Conduct the appropriate test. A simple random sample of size n=65 is drawn from a population. Th

Conduct the appropriate test. A simple random sample of size...

Key Concepts

P-Value

The p-value is the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true. It quantifies the evidence against the null hypothesis; a smaller p-value indicates stronger evidence in favor of the alternative hypothesis, guiding the decision on whether to reject the null hypothesis.

Significance Level

The significance level, denoted by alpha (?), is the threshold for determining whether the observed data is sufficiently extreme to reject the null hypothesis. It represents the probability of making a Type I error, which is the error of rejecting a true null hypothesis. A lower significance level means that stronger evidence is required to reject the null hypothesis.

Null and Alternative Hypotheses

In the context of hypothesis testing, the null hypothesis is a statement of no effect or no difference, while the alternative hypothesis represents the presence of an effect or difference. The formulation of these hypotheses is critical because it defines the framework of the test and determines the direction and type of statistical test to be used.

One-Sample t-Test

The one-sample t-test is used to compare the sample mean to a known or hypothesized population mean when the population standard deviation is unknown. This test is particularly useful when dealing with small or moderate sample sizes because it accounts for the additional variability by using the sample standard deviation to estimate the standard error of the mean.

Hypothesis Testing

Hypothesis testing is a statistical method used to make inferences or decisions about a population parameter based on sample data. It involves setting up a null hypothesis that represents a default or no-effect scenario and an alternative hypothesis that represents a claim or difference that one is testing for. The testing procedure quantitatively evaluates whether the sample evidence is strong enough to reject the null hypothesis in favor of the alternative hypothesis.

Transcript

00:01 The following is the solution to number six, and this gives us some information that 65 randomly selected individuals, or whatever, there's no context to this problem, but the sample mean of that sample was 583 .1, with a sample standard deviation of 114 .9.

00:18 And we're supposed to test at the significance level of 10 % or 0 .1 if the population mean u is different from 600.

00:27 So first off, the reason why we don't care about how the population is distributed is because the sample size is large enough.

00:35 So as long as the sample size is 30 or more, it doesn't matter how the population is distributed.

00:40 And we're going to use a t test here.

00:43 And the reason why we have to use a t test is because of that right there.

00:46 We're given the sample standard deviation, not the population standard deviation.

00:52 Okay, so because we're given s, we need to use the t test.

00:55 And it's a five -step process.

00:57 The first step is to state our hypotheses.

01:01 So there's a null and alternative.

01:03 And the null always says something about equality.

01:06 So the population mean u is equal to the 600.

01:09 And the alternative, you kind of have to do a little bit of searching, but it says, is it different? and any time we don't know if it's greater than or less than, then we're just going to say not equal to.

01:19 So it's different.

01:20 So this is a two -tail test here, so not equal to 600.

01:24 Okay, so that's the first step.

01:25 Second and third step, they kind of go hand in hand.

01:30 So i'm going to say t equals and the p value equals.

01:32 So in step two, you find the test statistic, and you're going to find that.

01:37 You can use the formula or you can use technology.

01:40 I'm going to use technology.

01:41 And then you can also use the p value.

01:42 They're using a chart or technology.

01:44 And again, i'm going to use technology.

01:46 So t -i -84 is a good tool to use here.

01:49 If you go to stat and then arrow over to tests, we're going to go to that t -test, and then just make sure that the, the stats is highlighted...

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