In example 3, we're given the following data that represents the age in weeks of which a baby first crawls based on a survey done with 12 mothers. We're going to assume that the age of these babies crawling, that the data is normal. And why is that important?
Because that means we can actually find the confidence symbol since we're just told that our distribution is normal. Okay, so in example... you're asked to determine the point estimate for the mean age baby's first crawl.
Alright, so to find the point estimate that means we need x bar. Now what you could do is you can take all these values, add them up, and then divide by 12 because they're 12 data values. Okay, or what you can do is remember back in the day when we started talking map data, we can do the following. We can use our calculator, go to stat, go to edit, and then enter your data values here. And so I have all 12 data values already in my calculator, and what I'm going to do now is go to stat, go to the right where it says calc, and select the first option, one bar stat.
Why? Because look, it already gives me the the statistics I want. It gives me the sample mean. It also gives me the sample standard deviation.
Remember to use s, not sigma, because I want the sample standard deviation. So let's write down what these values were. They were 38.25, s is 10.001, and n equals 12. So Without having to actually do all this work, you can use your calculator to get your x bar.
So x bar is 38.25. Okay, in part b, you have to find the margin error to construct a 90% confidence interval. So when we are constructing a 90% confidence interval, that means the middle of the curve represents 0.90. That means each tail then should be represented by 0.05. Okay, if each tail represents 0.05 and our degree of freedom in this case is 11 because one less than 12 is 11, then we go to our table and if we go to our table, let's see.
So the right tail is 0.05 and our degree of freedom is 11. So it looks like it's... 1.796 that we are interested in. Okay, so that's our critical value. Once again, it was 1.796. Okay, and our margin error, once again, is going to be the critical value.
times the s which we got on our calculator, divided by the square root of our n which is 12. And if you type this on your calculator, it's approximately 5.18 psi. Okay, then in part c, you're asked to construct and interpret a 90% confidence zero for the true mean age that babies first crawl. Okay, okay, so Our lower bound is going to be x-bar minus the margin error, so 38.25.
Subtract the margin error, which gives us 33.065. Our upper bound is x-bar plus the margin error. So this gives us an upper bound of 43.43.
Now let's actually interpret this. So an interpretation could be, we are 90% confident that the true mean age Baby's first crawl. is between 33.065 and 43.435 what? What are the units of these numbers?
Percent, times, what do they represent? They represented the number of weeks that babies first crawl. weeks so the units for this will be weeks