A grocery store is interested in determining whether or not a difference exists between the shelf life of Tasty Choice doughnuts and Sugar Twist doughnuts.A random sample of 100 boxes of each brand was selected and the mean shelf life in days was determined for each brand.A 98% confidence interval for the difference of the means, $μTC\mu \mathrm { TC }$ - $μST\mu \mathrm { ST }$ ,was determined to be (1.1,2.8) .

A) We are 98% confident that a randomly selected box of Tasty Choice doughnuts will have a shelf life that is between 1.1 and 2.8 days longer than a randomly selected box of Sugar Twist doughnuts.
B) Based on this sample,we are 98% confident that Sugar Twist doughnuts will last on average between 1.1 and 2.8 days longer than Tasty Choice doughnuts.
C) Based on this sample,we are 98% confident that Tasty Choice doughnuts will last on average between 1.1 and 2.8 days longer than Sugar Twist doughnuts.
D) Based on this sample,we know that 98% of Tasty Choice doughnuts last between 1.1 and 2.8 days longer than Sugar Twist doughnuts.
E) We know that 98% of all random samples taken from the population will show that the mean shelf life of Tasty Choice doughnuts is between 1.1 and 2.8 days longer than the mean shelf life of Sugar Twist doughnuts.

Question

A grocery store is interested in determining whether or not a difference exists between the shelf life of Tasty Choice doughnuts and Sugar Twist doughnuts.A random sample of 100 boxes of each brand was selected and the mean shelf life in days was determined for each brand.A 98% confidence interval for the difference of the means,

μTC\mu \mathrm { TC }

-

μST\mu \mathrm { ST }

,was determined to be (1.1,2.8) .

A) We are 98% confident that a randomly selected box of Tasty Choice doughnuts will have a shelf life that is between 1.1 and 2.8 days longer than a randomly selected box of Sugar Twist doughnuts.
B) Based on this sample,we are 98% confident that Sugar Twist doughnuts will last on average between 1.1 and 2.8 days longer than Tasty Choice doughnuts.
C) Based on this sample,we are 98% confident that Tasty Choice doughnuts will last on average between 1.1 and 2.8 days longer than Sugar Twist doughnuts.
D) Based on this sample,we know that 98% of Tasty Choice doughnuts last between 1.1 and 2.8 days longer than Sugar Twist doughnuts.
E) We know that 98% of all random samples taken from the population will show that the mean shelf life of Tasty Choice doughnuts is between 1.1 and 2.8 days longer than the mean shelf life of Sugar Twist doughnuts.

Dhruvil Barot · Accepted Answer

Final Answer : C, Explanation :   The confidence interval (1.1, 2.8) for the difference in means (  μ T C \mu \mathrm { TC } μ TC   -   μ S T \mu \mathrm { ST } μ ST  ) indicates that, on average, Tasty Choice doughnuts have a longer shelf life than Sugar Twist doughnuts by between 1.1 and 2.8 days. This interval does not refer to individual doughnuts or the proportion of samples, but rather the average difference in shelf life between the two brands.

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