5

Thls Question:0122 complete)This Test: 58 pisConsider Iho discreto probabilily dsinbution tha nght Complcte purebuloxOutcomeProbubillty?0.29 0.12Calculale tho mcan ...

Question

Thls Question:0122 complete)This Test: 58 pisConsider Iho discreto probabilily dsinbution tha nght Complcte purebuloxOutcomeProbubillty?0.29 0.12Calculale tho mcan [nis distnouton(Type an integerdecimal )Calculate tne sandard deviation Iis Dislnbuiono-D Rourd (hrce dccimal Pacc? = nceded )

Thls Question: 0122 complete) This Test: 58 pis Consider Iho discreto probabilily dsinbution tha nght Complcte pure bulox Outcome Probubillty? 0.29 0.12 Calculale tho mcan [nis distnouton (Type an integer decimal ) Calculate tne sandard deviation Iis Dislnbuion o-D Rourd (hrce dccimal Pacc? = nceded )



Answers

Use a computer or calculator to complete the hypothesis test with alternative hypothesis $\mu_{d}<0$ based on the paired data that follow and $d=M-N .$ Use $\alpha=0.02 .$ Assume normality.$$\begin{array}{lllllll}\hline \mathrm{M} & 58 & 78 & 45 & 38 & 49 & 62 \\\mathrm{N} & 62 & 86 & 42 & 39 & 47 & 68 \\\hline\end{array}$$

Question 20 says, find the standard deviation. The standard deviation can be found by taking the square root of the Somme of the X values minus the mean squared multiplied by the expected probability. So in question 20 either given us a probability distribution with additional information, we have the X times, the probability of their X. And then we also have 1/4 column in which they have already given us each value of X subtracted by the means already been squared, multiplied with probability. So we're gonna take those values and add them together, never gonna take the square root of their values. So we're giving 1.16 is the euro. I have a date zero 0.144 and 1.352 Some of those four values would be 3.4, and we take the square root to get our center deviation to be 1.8

So thirties, looking for the theoretical standard deviation of the uniform distribution from 0 to 12. So that formula is the square root of be minus a squared over 12. So that would be 12 minus zero. Squared 12 or 12 squared over 12 or the square root of 12 which approximately is 3.46

Okay, so we're given this hypothesis test on where asked Tiu amuse a critical value approach to come to a conclusion. A certain of the data values s O. The first step is just to find the critical value. So what this means is that we want to find values that Alfa. So the probability observing a more extreme value tested a stick, then sell a fur is you want to know why not five? Because no one, not five p value on in this case, more extreme means that that will be strictly greater than that out. Because my alternative hypothesis involves the mean being strictly greater than 50 s o. If you go to your normal tables, uh, you can find out what this is because that is just normally distributed with means here in various one. Um, so if you look up minus 1.96 so I won't minus 1.6 in the normal tables, you'll see that the probability of being lesson that is equal toe roughing up window five eso by symmetry. This means if we take plus bomb 0.6 instead, then the probability of being more than that is also no point, no fire. So this means that are critical. Value is equal toe 1.6. So then if you want to use a critical variety approach, it means that each of the three cases we have to compute and what's Ed is on decide whether it's more or less extreme than the critical value of 1.6. Okay, so let's do that. Okay. So just remind you, um, So, um, we can plug in, um X in tow. Um, forever said so. If I just remind you said it's given by expert minus 50 divided by ate a bite of a skirt of 60 says you're given x bar. Then you could just compute. What's that is okay, s. So if you pluck an expose good food to 2.5 then said comes out was 2.42 on Because this is more extreme than the critical valuable 1.6, this means that it's strong enough to reject it. Rose, If you take exploited with 51 thing, you can plug it in again. And this time you get those X equal to north 510.97 And by this time, the observed value of that is less extreme than the critical value. So in this case, we do not have enough information to reject agent. And then finally, if we take expires, you go to 51.8. And then again, if you talk this in tow, a formula that we get that sword is equal to 1.74 on again. This is more extreme than 1.6. So in this case, we again rejected north s o the point of critical values that you have to compute your critical value offset offer and then compared the calculated values who said and see whether that more extreme ones.

Okay, so you can use any programming language you want or statistical software in order to solve this question. But I'm going to be using these statistical programming language are with the i. D. Called our studio. So we're asked to select 36 random numbers from a standard or are sorry from a normal distribution with mean 100 standard deviation. 15. So, um, we're going to start by creating that sample. Something create invariable called money Sam. And then they function and are that draws random numbers from a normal distribution is called our norm for random Normal. The first value that we specify is the size of our sample that we want so and equals 36 next week, expressed by our mean, which is 100 our standard deviation, which is 15. Okay, so if I create that sample and then take a look at it, I should see 36 random numbers coming from a normal distribution with mean 100 standard deviation. 15. So that worked as we expected it to next. I'm going to define my level of significance, Alfa, which we're told is 0.5 Most are going to specify the size of my sample and which was 36 Um, the mule that were given in the null hypothesis is 100. Next, we're going to calculate the sample mean and standard deviation. So X bar is my sample mean? And that's I mean of my sample. And next, we're gonna populate the sample standard deviation. So that's the standard deviation of my Sam. And now we can calculate our test statistic. So my test statistic is going to be given by Ex Bar minus mu, divided by sigma over the square root of. So I'm gonna go ahead and run these lines of code. And now I'll see that my statistic was found to be 0.78 Okay, And now we need to find our critical value. So to do that, we use our standard normal distribution and the function that does that are is cute or so friends quintiles of the normal distribution, and we need to specify the probability that we're looking for So, um, since we're doing a to tail test, are, um, critical value is going to be found by looking at, said off over to Somalia, type off over two in here, and I see that my critical value is 1.96 So the reason why it's a negative here is because the queue norm function finds the area to the left with the specified value. But since we're doing it to tail offices test, we're gonna be taking the absolute value of both our test statistic and a critical value. Anyway, So it's up to you. Um, if you would rather see the positive critical value and just do one minus self over to and that will give you positive 1.96 So now we're going Teoh, right? Some logic that will tell us whether or not we reject the null hypothesis. So if our if the absolute value of our test statistic is greater in the absolute value of our critical value, we are going to print out the words projects than all hypothesis. And otherwise we're going to print out the words fails to reject, you know, hypothesis. So what should happen for the values that we have right now for test statistic? In a critical value, we see that 0.79 is less than 1.96 so we should be failing to reject the null hypothesis. So if I run this block of code and should print out in the console, fails, rejecting all hypothesis, which it does, so it does as we expect it to dio. Now we're going to repeat this simulation many, many times. I'm going to do that by highlighting all of the code. It's going to generate new random numbers each time, and it's going to tell us whether we reject or failed to reject the no head office for that specific sample. So I'm going to run it again. We get a failed to reject again, fails to reject. I'm gonna run in a bunch of times in a row and see if we ever get a reject. So now I've run it like maybe 20 times. I still haven't seen a reject, and this is kind of what we would expect because we are actually drawing from a normal distribution with a mean of 100. So we expect that most of the time we should get a sample mean that is very close to the expected 100


Similar Solved Questions

5 answers
Determine each compound and write the reagents needed on the arrows_Synthesis Problem 1:Compound A CzH:Compound BCompound C CzHBOCompound D CzHqBrCompound ECOOHCompound F
Determine each compound and write the reagents needed on the arrows_ Synthesis Problem 1: Compound A CzH: Compound B Compound C CzHBO Compound D CzHqBr Compound E COOH Compound F...
4 answers
Determine convergence or divergence of 5n2052(8)" so the series diverges_05-2 drO, SO the series diverges_42()" so the series converges: By the p-Series Test; n? Z p Z 1,$0 the series converges
Determine convergence or divergence of 5n2 052(8)" so the series diverges_ 0 5-2 dr O, SO the series diverges_ 42()" so the series converges: By the p-Series Test; n? Z p Z 1,$0 the series converges...
5 answers
Aline s graph shown bclow you would like entarge the graph or make numbers and elters easier = edu new wndow: YOU may Ihen you may click on it lo open im enlaige ` that window with your Mouse further enlarge the image, use YOUr browsers zoom capabilities Ona PC Uhis usually cul shitt = (and zooming out IS ctrI -) On an Apple computer Ihis usually apple shift- (and zooming out IS appleThe slope of this line(It tne slope does not existDNE NONE
Aline s graph shown bclow you would like entarge the graph or make numbers and elters easier = edu new wndow: YOU may Ihen you may click on it lo open im enlaige ` that window with your Mouse further enlarge the image, use YOUr browsers zoom capabilities Ona PC Uhis usually cul shitt = (and zooming ...
5 answers
Show that for auy n €N where n > 1 1(+4)- =n+1
Show that for auy n €N where n > 1 1(+4)- =n+1...
5 answers
Aua F # rexton 5 A 8 #x Jx #dx =Ja 3 56_JX ) dz [: x" 5.2 ] 4 JS(s-+x) &x 1 [6x-#4]3 4 Css @) _ +0)] 4 [ 56 () 462)] < [? ( 56-28)] 28
Aua F # rexton 5 A 8 #x Jx #dx =Ja 3 56_JX ) dz [: x" 5.2 ] 4 JS(s-+x) &x 1 [6x-#4]3 4 Css @) _ +0)] 4 [ 56 () 462)] < [? ( 56-28)] 28...
5 answers
3. Find the general solution of the following linear system: (3 Points) +3z = | 2x + y = 3(8 _ 4 '-5(-3t + 1. 9 - 2 t(-3t + 1. 6t + 1. 0)(3'+2 '- 1,None
3. Find the general solution of the following linear system: (3 Points) +3z = | 2x + y = 3 (8 _ 4 '-5 (-3t + 1. 9 - 2 t (-3t + 1. 6t + 1. 0) (3'+2 '- 1, None...
5 answers
If the $r$ th term, $t_{r}$ of a series is given by $t_{r}=frac{r}{r^{4}+r^{2}+1}$, then $lim _{n ightarrow infty} sum_{r=1}^{n} t_{r}$ is(A) 1(B) $frac{1}{2}$(C) $frac{1}{3}$(D) None of these
If the $r$ th term, $t_{r}$ of a series is given by $t_{r}=frac{r}{r^{4}+r^{2}+1}$, then $lim _{n ightarrow infty} sum_{r=1}^{n} t_{r}$ is (A) 1 (B) $frac{1}{2}$ (C) $frac{1}{3}$ (D) None of these...
1 answers
An electric current is passed through two electrolysis cells connected in series (so the same amount of current passes through each of them). One cell contains $\mathrm{Cu}^{2+}$ and the other contains $\mathrm{Ag}^{+} .$ In which cell will the larger number of moles of metal be deposited? Explain your answer.
An electric current is passed through two electrolysis cells connected in series (so the same amount of current passes through each of them). One cell contains $\mathrm{Cu}^{2+}$ and the other contains $\mathrm{Ag}^{+} .$ In which cell will the larger number of moles of metal be deposited? Explain y...
5 answers
QI) The function f (x) called invariant under differentiation operator function (IUDO. function) if: f' (x) f(x): AJ Show that: if u(x) ~2cosh(x) and v(x) sinh (x) + cosh(x) then both of u(x) and v(x) is not IUDO. function but h(x) u(x) + v(x) is IUDO. function. ([7 marks)B) give an example rather than h(x) in part A in this question_marks)
QI) The function f (x) called invariant under differentiation operator function (IUDO. function) if: f' (x) f(x): AJ Show that: if u(x) ~2cosh(x) and v(x) sinh (x) + cosh(x) then both of u(x) and v(x) is not IUDO. function but h(x) u(x) + v(x) is IUDO. function. ([7 marks) B) give an example ra...
5 answers
Suppose that f:Rcontinuous function for whichf(u) du=12Find the value off(4x- 5) dx Your answer should be an integer:
Suppose that f:R continuous function for which f(u) du=12 Find the value of f(4x- 5) dx Your answer should be an integer:...
5 answers
Exactness first order differential equation is written in the form of;N(x,y)dx + M(x,y)dy 0M(x,y)dx + N(x,y)dy = 0 N(x, y)dx M(x,y)dy = 0 M(x,y)dx N(x,y)dy = 0
Exactness first order differential equation is written in the form of; N(x,y)dx + M(x,y)dy 0 M(x,y)dx + N(x,y)dy = 0 N(x, y)dx M(x,y)dy = 0 M(x,y)dx N(x,y)dy = 0...
5 answers
Let X, the number of flaws on the surface of a randomly selected boiler; have Poisson distribution with mean 5.5 Find the following probabilities Answer up to three digits after decimal:P(X = 9)Submit AnswerTries 0/5P(X < 9)Submit AnswerTries 0/5P(X 2 9)Submit AnswerTries 0/5P(X > 9)Submit AnswerTries 0/5P(X < 9) Submit Answer Tries 0/5
Let X, the number of flaws on the surface of a randomly selected boiler; have Poisson distribution with mean 5.5 Find the following probabilities Answer up to three digits after decimal: P(X = 9) Submit Answer Tries 0/5 P(X < 9) Submit Answer Tries 0/5 P(X 2 9) Submit Answer Tries 0/5 P(X > 9)...
5 answers
QUESTION 41What Is the most Iikely pattern of inherltance of this disease tralt? What are the most Iikely genotype of all Individuals In generations and IV?femalemale
QUESTION 41 What Is the most Iikely pattern of inherltance of this disease tralt? What are the most Iikely genotype of all Individuals In generations and IV? female male...
5 answers
TrialMass (g) of CaCO3 at start Mass (g) of CaCO3 at end6.2432.6087.1253.4996.8454.3927.2563.6228.1394.501
Trial Mass (g) of CaCO3 at start Mass (g) of CaCO3 at end 6.243 2.608 7.125 3.499 6.845 4.392 7.256 3.622 8.139 4.501...
5 answers
In the figure shown on the right; a potential, battery provides 24 (a) Calculate the total resistance of this circuit Find It; H and 1z using = ohms' law and combination of resistorsR1 = 6 nR2 = 8 nR4 = 12 0RJ = 4 nlRS = 12 0
In the figure shown on the right; a potential, battery provides 24 (a) Calculate the total resistance of this circuit Find It; H and 1z using = ohms' law and combination of resistors R1 = 6 n R2 = 8 n R4 = 12 0 RJ = 4 nl RS = 12 0...

-- 0.030118--