Question

question 1 (3 points)
a machine is designed to fill cereal boxes with 368 grams of cereal. a random sample of 25 boxes yields a mean of 365 grams with a standard - deviation of 15 grams. a 95% confidence interval for the true mean weight is calculated. if the interval includes 368 grams, what can you conclude?
there is not enough evidence to conclude that the machine is operating improperly.
the machine is operating improperly.
the sample size is too small to make a conclusion.
the machine is operating properly.
question 2 (3 points)
what of the following is most useful for comparing the costs of living in two different cities?
a scatter plot of income vs. expenses.
a list of median house prices in both cities.
side - by - side bar graph of expense categories in both cities.
pie chart of expenses in one city.

Explanation:

Question 1

A 95% confidence interval gives a range of values within which the true population mean is likely to lie. If the target value (368 grams in this case) is within the confidence interval, we do not have enough evidence to say the machine is operating improperly. It could be operating properly, but we don't have conclusive evidence either way.

To compare the costs of living in two different cities, looking at side - by - side bar graphs of expense categories in both cities allows for a clear visual comparison of different cost components. A scatter plot of income vs expenses is not relevant for comparing cities' cost of living directly, a list of median house prices only focuses on one aspect (housing), and a pie chart of expenses in one city doesn't help with comparison between two cities.

Answer:

There is not enough evidence to conclude that the machine is operating improperly

Question 2