5

Problem 9_ Consicler the accompanying sample data. 0.2 0,5 1,1 0.8 0.3 Apply the One-Sample Test for hypotheses for signilicance level 0.05_ Ho : / - 1 Ha : / < ...

Question

Problem 9_ Consicler the accompanying sample data. 0.2 0,5 1,1 0.8 0.3 Apply the One-Sample Test for hypotheses for signilicance level 0.05_ Ho : / - 1 Ha : / < 1.

Problem 9_ Consicler the accompanying sample data. 0.2 0,5 1,1 0.8 0.3 Apply the One-Sample Test for hypotheses for signilicance level 0.05_ Ho : / - 1 Ha : / < 1.



Answers

Using Confidence Intervals to Test Hypotheses Test the hypotheses in Problem 25 by constructing a $99 \%$ confidence interval.

The following is a solution video to number 10 and we look at Hypothesis test where the difference of two, population proportions is .15 and then the difference of two populations is greater than .15. We're testing at the 10% level of significance using this data. So we're going to find the Z value first, the test statistic and we take the observed differences which is 0.41 minus 0.23 minus the expected or the hypothesized difference, which is 0.15. And then I divide that by the standard error which is .41 And then times 1 -11 which is 59. And that's divided by that sample size of 950 plus two, three Times 1 -13 which is .77 And divided by the sample size of 500. And then we should get 1216. Okay, so 1.216. Now I need to find the p value and the p values the probability That I get a sample statistic greater than 1.216. This is the right tail test. So I go to a normal CDF And I go to 1.216. And then here is a just a large number, Positive No. I put the 99 and then I paste and I get point 112. Okay, so the p value is 0.112 and then I compare that to my alpha value of 10. That is in fact greater than α. So I'm going to fail to reject h not any time the PV is greater than alpha we do not reject the null hypothesis. Okay, very similar for number two. This time it's just a two tailed tests. Were testing that it's not equal to. So that tells us it's a two tailed test and we're testing at the 10% level of significance. So Z Is equal to the again the observed differences .9 to -18 minus the hypothesized difference of 0.10 divided by square root Of .92 Times 1 -12, divided by that sample size Plus .78 Times 1 -18. Which is .22 divided by that sample size. And whenever you plug that in you should get 1.066 as your test statistics. So now this one's a little bit tricky I'm going to find the probability for the p value. I'm gonna try to find the probability That I get a sample statistic greater than 1.066 or less than negative 1.066. So because the two tailed tests I'm essentially just going to find the probability that I get a sample statistic greater Than at one um 066. And then I'm just gonna multiply by two. So that's the one thing you need to remember for p value with the two tail test is you need to multiply things by two. So you should get .2864 Whenever you do that. So zero 0.2864 is my P value. Then we explicitly compare that P value with the alpha and that's bigger than basically in the alpha you're ever gonna have. So we're gonna fail to reject this one as well, so fail to reject H. Not so whenever the P value is greater than alpha, we do not reject the null hypothesis.

I don't know this for sure to find out about 95% or more in the book. Find out you 95% one minute interval that only the finance. What is the 23.6 sample and division is similar to be done for seven the sopranos Temple leather Around 40 others coming up we have as 11.7 or words meant to be route and and and sporty so they calculate that next told us So we got the values, see that's coming up to be raising interest coming up at 1.85 1.85 Next to the confidence interval. We just do hear experts. So we are only 3.6 plus minus critical value of T and an independent homeland interval are similarly with 2.2 9 1.85 to solve this and get a competent trouble. We're in trouble. That's coming out to be 19.85 19.85 days. The lower bound And after one is coming from 7.3 board from the standpoint before too. Upper bound bigger population means coming out of the 35.1 he here 35.1 is out of this range, right? 25.1 out of this rain. So their properties including the question therefore we have uh it's not right, it's out of range here, not like the interval who reject that's north right. That is God thank you

The following is a solution to number nine and were asked to perform a two sample Z test to test the difference population means being 57 or less than 57 we're gonna test it at the 10% level of significance. Now, the reason why we're able to use the two simple Z test is because these sample sizes are large enough. Typically, if you don't know the population standard deviation, you need to use the T test. But after a certain point, in fact, whenever the sample sizes are greater than 30 Z and the T test essentially will converge the same thing and these sample sizes are plenty big in order for that to happen. So we're gonna use the Z test and we're gonna use the p value method. So first we need to find the test Statistic and we'll find that probability here in a second. So it's the difference of the sample means which is 1309 -12, 58 And then minus the hypothesized difference, which was 57, so -57, and then that's divided by the square root of the Sample standard deviation squared or the variance, which is 42 squared divided by that sample size, 117 plus the 37 squared. So that second standard standard deviation squared And divided by that sample size, which was 133. And whenever you plug that in the calculator carefully, you should get at least a negative 1.191. So that's our test value. Now we don't need to find a critical value. So we can jump right into the p value and we need two things for to find the p value first. We need to know whether this is a one taylor to tail and is it one tail? Because it's it's less than sugar lesson, it's the left tail. And we also need to know the area, the alpha value of .10. So you can use a chart for that, but I like to use a calculator. You can also use a calculator if you go to a normal CDF and the lower boundary will just be some negative large number and then the upper bound will be negative 1.191 and the standard deviation zero and one. The mean and standard deviation will be zero and one. And you get this .1 17. Now actually I misspoke you don't even even know you know that stuff because all we're gonna do this is the nice thing about a p value method. All we need to do here is take the p value, the probability which is 170.117 and compare it to the alpha value and 0.117 is slightly greater than that alpha value of 0.10, and any time the alpha value is greater than 10 than or greater than the I'm sorry, any time the p value is greater than the alpha value than we fail to reject H knob. So we're failing to reject the null hypothesis. So part two or part B. It's essentially the same thing, but this time it's gonna be a two tailed tests are p value. We just have to double check. We need to make sure that we multiply by two at the end, but we're giving pretty similar data here. Again, we're going to use the Z test because those sample sizes are big enough. So let's find that test statistic. It's the difference of the sample means which is 16.9 -18.6 minus the hypothesized difference, which was negative 15. And then that's divided by the sample variance, which is the standard deviation squared Divided by that sample size of 65 plus the other standard deviation squared Divided by that sample size, which is 57. And whenever you carefully put that in the calculator, I got about negative point 9 to 0. So we're going to find the probability that it's less than that. And then we'll multiply by two. So the p value, we're going to again turn to the calculator or table if you so wish. But I'm gonna use a calculator distribution, normal CDF, the lower bound is a negative large number. The upper bound will be negative 0.92 And then the mean and standard deviation remain 01 and we paste that's .18 essentially. But we're not going to use that, that is less than .2. So you would think okay, I'm gonna reject. Um no you have to multiply that by two to account for the other tail. So it's actually .358 as the p. value. So it's zero 358 which is larger than that alpha. So it's greater than .2. Which means once again we're going to fail to reject. H not so don't forget any time there is a two tailed test. You just multiply your P. Value by to in order to account for that other tail.

The following is a solution for number 35 and this gives us a 95% confidence interval Where the hypothesized value is 31.8. This is the volume of dell computer stock and millions of $31.8 million dollar value for the stock and The standard deviation for the populations 14.8. We sampled 35 I think, days or something in some year And the x bar was 23.5. Which kind of is a big difference. I'm thinking that it's gonna be different. Um but were asked to do a 95% confidence that were given this data here. So we're gonna do is easy interval if you go to stat on your T I 84 go over the test and it's going to be the seventh option here. The z interval, make sure stats is highlighted. Go ahead and type in 14.8 for your sigma. The X bar was 23.5. The end was 35 the confidence almost 350.95. And we get this 18.597 to 28 point 403. Okay, so let's go write that down 18, Change colours, that's fine, 18 597 To 28.403, meaning we can be 95% confident that the main value of the Dell computer stock is between 18.6 and 21 $28.4 million. So the question was, is this different? Yes, it would be different than this hypothesized value of 31.8. So yes It is different. And the reason why I can tell it's different is because that 31.8 is not contained in this interval now. Had it been you know, 25? Yes, that is contained. So it wouldn't be any different. But 31.8 is outside the interval. So we can say with reasonable certainty with 95% confidence at least, that It is in fact different than 38,


Similar Solved Questions

5 answers
Paint) Conslder the sum _tne sericswhere @n dafined by6 cos(ln? )By comparing this seriessuitableof Ihe fomwhere cos(I/n* 2Vn"3one can conciude (narconvergesNow use the Remainder Estimate for tte Integral Test (see top page 701 Of the text) estimate the error if the pantialWseTapproxirriateAt most the error is;
paint) Conslder the sum _ tne serics where @n dafined by 6 cos(ln? ) By comparing this series suitable of Ihe fom where cos(I/n* 2Vn"3 one can conciude (nar converges Now use the Remainder Estimate for tte Integral Test (see top page 701 Of the text) estimate the error if the pantial WseT appro...
5 answers
Compute Iue oltne following ordmary annuities For full (arks YOU &nsieris Jalln roundeo Perodic Payment Interest Compounding Future Payment Interval Term Rale Frequency Value 5450.00 Every month montns 50% Monthly 0.00Mkotasi cent
Compute Iue oltne following ordmary annuities For full (arks YOU &nsieris Jalln roundeo Perodic Payment Interest Compounding Future Payment Interval Term Rale Frequency Value 5450.00 Every month montns 50% Monthly 0.00 Mkotasi cent...
5 answers
Flnd the derivativefunction_(t) arccsc( -722)f"(t) Idartcot( -7/ )csc(-72_Subnit AnswerSave ProgrossH0 polnta LuCukI1 0z Bubuniaa lona Unad Find the Indefinite integral. (Remumbur use absolute values wner approprnie Ust; for the constant 'Intagratlon.)
Flnd the derivative function_ (t) arccsc( -722) f"(t) Idartcot( -7/ )csc(-72_ Subnit Answer Save Progross H0 polnta LuCukI1 0z Bubuniaa lona Unad Find the Indefinite integral. (Remumbur use absolute values wner approprnie Ust; for the constant 'Intagratlon.)...
5 answers
Auto-brewery syndrome is very rare disorder in which glucose fermented alcohol in the gut by an overgrowth of veasts or certain bacteria: CoH12O 6(aq) CzHsOHlaq) COzlg) [unbalanced] A patient with this disorder consumes 100. potato which contains 20.% glucose (MM 180.18 g/mol) from starch: How many grams of ethanol (MM 46.08 g/mol) are produced?51 g13 g26 8Question 35 (5.72 points) Which compound has thc most positive oxidation slale for carpon?C6Hizo6CH4CHzOCCI4
Auto-brewery syndrome is very rare disorder in which glucose fermented alcohol in the gut by an overgrowth of veasts or certain bacteria: CoH12O 6(aq) CzHsOHlaq) COzlg) [unbalanced] A patient with this disorder consumes 100. potato which contains 20.% glucose (MM 180.18 g/mol) from starch: How many ...
5 answers
A constant force of 30N in the positive direction acts on 4 4.0-kg object as it moves from the origin to the point (6i 8i) m: How much work is done by the given force during this displacemen in Jouls4. 60 b. 120 c. 180 d 2400 1.60 2 b0 %d43
A constant force of 30N in the positive direction acts on 4 4.0-kg object as it moves from the origin to the point (6i 8i) m: How much work is done by the given force during this displacemen in Jouls 4. 60 b. 120 c. 180 d 240 0 1.6 0 2 b 0 %d 43...
5 answers
Two vertices of a triangle are $(0,2)$ and $(4,3)$. If its orthocentre is at the origin, then its third vertex lies in which quadrant? $quad$ [Jan. 10, 2019 (II)](a) third(b) second(c) first(d) fourth
Two vertices of a triangle are $(0,2)$ and $(4,3)$. If its orthocentre is at the origin, then its third vertex lies in which quadrant? $quad$ [Jan. 10, 2019 (II)] (a) third (b) second (c) first (d) fourth...
5 answers
If $p=q_{1}^{2}+q_{2}^{2}+q_{3}^{2}$, where $p, q_{1}, q_{2}$, and $q_{3}$ are all primes, show that some $q_{i}=3$.
If $p=q_{1}^{2}+q_{2}^{2}+q_{3}^{2}$, where $p, q_{1}, q_{2}$, and $q_{3}$ are all primes, show that some $q_{i}=3$....
5 answers
19. Evaluale definite inlegrals by Fundamental Thoorem of Calculus [(rt -xt)dr K(a)
19. Evaluale definite inlegrals by Fundamental Thoorem of Calculus [(rt -xt)dr K(a)...
5 answers
4 What is the largest number of kings which can be placed on a chessboard so that no two of them put each other in check?
4 What is the largest number of kings which can be placed on a chessboard so that no two of them put each other in check?...
1 answers
Work Problem One pipe can fill a tank in $2 \mathrm{h}$, a second pipe can fill the tank in 4 $\mathrm{h}$, and a third pipe can fill the tank in $5 \mathrm{h}$. How long would it take to fill the tank with all three pipes operating?
Work Problem One pipe can fill a tank in $2 \mathrm{h}$, a second pipe can fill the tank in 4 $\mathrm{h}$, and a third pipe can fill the tank in $5 \mathrm{h}$. How long would it take to fill the tank with all three pipes operating?...
5 answers
Whet is the PH ofa 0.00745 M solution of calcium hydroxide (Ca(OH)2)?112Z5
Whet is the PH ofa 0.00745 M solution of calcium hydroxide (Ca(OH)2)? 112 Z5...
5 answers
Choose the equation that can be used to solve the following problem: If the same number is added to the numerator and the denominator of the fraction $ rac{5}{8},$ the result is $ rac{2}{3} .$ Find the number.(i) $ rac{5}{8}+x= rac{2}{3}$(ii) $ rac{5+x}{8}= rac{2}{3}$(iii) $ rac{5+x}{8+x}= rac{2}{3}$(iv) $ rac{5}{8}= rac{2+x}{3+x}$
Choose the equation that can be used to solve the following problem: If the same number is added to the numerator and the denominator of the fraction $\frac{5}{8},$ the result is $\frac{2}{3} .$ Find the number. (i) $\frac{5}{8}+x=\frac{2}{3}$ (ii) $\frac{5+x}{8}=\frac{2}{3}$ (iii) $\frac{5+x}{8+x}=...
5 answers
CuescnWhat are the full adder outputs for the irpulsCi =Kotyet MaserctcoAnswei the lomm Of a bi: binary numbe observing the proper Dit significarce:Pointz ouiotFho Al2:jonAnsuNext pagePrevious page
Cuescn What are the full adder outputs for the irpuls Ci = Kotyet Maserctco Answei the lomm Of a bi: binary numbe observing the proper Dit significarce: Pointz ouiot Fho Al2:jon Ansu Next page Previous page...
5 answers
8 j Durang % "whaey revenues year corresponds did gambling the billions the 3 of US Ha [ re velacet reach generated 20182 104(1,346) U Macau China can decimal places) approximated by the
8 j Durang % "whaey revenues year corresponds did gambling the billions the 3 of US Ha [ re velacet reach generated 20182 104(1,346) U Macau China can decimal places) approximated by the...

-- 0.021433--