You research prices of cell phones and find that the populatio...

Question

You research prices of cell phones and find that the population mean is $431.61. In Exercise 19, does the t-value fall between -t0.95 and t0.95?

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says a nutritionist examines the average sugar content in breakfast cereals and finds that the population mean is 10.3 g. In a sample of 25 cereals, the calculated T value for the sample mean is 2.65. At the 95% confidence level, does this T-value fall between minus T 0.95 and T 0.95 or the appropriate degrees of freedom? So the first thing we need to do is to find our critical T value for the 95% confidence level, and in order to do that, we'll need to determine the number of degrees of freedom that we have. So we call that the degrees of freedom, which we'll label as DF, is going to be equal to N minus 1, where in here is our sample size. And we look at our problem, we see that we're told that we have a sample of 25 cereals. So that means N is equal to 25. So our degrees of freedom is going to be equal to 25 minus 1, which is equal to 24. So now we can look up the critical T value or the 95% confidence level, and 24 degrees of freedom. So, we'll be looking up T sub 0.975 with 24 degrees of freedom. And we'll look that up at our table, we see that our criticality value is going to be approximately equal to. 2.064. Now note that for the 95% confidence interval, we're actually using 0.975 in our tea tables, and that's because we actually have a two tail distribution so we're gonna have 2.5% in each tail. And so if I take 100% and subtract 2.5%, I get 97.5%, which is 0.975. So that's why we use that value to calculate our critical T value. So now that we have our critical devalue, this means that the critical range is going to go from -2.064. 22.064. And so now we just need to look at our calculated T value. Which is 2.65 and compare it to this critical range. And here we see that 2.65 is actually greater than the upper bound of our range of 2.064. That means that our calculated T value falls outside of our critical range. So that means that the answer to this question is going to be no. Our T value does not fall in between minus T 0.95 and T 0.95. That's because our T value falls outside of that critical range that we calculated. So that is going to be the answer for this problem. So I hope that this explanation has been useful, and I'll see you in the next video.

You research prices of cell phones and find that the population mean is $431.61. In Exercise 19, does the t-value fall between -t0.95 and t0.95?

Key Concepts

Population Mean

t-Distribution

Hypothesis Testing

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