Q. 98 A sample of 16聽small bags of th... [FREE SOLUTION]

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.

$a . i . x 虅 =________i i . 蟽 =________i i i . s x =________$

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

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

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.

Define the random variable $\overset{炉}{X}$ in words.

The mean age for all Foothill College students for a recent Fall term was $33.2$ . The population standard deviation has been pretty consistent at $15$ . Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was $30.4$ . We are interested in the true mean age for Winter Foothill College students. Let $X =$ the age of a Winter Foothill College student.

$___= 15$ .

If you decreased the allowable error bound, why would the minimum sample size increase (keeping the same level of

confidence)?

132. Public Policy Polling recently conducted a survey asking adults across the U.S. about music preferences. When asked, $80$ of the $571$ participants admitted that they have illegally downloaded music.

a. Create a $99 %$ confidence interval for the true proportion of American adults who have illegally downloaded music.

b. This survey was conducted through automated telephone interviews on May 6 and 7,2013. The error bound of the survey compensates for sampling error or natural variability among samples. List some factors that could affect the survey's outcome that is not covered by the margin of error.

c. Without performing any calculations, describe how the confidence interval would change if the confidence level changed from $99 % t o 90 %$ .

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