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Hashtag University is conducting a study to see how much time freshmen spend using social media. The university asked a random sample of $150$ freshmen how much time they spend on social media apps per day. Hashtag University calculated a $99\%$ confidence interval of for the mean number of hours freshmen spend on social media apps per day. $\newline$ Is the following conclusion valid? $\newline$ There is a $99\%$ chance that the mean number of hours freshman at Hashtag University spend on social media apps daily is in the interval . $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no $\newline$

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Interpret confidence intervals for population means

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Q. Hashtag University is conducting a study to see how much time freshmen spend using social media. The university asked a random sample of

150

freshmen how much time they spend on social media apps per day. Hashtag University calculated a

99\%

confidence interval of for the mean number of hours freshmen spend on social media apps per day.

\newline

Is the following conclusion valid?

\newline

There is a

99\%

chance that the mean number of hours freshman at Hashtag University spend on social media apps daily is in the interval .

\newline

Choices:

\newline

(A)yes

\newline

(B)no

\newline

Confidence Interval Definition: A confidence interval gives us a range in which we expect the true mean to fall, given a certain level of confidence. It does not mean there is a $99\%$ chance that the mean number of hours is within the interval.
Correct Interpretation: The correct interpretation of a $99\%$ confidence interval is that we are $99\%$ confident that the interval contains the true mean. It's not about the probability of the mean being in the interval on any given day.
Misunderstanding of Interval: The conclusion that there is a $99\%$ chance that the mean number of hours is in the interval is a common misunderstanding of confidence intervals. The interval itself is fixed once calculated; it either contains the true mean or it doesn't.
Validity of Statement: Therefore, the statement is not valid because it misinterprets the meaning of a confidence interval.

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