Large Data Sets from Appendix B. Use the data set from Appendix B to test the given claim. Ident

step 1 So for this problem, we're using alpha or significant flow of 0 .01. And there's a claim that wh

Large Data Sets from Appendix B. Use the data set from...

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 formulating two competing hypotheses — the null hypothesis and the alternative hypothesis — and using a test statistic calculated from the data to determine whether there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.

Null Hypothesis

The null hypothesis is a statement that assumes no effect or no difference in the population parameter being tested. It serves as the baseline or default assumption, and the statistical test is designed to determine whether there is enough evidence to challenge this assumption. In hypothesis testing, the null hypothesis is generally stated in a way that indicates status quo or equality.

Alternative Hypothesis

The alternative hypothesis is a statement that contradicts the null hypothesis. It represents what the researcher is trying to provide evidence for, such as a difference, effect, or relationship in the population. The direction of the alternative hypothesis (one-tailed or two-tailed) depends on the research question and the specific claim that is being tested.

Test Statistic

The test statistic is a calculated value from sample data that is used to decide whether to reject the null hypothesis. It quantifies the degree of agreement between the sample data and the null hypothesis, and its distribution under the null hypothesis is known. Common test statistics include the z-score and t-score, depending on the type of test and the data characteristics.

P-value

The P-value is the probability of observing a test statistic as extreme as, or more extreme than, the value computed from the sample data, assuming that the null hypothesis is true. It provides a measure of the evidence against the null hypothesis; a smaller P-value indicates stronger evidence in favor of the alternative hypothesis.

Critical Values

Critical values are the threshold points on the probability distribution of the test statistic that define the boundaries of the rejection region. These values are determined by the chosen significance level (alpha) of the test. If the computed test statistic falls beyond the critical value(s), it suggests that the observed data is unlikely under the null hypothesis, leading to its rejection.

Conclusion about the Null Hypothesis

Based on the comparison of the test statistic with the critical value(s) or the evaluation of the P-value relative to the significance level, a conclusion is drawn regarding the null hypothesis. This decision will be either to reject the null hypothesis if there is sufficient evidence, or to fail to reject it if the evidence is not strong enough.

Final Conclusion Addressing the Original Claim

The final conclusion involves interpreting the result of the hypothesis test in the context of the original research claim. It summarizes whether there is significant evidence to support the claim or whether the data do not provide adequate evidence to refute the status quo described by the null hypothesis, thus directly addressing the question posed.

Transcript

00:01 So for this problem, we're using alpha or significant flow of 0 .01.

00:05 And there's a claim that wheat paintings are manufactured so that the weights have a standard deviation equal to 0 .03 grams.

00:13 And the data we're using is the data set 29 from the text book.

00:17 And we're mainly going to be looking at the column post -1983 pennies.

00:22 So first, let's identify the null hypothesis.

00:27 We're testing our standard deviation, since standard deviation is equal to the 0 .0 .03 grams.

00:39 Our alternative is going to be that sigma.

00:43 There's no indication less than or greater than, so as long does not equal 0 .0 to 330 grams.

00:52 So this is a two -tail test.

00:55 So first let's get our test statistic.

01:02 Since this data is relatively large, i've done everything with an r and i'll write down codes when they're necessary.

01:09 But first, before we even get our test statistic, if you're at least, looking at the data set, there's a few columns that will say n .a.

01:18 So there's just some information that's not a variable, and this does affect our calculations within r.

01:25 So to get big set, when you're saving your data set, or when you're saving your column to something else, so i called it post .pennies, you're going to use the function na.

01:44 Omit.

01:46 And then this will be the data set.

01:56 So this will emit any nas columns or any value values that will be there.

02:04 So with that little side note out of the way to calculate the test statistics, since we're testing the standard deviation, it's going to be at kai squared and it's going to be n minus 1 s squared divided by sigma squared and this is about equal to 18 .482.

02:33 Next we can calculate the p values or the p value again i'm doing this with an r and to calculate the p value for our kai square distribution is going to be p kai squared and where i put in our test statistic our degrees of freedom and minus one and where i have lower dot tail equals something.

03:04 So this is since this is a two -tail test, we're going to take the p -value and we're going to multiply by two...

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