Question

Fun size candyA candy bar manufacturer sells a “fun size” version that is advertised to weigh $17$grams. A hungry teacher selected a random sample of $44$fun size bars and found a $95\%$confidence interval for the true mean weight to be $16.945$grams to $17.395$grams.

a. Does the confidence interval provide convincing evidence that the true mean weight is different than $17$grams? Explain your answer.

b. Does the confidence interval provide convincing evidence that the true mean weight is $17$grams? Explain your answer.

Short answer

a. There is no convincing evidence that true mean is different from $17$grams.

b. There is no convincing evidence due the presence of other values for true mean also.

Step-by-step solution

Given Information

It is given that for $95\%$confidence interval, true mean weight is $(16.945\text{grams}-17.395\text{grams})$

a. Whether the confidence interval provides convincing evidence that the true mean weight is different than 17 grams.

As confidence interval has $17$grams.

True mean weight is $17$grams is likely.

Hence, there is no evidence that true mean weight is different from$17$grams.

b. Whether the confidence interval provides convincing evidence that the true mean weight is 17 grams.

From above, it is clear that true mean weight is $17$grams.

Also, all weight between $(16.945\text{grams}-17.395\text{grams})$are equally like to be the true mean. True mean weight is not surely $17$grams.

Hence, there is no convincing evidence.