Question: A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results (measured in grams) were:

3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477

Assume the weight are normally distributed.

(a) Construct a 95% confidence interval for the true mean weight.

(b) What sample size would be necessary to estimate the true weight within 0.03 grams of the true mean with 90% confidence?

(c) The company claimed that each piece should weight over 3.45 grams. With 5% level of significance, do the data support the claim?

(d) Explain if you can (or cannot) use result in part (d) to answer part (c).