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5. (20 points) Usingthe followingdata. let p1 bethe true proportion ofmen that are Left- Handedand pz be the true proportion of Left- Right- wonen that are Leff-Han...

Question

5. (20 points) Usingthe followingdata. let p1 bethe true proportion ofmen that are Left- Handedand pz be the true proportion of Left- Right- wonen that are Leff-Handed_ Handed Handed Ambidextrous Test Ho: p = pi against HA: P1 pz . Women 141 Men 21 123 a) Which test statistic should be used?b) What is the value ofthe test statistic for this data? c) What is the p-valuecorespondingto the valueof the test statistic? d) Ifa = .05. based on the p-value what is Your conclusionabout the nullhypothesis

5. (20 points) Usingthe followingdata. let p1 bethe true proportion ofmen that are Left- Handedand pz be the true proportion of Left- Right- wonen that are Leff-Handed_ Handed Handed Ambidextrous Test Ho: p = pi against HA: P1 pz . Women 141 Men 21 123 a) Which test statistic should be used? b) What is the value ofthe test statistic for this data? c) What is the p-valuecorespondingto the valueof the test statistic? d) Ifa = .05. based on the p-value what is Your conclusionabout the nullhypothesis Briefly explain.



Answers

To investigate a possible relation between gender and handedness, a random sample of 320 adults was
a. Give a point estimate for the difference in the proportion of all men who are left-handed and the proportion of all women who are left-handed. b. Construct the $95 \%$ confidence interval for the difference, based on these data. c. Test, at the $5 \%$ level of significance, the hypothesis that the proportion of men who are left- handed is greater than the proportion of women who are. d. Compute the $p$ -value of the test.taken, with the following results:

What in this problem, we want to determine the follow if the output voltage is normally distributed with standard deviations 0.25 volts and the manufacturer, which is to test the null hypothesis new equals five volts because the alternative is not equal five. Using a sample size, n equals eight, calculate the p value of the observed test statistic is one of a few. See this question is challenge your understanding of the language hypothesis testing and proper implementation to solve it to determine the p w i E. The probability we observed data as a more extreme than he's given X five. So we utilize the standard normal distribution to find first, calculate Z. So for export equals 5.20 is 5.2 minutes, 5.25, 28 people, 2.26. That's because it's a two tailed tests, you cannot equal five. Our p value is two pz greater than zero equals 00.119. We follow identical steps, A, B and C and B. R. Z values 3.39. Thus two pz lessons or not because this is a negative value is 20.3. Finally, and see, Xena is 1.13. That's the p value is two pz greater than zero equals 00.1292

What in this problem, we want to determine the follow if the output voltage is normally distributed with standard deviations 0.25 volts and the manufacturer, which is to test the null hypothesis new equals five volts because the alternative is not equal five. Using a sample size, n equals eight, calculate the p value of the observed test statistic is one of a few. See this question is challenge your understanding of the language hypothesis testing and proper implementation to solve it to determine the p w i E. The probability we observed data as a more extreme than he's given X five. So we utilize the standard normal distribution to find first, calculate Z. So for export equals 5.20 is 5.2 minutes, 5.25, 28 people, 2.26. That's because it's a two tailed tests, you cannot equal five. Our p value is two pz greater than zero equals 00.119. We follow identical steps, A, B and C and B. R. Z values 3.39. Thus two pz lessons or not because this is a negative value is 20.3. Finally, and see, Xena is 1.13. That's the p value is two pz greater than zero equals 00.1292

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.

We have n equals 25 values, transformers, symmetric, mound shaped distribution sample mean is equal to 10 and the sample standard deviation is equal to two. Using a significant level of alpha equals 20.5 conducted to tail test of new equals 9.5 on the stand for the population. Me first, you have to answer A. Is it appropriate to use a distribution for hypothesis test for this? Yes. It's the distribution of symmetric and mount shape so we can use a student's T distribution. Note that the degrees of freedom is equal to end minus one is equal to 24 in this case, next one of the hypotheses, the hypotheses are h not mu equals 9.5. An alternative hypothesis. You does not equal 9.5. Next let's compute t remember the formula for tea, which is given here. This computes out the T value 1.25 Next let's compute the p p interval using a T interval. We see that P falls between 0.2 and 0.25 for this T statistic. Next we deserve and whether or not we reject asian art. No, the entire P interval is greater than our significant level alpha. So we do not reject a chart, and we interpret this to mean that we lack evidence that suggest new. It's not equal to 9.5.


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