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Cuestion 1ptsTwo samples are shown in the table: Both have normal distributions The means for the two populations are thought to be the same: Is there dlifference i...

Question

Cuestion 1ptsTwo samples are shown in the table: Both have normal distributions The means for the two populations are thought to be the same: Is there dlifference in the means? Test at the 5%6 level of significance: What is the null hypothesis?Sample Standard DeviationSample SizeSample MeanPopulation Population 80 Pa > #B0 #4 $ #B0 /4

Cuestion 1 pts Two samples are shown in the table: Both have normal distributions The means for the two populations are thought to be the same: Is there dlifference in the means? Test at the 5%6 level of significance: What is the null hypothesis? Sample Standard Deviation Sample Size Sample Mean Population Population 8 0 Pa > #B 0 #4 $ #B 0 /4



Answers

Use Table 5 in Appendix $B$ to find the critical value(s) for the alternative hypothesis, level of significance $\alpha,$ and sample sizes $n_{1}$ and $n_{2}$. Assume that the samples are random and independent, the populations are normally distributed, and that the population variances are (a) equal and (b) not equal. $$H_{a}: \mu_{1}>\mu_{2}, \alpha=0.01, n_{1}=12, n_{2}=15$$

Question number nine question eight. When testing actually empower the difference of population means. We use the students, the distribution or the normal distribution, exact population standard divisions All for one and also to are both known. Then the sample test statics follows the normal the normal distribution. Thanks it follows the students distribution since alpha one aimed also to our post unknown assemble test statics follows the student's T. Distribution question and maybe then I'll hype with the state that the population means or equal or that there is no difference between the population means. So it's not two new one equal you too. The alternative hypothesis. State the opposite of the null hypothesis according to the claim. Different or not equal. So each one, two New 1, not equally you too. So the reason it would be each note to new one equal New too And each one to new one not equal new too. Number two. Mhm. Given it's not To me one equal you too. Each one to a new one not equal you too explore one equal 10 is one equals 3 In one. Equal 49 export to equal 20. Is to be crawling four into equal 64 and go more equally. Point is you want do you mind the difference in sample means Explore 1- Explore to equal then minus 12. Equal minus two, remind the test statics. See England Explore one export to over square root. It's one square over in one plus is to squared over and to equal 10 minus 12. Mhm. Playing route three or 2/49. Yes. Hold on to over 64. This equal -3 points. You 3 7 question number D. Yeah, it's known to new one equal youtube and each one To Me one Not Equal Mewtwo. And it's it's one bold equipment. It's one equal 3 In one. Equal 49. It's 24 full. Well is to 24 into equals 64. And Grandma Equal Brings You one. Did you mind the difference in sample rooms? I'm bored minus extra bro, equally. 10 minus 12. Equal minus two. Let's remind the test statics T equal 10- toiled over square root 342 over 49 plus 442 over 64. Equal .3.037. The b value is the probability of obtaining the value of the test, static or a value more extreme. The p value is a number or interval In the column title of Table six containing the t. value in the room. The uh the f equal minimum In 1 -1 And into -1 equal minimum 49 -1 and 64 -1. Equal 48 is bigger than 45. So the it's bigger than .0010. And listening 0.1 you issue number. Eat the same steps of question number the and in the christian review we obtain that be his biggest sin .001. And listen point you want to do. If the P value is less than or equal to the significance level, then the null hypothesis is rejected. So P is less than .01. So reject H no question the same steps for the number question number D. and in question # three We obtain that B is less than .01. So reject. To each note. There is sufficient evidence to support the claim that the population means or different.

Problem. Six degree of freedom in the variance are equal degree freedom. Equal toe end one was any to minus two if the various not equal so is equal to the minimum between anyone minus one and any to minus one. So we turned 80. So the critical value corresponding to the degrees of freedom using table five and also equal to open toe one to thine eso they're critical. Very equal toe posted warning and 2.7 or eight and the corresponding toe. This degree of freedom physical value is equal to possible negative. 2.87 Yeah.

If the population variances are equal. So the degree of freedom is equal to anyone was in two minutes to 15 plus eight. Mine assumes you put 19. You know the population variances are not equal. So degree freedom equal to the minimum off. Anyone minus one is 12 and into minus one, which is which is 7727 Accordingly, the critical value Using table five it happened experience offer able toe open or 51 team. So the critical very first correspondent degree freedoms equal toe 1.7 to 9 and the critical very corresponding to the degree freedom is equal toe 1.895

Little mind the degree of freedom So the population variants are equal. So the degree of freedom is equal toe and one plus end to more than US two, which is equal to 11 plus 14. 12 23. If the variance are not equal, degree of freedom is minimum. Oh, yeah. In one win this one which is 10 and in the Tu minus one inches 13. So we should stand. So the critical value are in the role with degree of freedom and all for April toe 0.1 to tell 10. 5 appendix B. So for a he is equal to positive or negative. 4.714 A. T is equal most of many things. 1.812


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