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Chapin Social Insight test is designed to measure how accurately the subject other people. The possible scores 4Ppquises = range from t0 41. The test was given EWO ...

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Chapin Social Insight test is designed to measure how accurately the subject other people. The possible scores 4Ppquises = range from t0 41. The test was given EWO random groups 0f 13 male students and 16 female students: The results are shown below: Group Sex Sample Mean Score Sample Standard Deviation Male 26.97 5.05 Female 23.86 5555%/ level 'significance test {0 assess if the data support the contention that Conduct differ in average social insight: Since the population standard male an

Chapin Social Insight test is designed to measure how accurately the subject other people. The possible scores 4Ppquises = range from t0 41. The test was given EWO random groups 0f 13 male students and 16 female students: The results are shown below: Group Sex Sample Mean Score Sample Standard Deviation Male 26.97 5.05 Female 23.86 555 5%/ level 'significance test {0 assess if the data support the contention that Conduct differ in average social insight: Since the population standard male and female students f-test is indicated instead of a z-test: deviations are not known: appropriate E hypotheses: Write down for this Iest? statistic - Whai is the (eS for tlc test? -vulue What is the 'conclusion ItiCnns cunclude? Explain what your What You



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Testing the Difference Between Two Means (a) identify the claim and state $H_{0}$ and $H_{a}$, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic t, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology. Annual Income A personnel director from Pennsylvania claims that the mean household income is greater in Allegheny County than it is in Erie County. In Allegheny County, a sample of 19 residents has a mean household income of $\$ 49,700$ and a standard deviation of $\$ 8800 .$ In Erie County, a sample of 15 residents has a mean household income of $\$ 42,000$ and a standard deviation of $\$ 5100 .$ At $\alpha=0.05,$ can you support the personnel director's claim? Assume the population variances are not equal. (Adapted from U.S. Census Bureau )

All right. We have a sample of size and equal 73 of the 73 objects in the sample, 56 meet a certain criteria. And you want to observe our equals 56. We want to use this data to test the claim that the population proportion P does not equal 560.82 at a confidence level of 1% or alpha equals 10.1 Now that we've identified the confidence level, we can proceed in the following steps to conduct this test first is the normal distribution appropriate to use? Yes, it is because both NP and qpr greater than five. What hypotheses are retesting? We're testing them. No P equals 0.8 to the alternative. P does not equal 0.82 meaning we're testing or rather conducting a two tailed tests for this population proportion. Next compute p hat in your test statistic Piatt is simply are over and equals 20.77 We plug that along with PQ and and into the Z stat formula on the right to obtain Z equals negative 1.18 next to the P value. The p value can be found using it a lot google and textbook. And is the area outside of our positive, negative Z scores. This is a two tailed test, A. K. A. The area to the left of negative 1.18 An area to the right of 1.18 as is highlighted on the graph on the right. This gives P equals 0.2380 Next we reject H not no, we do not because he is greater than alpha. And we interpret this finding suggests we lack evidence that P does not equal 0.82

18. So it's no if that new one is equal to mean to, and each one is that anyone is not equal commute. So the degree of freedom, the minimum off in one way, this one, which is 17 and 18 to minus one, which is 19th. So the video is 17, using all for April toe 0, 00.11 teen. So for table five, the critical, very equal toe postive or negative 1.74 So the rectory, then they contain all value smaller than negative 1.74 and all various larger than 1.74 So that is the statistic, if that makes one minus x two bar. So it's 56900 minus five 7800 minus me one minus me, too over square root off this one squared over in one, which is one toe. Once you lose your square over and once with the 18 lost, it's too square. So it's 8000 square over into approximately negative 4.267 So it's a very off statistics. Even in the final hypotheses rejected so and this value realize between the booze values. So we failed to reject the null hypothesis

Yeah, friend. Is there a difference between how competence, social acceptance and attractiveness influence our self esteem? That's what this question analyzes and we're going to be using confidence intervals to look at the differences between these. So I've written our confidence interval formula for quantitative data and I've plugged in our means are standard deviations and sample sizes for all the groups and for an 85% confidence level with degrees of freedom of 14. RtC is 1.5 to 3. Now as we go and calculate here, the difference in our averages between competence and social acceptance is is 0.52 And then our margin of error for this is 1.8665 And when we add and subtract 0.52 plus or minus 0.1 point 8665 we're going to get a confidence interval from negative 1.3465 up to positive 2.39 Okay, now notice in this interval zero is inside of this interval. So there is a good chance there is zero difference between competence and social acceptance for the second question where analyzing competence versus attractiveness. So when we run our calculations here, the difference in the means is 1.96 and our margin of error is 1.9 which leads to a confidence interval of 0.6 to 3.86 This interval is entirely positive so it definitely appears like there is a difference between competent, how competence and and attractiveness influence is our self esteem. And in our last one where we're comparing social acceptance and attractiveness, the difference in the means is 1.44 and the margin of error comes out to be two point oh 47 So our confidence interval here runs from negative 0.607 to positive 3.487 and zero is in this interval. So there is a good chance there is no difference between social acceptance and attractiveness. So the only two groups where there is a difference, is let her be comparing competence and attractiveness.

Yeah. Alright, for this problem, we want to identify the null hypothesis, the alternative hypothesis testing six. This p value or critical values are daily. We just want to do something so we can come to a conclusion about our claim. So we're giving the following information that the sample size of 56 males are mean as 16,576 words. The size of 7870. The standard deviation is 7,871 words. And we're using a significant level of 0.01. We have a claim that mills have a higher, have a standard deviation is greater than the standard deviation of 7,476 words for females. So, first we wanted to find that no hypothesis so that we are h not our highlights, some key things and claims already. So we have the standard deviation. So that's what we're testing and we are testing that standard deviations Go to 707,460 words. So that's our no hypothesis. Our alternative. We're still testing the standard deviation, but that is greater than The 7460 words. So that's our no alternative hypothesis, nests are testes cystic. Since we're testing the standard deviation is going to be a chi squared and it's going to use the formula and minus one times S squared divided by stigma squared. Yeah. And luckily here, all this information is given to us. So we just plugged it in. We should get 61 point 227 next we can find the P value. Uh huh. Um You can find the P value either through the tables or with technology like our stack crunch. Um I personally I'm using are so if we're using our you can use a function p chi square. And what we're gonna play is gonna be the test at RN -1 or degrees of freedom. And that lower don't tell is equal to false. Yeah. So the reason why this whole as far lower dot tells equal to false is if normally we're doing a one tailed test, it will assume that it's true. That's our normal position for the peace chi squared. Well if we look back up here we're doing an upper tail test. So we want a slower detail to be called false. So if you plug this in you'll see that the p value of 0.2 64 Or 0.62 four. Sorry. Yeah. And just from the p value in apple, we can make conclusions. So remember if the p value is greater than alpha, we will acceptable have assists or if the p value it's greater than alpha, we will reject the null hypothesis. So if we look at our p value we have zero 2624 And we can see that this is greater than our alpha which is 0.01. Thus we can come to a conclusion that we will accept our no hypothesis or we will fail to reject are no hypothesis at Alpha equals 0.01. Yeah, so that the results is not statistically significant.


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