La Leche League International reports that the mean age of...

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to make inferences or decisions about a population parameter based on sample data. It involves establishing a null hypothesis, which represents a default position or a statement of no effect, and an alternative hypothesis that reflects the research question or the presence of an effect.

Null Hypothesis and Alternative Hypothesis

The null hypothesis (H0) is a statement that there is no significant difference or effect, while the alternative hypothesis (H1) is a statement that there is a significant difference. In the context of testing mean weaning age, the null might assert that the mean weaning age is equal to or greater than a specific value, while the alternative would assert that it is less than that value.

Test Statistic

The test statistic is a standardized value calculated from sample data, used to assess how much the sample diverges from the null hypothesis. In many cases, especially with small sample sizes and unknown population variance, this statistic follows a t-distribution, and is computed using the sample mean, the hypothesized mean, the sample standard deviation, and the sample size.

t-Distribution

The t-distribution is similar to the normal distribution but has heavier tails, which allows for the extra uncertainty introduced by estimating the population standard deviation from a small sample. It is particularly useful in hypothesis tests involving small sample sizes, where the true population variance is unknown.

p-value

The p-value quantifies the probability of obtaining a test statistic at least as extreme as the one computed from the sample data, assuming the null hypothesis is true. A small p-value indicates that the observed data is unlikely under the null hypothesis, leading to its rejection in favor of the alternative hypothesis.

Significance Level

The significance level, often denoted by ?, is a threshold chosen by the researcher to decide when to reject the null hypothesis. It represents the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true. Common significance levels include 0.05 or 0.01.

Transcript

00:03 Hi and thank you for taking my answer.

00:05 This question.

00:07 So this is question 103 from the textbook, and it's talking about the mean age of we need and la leche league claims that the mean weaning age is greater than four for greater.

00:24 And we took a sample in america and we're trying to test if that claim, uh, is valid or not.

00:34 So first we want to set up our knoll and alternative hypothesis.

00:40 So what i have here is that the no hypothesis is the claim by little h a league that the mean winning age is four years or greater.

00:53 An alternative hypothesis is gonna be that the meanest less than for so now the question says that they took a sample of 21 children, and they said that the mean and i'm gonna put the mean in years, so the mean is gonna be 9/12 of a year because we take months and divided by 12.

01:23 That'll give us the same units as our claim, and the standard deviation is gonna be four out of 12 years for 12.

01:33 So because we're not given a population standard deviation, we were never told the true standing ovation of the population.

01:43 Our random variable for the sample x bar.

01:48 Our random variable is gonna follow a t distribution aura.

01:53 Students to distribution.

01:58 Now we're given the sample mean the sample standard deviation in the sample science.

02:03 So we can go ahead and calculate our test statistic for the students to distribution our test statistic on your race.

02:25 Make some more room here.

02:35 Okay? our test statistic t is gonna follow like this.

02:46 We're gonna take our sample, mean expert, we're gonna subtract away the i mean, under the no hypothesis of the claim you.

02:56 Now we're gonna divide it by our sample standard deviation divided by the square root of our sample size.

03:04 So now, using our data from our sample, she is gonna equal nine over 12.

03:13 That's our sample.

03:14 Mean we're gonna subtract away the claim, which is four years, and divide that by our sample standard deviation s, which is four out of 12 yours divided by the square root of our sample size.

03:39 Which is tor you.

03:44 Okay.

03:45 And when you calculate that you're going to get a value of about 44.

03:52 Excuse me? negative 44 the 0.52 so that is our test statistic.

04:02 Now, using that in the calculator, we can calculate a p value.

04:08 So let me draw occur for this.

04:13 So remember, this is gonna be a t distribution zero and then blew.

04:24 Negative.

04:25 44.5 is gonna be very far away from the curve.

04:30 It's gonna live somewhere out here.

04:33 That's our test statistic from our sample and r p value is going to be remembered the area to the left...