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Test the claim that the proportion of people who own cats is significantly different than 10% at the 0.05 significance level. The null and alternative hypothesis wo...

Question

Test the claim that the proportion of people who own cats is significantly different than 10% at the 0.05 significance level. The null and alternative hypothesis would be:Ho:p > 0.1 Ha:p < 0.1 Ho: p > 0.1 Ha: p 0.1 Ho: p = 0.1 Ha:p = 0.1 Ho:p < 0.1 Ha:p > 0.1 Ho: u = 0.1 Ha: / / 0.1 Ho: p < 0.1 Ha: p > 0.1The test is:left-tailedright-tailed two-tailedBased on a sample of 200 people, 1% owned catsThe test statistic is:(Round to 2 decimals)The p-value is:(Round to 2 decimals)B

Test the claim that the proportion of people who own cats is significantly different than 10% at the 0.05 significance level. The null and alternative hypothesis would be: Ho:p > 0.1 Ha:p < 0.1 Ho: p > 0.1 Ha: p 0.1 Ho: p = 0.1 Ha:p = 0.1 Ho:p < 0.1 Ha:p > 0.1 Ho: u = 0.1 Ha: / / 0.1 Ho: p < 0.1 Ha: p > 0.1 The test is: left-tailed right-tailed two-tailed Based on a sample of 200 people, 1% owned cats The test statistic is: (Round to 2 decimals) The p-value is: (Round to 2 decimals) Based on this we: Reject the null hypothesis Do not reject the null hypothesis



Answers

Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Assume that a simple random sample is selected from a normally distributed population. Statistics Test Scores Tests in the author's statistics classes have scores with a standard deviation equal to 14.1. One of his last classes had 27 test scores with a standard deviation of 9.3. Use a 0.01 significance level to test the claim that this class has less variation than other past classes. Does a lower standard deviation suggest that this last class is doing better?

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.

Yeah. Okay. So way knows that. Yeah. No hypothesis. H not. Is that p is equal to 0.5 on that alternative hypothesis. H A. The P is not equal to 0.5. Okay, Now we can calculate our proportion, which is excellent. And her ex is 123 on on is 280. Uh huh. She'll give us your credit for For came. Now we can calculate the test statistic value using a calculator which will give us negative. Too unsure. Three. Um, And now you can use that to find the p value using the table. So give us a P value. She is equal to 0.0 for two. Three. Finally, since we know Alfa is your opinions your one under, if you use a two tailed critical value be find the table value for Z Alfa two, which is 2.5 eight. So now, since it's two tailed critical values, Yes, arranged to 58 Okay. And since 0.423 is greater than our the significance level of 0.1 we can fail to reject the null hypothesis. Um, and therefore it could be concluded that there was not sufficient evidence supporting the rejection of the claim that touch therapists use method equivalent around guesses failed to reject.

For this problem. We are given the following claim machines suspense amounts with standard deviation greater than 0.15 oz and we have the following information off to the side. So the first for this hypothesis tests the state or no hypothesis. So each not. We're talking about standard deviation. So sigma And it's gonna be our 1.5 oz are alternative since the claim is stating greater than it'll be sigma, Somebody greater than 0.15. So once we have our go on alternative hypothesis, let's find our testes cystic. Since we're talking about sanity, aviation, we're gonna be using the chi square distribution and the chi square testes cystic can be found by and before end minus one times as squared divided by sigma squared. Yeah, So this is going to be 27 -1. Yeah. Time 0.17 Squared Divide by 0.15 Squared. And the chi square tests should be approximately equal to 33 points 396. So I was the testes cystic, you can do the p value. There's two ways to do the people, you can either do since the sample size 27 we have a degrees of freedom. 26 But in the end -1. Since this degrees of freedom is relatively small, we can find it within the table or we can find the inequality arranged within the table. And since this is a right to test and the high score table, I'm using finds area right to the tip. Other critical values what we wanna do. We don't want to go down the degrees of freedom. Do we get to 26? We want to find the range where 33.396 is between the two numbers. So I found that is between 17 point 292. And it's gonna be less than 35 point 563. So now if we go all the way up we'll find that probably are the area to the right of the curve. So the 17.292 equivalent to 0.935.563 equivalent to 0.1. And now we have our P value. So RP values between 0.9 or 0.1 and 0.9. A more accurate where you can get your P value though is using software is like our you use the Arco p chi square which does it take the input of your chi square testes, cystic degrees of freedom and then lower dot L. Equals true or false. So the lord dot tails telling us whether it's a left tail test or right tail test. Since the right tail test, you want that to be false. If you plug in this information we should get to this p value is about 0.1 509. Which again agrees within the table method table inequality. So if you have the p value can make a conclusion by comparing your p value. What's your alpha. But you can also find your critical values. To find your critical value of critical values. Your again going to your chi square table is gonna be Since we're doing air to the right we just want our alpha. And so we are degrees of freedom. Remember that our alpha is 0.05. Our degrees of Freedom 26. So if we go to our high score table we can find were those two intersect and are critical values. 38 .885. All right. So, you can make conclusion with the critical values and your testes cystic. If you have a chi square distribution looking something like that, you're critical value. The states here Just 38.885. Okay, so you're critical value. We will reject any or don't have process. If it falls within this blue region, this is also called our rejection region. And if it falls anywhere within the non stated region, we will accept it. Which is also called our acceptance region. We see our test statistic as 33.396. So if you try to play set somewhere here that maybe belong around over there. Yeah. So that's archive square test. Yeah. And it falls within our acceptance region. So in this case for comparing test statistics and critical values we fail to reject If you want to compare with the P value and alpha. So a p value is greater than alpha. We failed to reject. H. Not. Yeah. and if P value is less than alpha, we reject H. Not again, we can look really quickly. We have AP value of 0.1509. And after a value of 0.05, our p value is greater than our alpha, so we failed to reject the null hypothesis. So in both cases we came to the same conclusion, which was we fail to reject H not.

So in this question, we have to use the right till test test on. We know that 0.1 significance level abused. That is our you, Alfa. We also know that are all hypothesis is P is equal to zero born five on their four h. A alternative hypothesis is a p is good and you're born five. Since it's a right tail test, you can show this distribution here where this is Super 15 Sure on this is the mhm. So for rejection. Okay, so now we can find peen X over and which is your one floor three and plugging if this value back into our Z. Just a statistic that test it is formula. Sorry, G p minus P not over. Square root of p. Not one minus, not over. And okay, so if you go ahead, unplug in our values. Answer with one for three minus to your point 15 over. Screwed 015 minus times old, manageable. Have over. And which is 5000 in this question and I will give us negative 1.307 Okay, so now you can use that to find r p value Yeah, And using the table, you find that it is your 0.95 six. Yeah. And this is greater than our level of significance. Is your point your one? Therefore we can reject. I don't know Auth Assis since this value folds rejection zone


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