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Hello, Welcome to the video. And today we're
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talking about hypothesis tests and specifically whether or not we
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have enough information to reject or fail to reject the
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note. So in this problem, we're told that
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an organization reports that the average amount of time that
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teenagers spent on the phone per week is equal to
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4.5 so we can create are null hypothesis from this
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information here that the population mean or in other words
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, mu is equal to 4.5. Um, it
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also tells us that a group of people were skeptical
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of this claim. They were actually convinced that the
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true value is greater than 4.5. So we can
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translate this into our no hypothesis that the value the
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true value of mu is great in there, 4.5
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. So these people who were skeptical of the original
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claim they conduct their own study, and they find
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that their sample mean is actually equal to 4.75 with
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a sample standard deviation of two were asked whether or
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not um, you were asked what the correct conclusion
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would be. So if we consider how far away
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the observed, um the observed mean is away from
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the proposed mean and we do this by considering what
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the standard deviation is. We can see that it's
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that there's actually not a lot of distance between the
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two values here. Um, so we know that
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Ah, 68% of all data in the normal distribution
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is contained within one standard deviation from both directions of
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the mean. So that being said, 68% of
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the data would be contained between, Let's say,
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like, uh, five and 1/2 in six and
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1/2. And because 4.75 is very much inside that
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range, it's essentially for our sake, for our
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sake. It's essentially the same as the as the
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mu of 4.5. Ah, we can say that
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we don't have enough information at an Alfa level of
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, let's say 0.5 That's kind of the standard Alfa
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level. We can say that we have enough information
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or we do not have enough information to claim that
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this no hypothesis is not right. So looking at
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our options, the true or the correct option would
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be C that there is not enough evidence to conclude
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that the number of ours is more than 4.5,
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so this may actually be true, but we do
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not have enough evidence to prove that is most likely
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true. So therefore see.