Data released by the National Center for Health Statistics...

Data released by the National Center for Health Statistics showed that the mean age at which women had their first child was 25.0 in 2006 (The Wall Street Journal, February 4 , 2009 ). The reporter, Sue Shellenbarger, noted that this was the first decrease in the average age at which women had their first child in several years. A recent sample of 42 women provided the data in the website file named FirstB irth concerning the age at which these women had their first child. Do the data indicate a change from 2006 in the mean age at which women had their first child? Use $a=.05$.

Transcript

00:01 So we want to perform a hypothesis test.

00:05 We need the hypotheses, first of all.

00:06 Now, we don't have the data, we can go through the steps.

00:10 So the mean age at which women had their first child was 25 in 2006.

00:17 And we have some new data, and we want to know if there's a change from 2006 to now.

00:26 So that would be, is the mean still 25, like in 2006? or has it changed? is it different? to that.

00:35 Now i'm not putting a direction here because it just asks, does the data indicate a change? so it could go either way.

00:42 So this is the correct alternative hypothesis.

00:46 Sample size is 42.

00:48 The level of significance is 5%.

00:50 The other two pieces of information we need to get from your dataset are the sample mean and the sample standard deviation.

00:58 Okay.

00:59 To perform a hypothesis test, we start by assuming the null hypothesis is true.

01:03 If you were to take every sample of size 42, take the sample means and plot them out, you'd get something approximately normal.

01:12 The sample means follow normal curve.

01:14 Their mean is same as the population mean, which we think is 25.

01:18 This standard deviation is sigma over root n.

01:21 Since we don't know sigma, the population standard deviation, we only have s.

01:25 We have to use a t -test.

01:28 If you know sigma, you get to use a z -test instead.

01:32 Now i'm going to use the critical value method.

01:35 What's my sample mean fall on this curve.

01:38 If your sample mean falls, say, here, it's not 25, but it's pretty close...

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