 Competing brand

99 F Between 20 and 40 Competing brand

100 F Between 20 and 40 Competing brand

101 F Less than 20 Competing brand

102 F Over 60 Competing brand

103 F Less than 20 Competing brand

104 F Between 20 and 40 Our brand

105 M Less than 20 Our brand

106 F Between 20 and 40 Our brand

107 F Between 20 and 40 Our brand

108 M Less than 20 Our brand

109 M Between 20 and 40 Competing brand

110 F Between 40 and 60 Competing brand

111 F Between 40 and 60 Our brand

112 F Between 20 and 40 Our brand

113 M Less than 20 Our brand

114 M Between 40 and 60 Our brand

115 F Between 20 and 40 Competing brand

116 M Over 60 Competing brand

117 M Over 60 Our brand

118 F Between 20 and 40 Competing brand

119 F Between 20 and 40 Competing brand

120 F Between 20 and 40 Competing brand

121 F Over 60 Competing brand

122 F Between 20 and 40 Our brand

123 F Between 40 and 60 Competing brand

124 F Between 40 and 60 Our brand

125 F Between 20 and 40 Our brand

126 F Between 20 and 40 Competing brand

127 M Between 40 and 60 Competing brand

128 M Between 20 and 40 Our brand

129 F Between 40 and 60 Our brand

130 F Between 20 and 40 Competing brand

131 F Over 60 Our brand

132 M Over 60 Competing brand

133 M Between 20 and 40 Our brand

134 F Between 20 and 40 Competing brand

135 F Between 40 and 60 Our brand

136 F Over 60 Competing brand

137 F Over 60 Competing brand

138 F Between 20 and 40 Competing brand

139 F Between 20 and 40 Competing brand

140 F Between 40 and 60 Our brand

141 F Between 20 and 40 Our brand

142 M Over 60 Our brand

143 F Between 40 and 60 Competing brand

144 F Between 20 and 40 Competing brand

145 F Less than 20 Competing brand

146 F Between 20 and 40 Competing brand

147 M Between 20 and 40 Competing brand

148 F Between 20 and 40 Our brand

149 M Over 60 Competing brand

150 M Over 60 Our brand

151 F Between 20 and 40 Competing brand

152 F Between 40 and 60 Competing brand

153 F Between 20 and 40 Our brand

154 F Between 20 and 40 Competing brand

155 F Between 40 and 60 Competing brand

156 M Between 20 and 40 Our brand

157 F Between 40 and 60 Our brand

158 F Between 20 and 40 Our brand

159 F Over 60 Our brand

160 F Between 20 and 40 Our brand

161 F Over 60 Our brand

162 F Between 20 and 40 Competing brand

163 F Between 20 and 40 Competing brand

164 F Between 20 and 40 Competing brand

165 F Between 20 and 40 Competing brand

166 F Between 20 and 40 Competing brand

167 F Between 40 and 60 Competing brand

168 M Between 20 and 40 Our brand

169 M Less than 20 Our brand

170 F Between 40 and 60 Our brand

171 F Over 60 Our brand

172 M Over 60 Our brand

173 F Between 20 and 40 Competing brand

174 M Less than 20 Competing brand

175 F Less than 20 Our brand

176 M Between 20 and 40 Our brand

177 F Between 20 and 40 Competing brand

178 F Between 20 and 40 Our brand

179 F Between 20 and 40 Our brand

180 F Between 20 and 40 Our brand

181 M Less than 20 Our brand

182 F Between 20 and 40 Our brand

183 F Over 60 Competing brand

184 M Between 20 and 40 Our brand

185 F Less than 20 Our brand

186 F Between 20 and 40 Our brand

187 F Between 40 and 60 Our brand

188 M Between 40 and 60 Competing brand

189 M Between 40 and 60 Competing brand

190 F Between 20 and 40 Our brand

191 F Less than 20 Competing brand

192 F Less than 20 Our brand

193 F Over 60 Our brand

194 F Between 20 and 40 Our brand

195 M Between 40 and 60 Competing brand

196 F Between 40 and 60 Our brand

197 M Over 60 Our brand

198 F Between 40 and 60 Our brand

199 F Over 60 Competing brand

200 F Between 20 and 40 Our brand

201 F Between 40 and 60 Our brand

202 M Between 40 and 60 Our brand

203 F Over 60 Competing brand

204 F Less than 20 Our brand

205 F Between 40 and 60 Competing brand

206 F Between 20 and 40 Our brand

207 F Between 20 and 40 Our brand

208 F Between 20 and 40 Our brand

209 M Between 20 and 40 Competing brand

210 F Over 60 Our brand

211 F Between 40 and 60 Our brand

212 F Between 20 and 40 Competing brand

213 F Less than 20 Our brand

214 F Between 20 and 40 Our brand

215 M Over 60 Our brand

216 F Between 20 and 40 Competing brand

217 F Between 40 and 60 Our brand

218 M Between 40 and 60 Our brand

219 F Between 20 and 40 Our brand

220 F Less than 20 Our brand

221 F Between 20 and 40 Our brand

222 F Between 40 and 60 Our brand

223 M Between 40 and 60 Competing brand

224 F Over 60 Our brand

225 F Between 20 and 40 Competing brand

226 M Between 40 and 60 Competing brand

227 F Over 60 Competing brand

228 M Less than 20 Our brand

229 F Over 60 Competing brand

230 F Between 20 and 40 Our brand

231 F Between 20 and 40 Competing brand

232 F Over 60 Our brand

233 F Over 60 Our brand

234 M Between 40 and 60 Competing brand

235 F Between 20 and 40 Our brand

236 F Between 40 and 60 Our brand

237 F Between 20 and 40 Our brand

238 F Between 40 and 60 Our brand

239 F Between 40 and 60 Our brand

240 F Between 40 and 60 Competing brand

241 F Between 40 and 60 Our brand

242 F Between 20 and 40 Our brand

243 F Between 20 and 40 Competing brand

244 F Over 60 Our brand

245 F Between 40 and 60 Competing brand

246 M Between 40 and 60 Competing brand

247 F Between 20 and 40 Competing brand

248 F Between 40 and 60 Our brand

249 M Between 20 and 40 Competing brand

250 M Over 60 Competing brand