Of a random sample of 69 health insurance firms, 47 did public relations in-house, as did 40 of

Of a random sample of 69 health insurance firms, 47 did...

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to decide whether there is enough evidence in a sample of data to infer that a certain condition holds true for the entire population. It involves setting up a null hypothesis, which represents a statement of no effect or no difference, and an alternative hypothesis that represents a research claim. The decision is made based on the outcome of a statistical test applied to the sample data.

p-value Interpretation

The p-value is a measure that helps determine the significance of the results from a statistical test. It represents the probability of obtaining test results at least as extreme as the ones observed, assuming that the null hypothesis is true. A small p-value indicates that the observed data is unlikely under the null hypothesis, providing evidence against it, while a large p-value suggests that the data is consistent with the null hypothesis.

Two-Sample Proportion Test

A two-sample proportion test is used to compare the proportions from two independent samples to determine if there is a statistically significant difference between them. This test is particularly useful when comparing rates, percentages, or proportions from two different groups. It involves calculating a test statistic usually approximated by a normal distribution when sample sizes are large enough, and it accounts for the variability in both groups.

Null and Alternative Hypotheses

In the context of comparing two population proportions, the null hypothesis typically states that the difference between the two proportions is zero, meaning they are equal. The alternative hypothesis is a two-sided statement asserting that the proportions are not equal. Formulating these hypotheses correctly is crucial for conducting the test and interpreting its outcome.

Statistical Significance

Statistical significance is a determination of whether the observed effect in sample data is strong enough to be considered not due to random chance alone. If the p-value falls below a predetermined significance level (commonly 0.05), the results are deemed statistically significant, leading to the rejection of the null hypothesis. This concept is central to making inferences about the population based on sample data.

Transcript

00:01 So we'll have our null hypothesis being that the two proportions for in -house public relations that they are equal for the health insurance and the casualty insurance companies, and alternately that they're different, so that their difference will not be zero.

00:19 We have our two proportions, our p -hap for the health insurance, is the 47 out of 69, and for the casualty insurance, they had a 40.

00:33 Out of 69 did theirs in -house.

00:36 And our pooled key will be the sum of these two, which will be 87 out of the sum of these two, which will be 138.

00:46 And that value comes out to be, let's see, that value comes out to be approximately 0 .63.

01:01 And each of these, this is approximately 0 .68, and this is approximately 0 .58.

01:07 So, you know, just looking at it, you might think, oh, that's a 10 % difference.

01:11 That should automatically be that there is a difference.

01:13 But we will see.

01:15 It depends on the sample size.

01:17 So let's calculate that test statistic.

01:19 The test statistic is the difference in these two proportions, so the 4769th minus the 40 69th.

01:28 And then divided by, and we'll take that pooled p, one minus the pool of p or its complement and i'll just write that down and one over 69 plus one over 69 and when we get that test statistic it comes out to be 1 .2345 no i'm not kidding it does come out to be 1 .2 345 and we want to find the p value for this and then interpret it so let's draw a picture we're doing a two -sided test so we're assuming that that this difference is zero...

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