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Numerade Educator

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Problem 106 Hard Difficulty

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test.
At a significance level of $a=0.05,$ what is the correct conclusion?
a. There is enough evidence to conclude that the mumber of hours is more than 4.75
b. There is enough evidence to conclude that the mean number of hore than 4.5
c. There is not enough evidence to conclude that the mumber of hours is more than 4.5
d. There is not enough evidence to conclude that the mean number of hours is more than 4.75

Answer

the correct option is $\mathrm{c}$ .

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Video Transcript

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