In a 1998 advertising campaign, the Nabisco Company announced a "1000 Chips Challenge," claiming that their 18-ounce bags of their Chips Ahoy cookies contain at least 1000 chocolate chips on average. Sixteen dedicated statistics students purchased some randomly selected bags of cookies and counted the chocolate chips. Their data are given below.
1122 | 1058 | 1130 | 1052 | 1117 | 1091 | 1061 | 1092 |
1159 | 1087 | 1129 | 1138 | 1007 | 1153 | 1165 | 1046 |
Find a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies. Use interval notation, smaller number first, with each number rounded to the nearest whole number.
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Based on this confidence interval, is the Nabisco Company justified in making this claim?