Please provide the following information. (a) What is the...

Please provide the following information. (a) What is the level of significance? State the null and alternate hypotheses. (b) Find the value of the chi-square statistic for the sample. Are all the expected frequencies greater than 5 ? What sampling distribution will you use? What are the degrees of freedom? (c) Find or estimate the $P$ -value of the sample test statistic. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories? (e) Interpret your conclusion in the context of the application. Census: Type of Household The type of household for the U.S. population and for a random sample of 411 households from the community of Dove Creek, Montana, are shown (based on Statistical Abstract of the United States). Use a $5 \%$ level of significance to test the claim that the distribution of U.S. households fits the Dove Creek distribution.

Please provide the following information.
(a) What is the level of significance? State the null and alternate hypotheses.
(b) Find the value of the chi-square statistic for the sample. Are all the expected frequencies greater than 5 ? What sampling distribution will you use? What are the degrees of freedom?
(c) Find or estimate the $P$ -value of the sample test statistic.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?
(e) Interpret your conclusion in the context of the application.
Census: Type of Household The type of household for the U.S. population and for a random sample of 411 households from the community of Dove Creek, Montana, are shown (based on Statistical Abstract of the United States).
Use a $5 \%$ level of significance to test the claim that the distribution of U.S. households fits the Dove Creek distribution.

Key Concepts

Confidence Interval

A confidence interval is a range of values, derived from sample data, that is likely to contain the true value of an unknown population parameter. In the context of comparing means, it provides a set of plausible values for the difference between the two population means, allowing us to assess the magnitude and direction of the difference.

Confidence Level

The confidence level, such as 90%, indicates the probability that the confidence interval constructed from repeated samples would contain the true parameter value. It quantifies the level of certainty we have in our estimation process and helps in determining how much trust we can place in the interval as a reflection of the true difference.

Inference about Difference of Means

When a confidence interval for the difference of means includes only positive values, it suggests that there is a statistically significant difference between the two population means at the given confidence level. This implies that one mean is consistently higher than the other, leading to the conclusion that there is strong evidence favoring a difference in a specific direction between the groups under study.

Transcript

00:01 Following is the solution to number six, and this compares the distribution of u .s.

00:05 Households with the dove creek distribution.

00:08 So i did a little preliminary work here with observed and expected.

00:11 So they give you the observed for, i think it was 411 residents, and there are 102 that were, you know, certain, i don't know if it was age range or something, 112, 33, 96, and then 68.

00:24 So that was given to you.

00:25 And then for the expected, they just gave you the percentage for the u .s.

00:30 Best population.

00:32 And what you have to do is you got to take that percentage times the sample size to get the expected value.

00:37 So i took 26 times 26%, so .26 times 411 and i got 106 .86.

00:43 And then 29 % times 411 to get 119 .19.

00:47 And so on and so forth.

00:48 So that's what i did first to get my observed and my expected.

00:51 So now we're ready to go.

00:53 Okay.

00:53 So the first part is the alpha value or the significance level, and that's given to you.

00:58 So the alpha value is the significance level and that's 0 .05.

01:00 And then we're also supposed to say what our null and alternative hypotheses are.

01:05 So i'm going to kind of paraphrase this, but the null hypothesis always says that these two distributions are equal.

01:10 So we're going to say the distribution of u .s.

01:15 Households fits dove distribution.

01:29 And you can kind of pretty that up if you want.

01:31 And then the alternative, i'm not going to write all of it, but it's just the opposite of it.

01:35 So it's not.

01:35 So it means the distribution of u .s.

01:37 Households does not fit the dove creek distribution.

01:40 Okay, so then the next thing, from here we're basically just going to use software.

01:44 So we're asked to find the kai square value, our test statistic, which you can use the formula, you can use excel, ti84, whatever software you want.

01:55 But before we do that, we have to find the expected values, make sure that they're all greater than five.

02:01 And if you go back here and double check, they are all greater than five.

02:05 So the expected value, that's one of those conditions for inference.

02:07 The expected values all need to be greater than five, and they are.

02:10 And we also need to say what type of distribution this is going to follow...

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