Question

A sample of $16$small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was two ounces with a standard deviation of $0.12$ounces. The population standard deviation is known to be $0.1$ounce.

a.

$$\begin{gathered} i.x¯=\_\_\_\_\_\_\_\_ \\ ii.\sigma =\_\_\_\_\_\_\_\_ \\ iii.sx=\_\_\_\_\_\_\_\_ \end{gathered}$$

b. In words, define the random variable $X$.

c. In words, define the random variable $X¯$.

d. Which distribution should you use for this problem? Explain your choice.

e. Construct a $90\%$confidence interval for the population mean weight of the candies.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

f. Construct a $98\%$confidence interval for the population mean weight of the candies.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

g. In complete sentences, explain why the confidence interval in part $f$is larger than the confidence interval in part $e$.

h. In complete sentences, give an interpretation of what the interval in part $f$means.

Short answer

a

Step-by-step solution

Step 1:

a