5

A sample of size 30 is collected to test the alternativehypothesis that the population mean is greater than 55.The average of the 30 observations is 55.9446. Assumi...

Question

A sample of size 30 is collected to test the alternativehypothesis that the population mean is greater than 55.The average of the 30 observations is 55.9446. Assuming apopulation standard deviation of 6.7, what is the P-value for thistest?

A sample of size 30 is collected to test the alternative hypothesis that the population mean is greater than 55. The average of the 30 observations is 55.9446. Assuming a population standard deviation of 6.7, what is the P-value for this test?



Answers

A population has mean 73.5 and standard deviation 2.5 . a. Find the mean and standard deviation of $x-$ for samples of size 30 . b. Find the probability that the mean of a sample of size 30 will be less than 72 .

Following is a solution to number six, and this gives us some information that 65 randomly selected individuals, Or whatever. There's no context of this problem. But the sample mean of that sample was 583.1. With a sample standard deviation of 114.9. And we're supposed to test at the significance level of 10% of .1 If the population means you is different from 600. So, first off, The reason why we don't care about how the population is distributed is because the sample size is large enough. So as long as the sample size is 30 or more, it doesn't matter how the population is distributed. And we're going to use a T test here. And the reason why we have to use a T test is because of that, right? There were given the sample standard deviation, not the population standard deviation. Okay, so, because we're given s we need to use the T test, and it's a five step process. The first step is to uh state or hypotheses. So, there's a Nolan alternative, and the knoll always says something about equality. So, the population mean U. Is equal to the 600. And the alternative you kinda have to do a little bit of searching, but it says um is it different? And any time we don't know if it's greater than or less than Then we're just going to say not equal to. So it's different. So this is a two tailed test here, so not equal to 600. Okay, So that's the first step. The 2nd and 3rd step, they kind of go hand in hand, so I'm gonna say T equals, and the p value equals. So in step two, you find the test statistic and you're going to find that um you can use the formula or you can use technology, I'm gonna use technology and then you can also use the p value for using a chart or technology and again I'm going to use technology. So T I 84 is a good tool to use here. If you go to stat and then arrow over two tests, we're going to go to that t test and then just make sure that the stats is highlighted. The immune not that's the hypothesized value in this case, remember that was 600. The X bar was 5 83 1. The sample standard deviation was 114 9 and the sample size was 65. And then we get down here for the alternative hypothesis and the alternative is that it's not equal to the null hypothesis. So then we can calculate and it gives us a lot of good information here. But really just that TMP is what I really care about. The T is negative one point we'll say negative 1.186 I like to do three decimal places, so negative 1.186. And then the P value is really the important thing. It's .24, It's a .24 which is a pretty big p value. Usually they're not that big. So the p value The 4th step is we compare that P value explicitly with our significance level alpha. And if you look back at the alpha really I mean this is the biggest alpha, we can get 0.1. I've never seen an alpha bigger than 0.1. So the 0.24 P value is definitely bigger than alpha. And any time the p values greater than alpha, then we fail to reject the null hypothesis. H not so we failed to reject h not now had this P value in less than alpha than we would reject. H. Not. We're rejecting the statement. But since it's greater than were failing to reject meaning for lack of a better phrase, we're accepting that null hypothesis to be true. So the fifth and final step is just kind of like a formal conclusion and these all kind of follow the same pattern. We're going to write that there is not sufficient evidence to suggest that the population mean you is different than 600 so there is not sufficient evidence to suggest that mean mu the population mean is different than 600. So there's your five step hypothesis test, A. T. Test since we only know the sample standard deviation.

I think. Question number 12 question number E. Donald Hypothesis states that the population mu is equal to the value mentioned in the claim. So it snowed. Two new equal 13 question number be the null hypothesis states that the population mean immune is equal to the value mentioned in claim so it snowed to mu equals 13. Honored. The alternative hypothesis states the opposite off the null hypothesis, according to the claim. Not equal so each one A to mu not equal. 13 Question number c not hypothesis. State that the population mean new is equal to the value mentioned in the claim. So it snowed two. New equal. 13. The alternative hypothesis state is the opposite. Off. The null hypothesis, according to the claim, is greater than so it won. Tome you is greater than 13. Question. Number 19 Donald Hypothesis states that the population mean new is equal to the value mentioned in the claim, so each node to mu equal 30. The alternative hypothesis state the opposite of the null hypothesis, according to the claim, not as large as, or less than so. Each one to mu is less than 30

The following is a solution for # seven. And this gives us a generic example where the sample Is size 15, but it comes from a normal distribution, so the population is normal. Therefore that sample size of 15 is okay. Now, had it not been normal? That sample size needs to be at least 30, but since it's normal, that sample size can be, you know, whatever, so 15 is fine, and the sample mean of this particular sample is 23.8. The sample standard deviation was 6, 3, And we're supposed to test at the significance level .01 If the mean is different than 25. Now, first off, we're going to use the T test, and the reason why we have to use a T test here is because we're given the sample standard deviation, were not given the population standard deviation sigma were only given the sample standard deviation. So, if we were given sigma, we could use the Z test, but since we're not we're given s we have to use the T test. So we're gonna do a five step hypothesis test, and the first step is to state our hypotheses and the null hypothesis h not Always assumes some sort of equality in this case, since we're testing a population mean μ equals 25. And the alternative, It says that we're just testing to see if it's different, so if it doesn't say up or down or greater than or less than, then we just assume that it's not equal to so different than 25, so not equal to 25, the 2nd and 3rd step, kind of, they kind of fall in line with each other. So I'm gonna do these together because um you can do it with the formula, but it's gonna take a little bit longer, so I'm gonna use technology. So if you have technology available, I really suggest you use that. If not, then you can start plugging in, you know, this stuff up here into your formula, but the T. Is stands for the test statistic, and then the p value is a probability. So if you go to the T. I 84 and go to stat and then air over to test, we're gonna use this T test right here, so go down, go to the T test and then make sure summary stats is highlighted. The mu not that's the hypothesized value of 25 in this case, that's just your h not The x bar, is your sample means that's 23.8 S stands for the sample standard deviation, and that was 63 And then the sample size remember was 15. And then we get down to this alternative and it's already set up as not equal to so we can just leave that the same. And then when wherever we calculate it gives us a lot of good stuff but this uh the T value and the P value are really the only things that I care about. So the T value is negative 0.74 and then the p value is 0.47 So let's go and write those down and then we'll talk about them. So the t value, the test statistic is negative zero point 738, which is pretty close to zero. So this is the so the p value is quite large, so 473 And what we do with that PVP PV I really is the most important thing um in this process. And step forward we explicitly compare the P value with our significance level alpha. And in this case it's significantly larger than alpha. P value is very much larger than our alpha value. So whenever it's larger than or whenever the PV is greater than alpha, then we fail to reject H nine. So we failed to reject the null hypothesis that μ equals 25 or more or less. We're accepting that the population mean is in fact 25 or at least we we say that it's we can't reject that. It's not or we can't say that it's not. Now. Had this been less than had the P value been less than alpha than we would reject H dot, but it's not. So we failed to reject. And then step five, we just kind of package that together into a nice conclusion and we'll say there is not sufficient evidence to suggest that the population mean, I'll just calm you for short. The population mean is different from 25. So whenever we fail to reject, that means there's not sufficient evidence to say that the whatever the alternative hypothesis is. Okay, so that's your five step T test using the P value method.

So in this question, were given a population with mean 557 standard deviation 35 were asked to find the mean and central division of the simple means, so mean of the sample, mean is 557. The standard deviation of the sample mean is population standard deviation over The square root of the simple size of squared of 15 35. Over answer is basically four 94 97 So we have our answer to a Now in beer us probably that the mean of a sample of size 50, so the assemble mean will be more than 5:17. So that's probably it is easy. It's more than the standard normal random very book. So we're going to get published easy, more than So we take 5 70 minus 557 Divided by 4.9497. See is more than 2.6. Kareen, that's one- The probability is is less than 2.63. So, from our table For 2.63, we're basically going to get 0.99 5 7. So 1 -0.9957 gives us 0.0043.


Similar Solved Questions

5 answers
Find the derivative of the function. 3x2 g(x) Jtan x V 5 + t49 (x)Need Help?Read ltTakkto @ Qutor
Find the derivative of the function. 3x2 g(x) Jtan x V 5 + t4 9 (x) Need Help? Read lt Takkto @ Qutor...
5 answers
Question 2 Notyet answeredWhich of the following is NOT an acid-conjugate base pair?NaHSO3/ NajS SO; HzSO-/ Na_SO_ NaOH/ Naz0Marked out of tooFlag ' questionHCN/ CN-HCV Nacl
Question 2 Notyet answered Which of the following is NOT an acid-conjugate base pair? NaHSO3/ NajS SO; HzSO-/ Na_SO_ NaOH/ Naz0 Marked out of too Flag ' question HCN/ CN- HCV Nacl...
5 answers
Enter a number rounded to six decimals_ The mean of 23,45,67,54,98,106,42,33,67,.9,24,67,111,13,14,39,45,197, 32,43,54,65,76,87,99, 104 if every number is multiplied by 17.123456 is
Enter a number rounded to six decimals_ The mean of 23,45,67,54,98,106,42,33,67,.9,24,67,111,13,14,39,45,197, 32,43,54,65,76,87,99, 104 if every number is multiplied by 17.123456 is...
5 answers
Simplify each power of $i$.$$i^{25}$$
Simplify each power of $i$. $$ i^{25} $$...
5 answers
Solve Prob. 14.86 , assuming that the chain is being lowered to the floor at a constant speed $v$
Solve Prob. 14.86 , assuming that the chain is being lowered to the floor at a constant speed $v$...
5 answers
Exercise 8.5.3. Derive the formulas(10)Om =f fk) cos(mx)dx and bmn = J_, f(r) sin(mx)dz for all m > 1.
Exercise 8.5.3. Derive the formulas (10) Om = f fk) cos(mx)dx and bmn = J_, f(r) sin(mx)dz for all m > 1....
5 answers
Question 810 ptsIn a series of experiments to study the purity of a chemical product; the effect of reactant A on the purity was of primary interest and three levels of A were used in the experiments. The variable reactant A isexpcrimenta variablcconcomitant variablccontrolled variablcblocking variableQuestion 910 ptsFor complete factorial study with 8 factors each with 3 levels; the number of observations is at least
Question 8 10 pts In a series of experiments to study the purity of a chemical product; the effect of reactant A on the purity was of primary interest and three levels of A were used in the experiments. The variable reactant A is expcrimenta variablc concomitant variablc controlled variablc blocking...
5 answers
2 ! ^ 1 { 1 1 88! 2 } 8 9 Hii 8 1 L 2 1 1 3 2 3 8 5 1 1 { F g 5 ; 3 2
2 ! ^ 1 { 1 1 88! 2 } 8 9 Hii 8 1 L 2 1 1 3 2 3 8 5 1 1 { F g 5 ; 3 2...
5 answers
Compute the limit:112n+1 '(-1)" 7n-'(2n)! n=l
Compute the limit: 112n+1 '(-1)" 7n-'(2n)! n=l...
5 answers
Submit Answer"/3 pointsUse the limit definition to evaluate the following definite integral:K" &-2x+x)dx0/4 pointsT/2 sin(x) dx=1.Evaluate the following definite integral using the fact that
Submit Answer "/3 points Use the limit definition to evaluate the following definite integral: K" &-2x+x)dx 0/4 points T/2 sin(x) dx=1. Evaluate the following definite integral using the fact that...
1 answers
Check whether the set of all 2x3 matrices with first row any multiple of (2 =] 31. a vector space or not. If it is a vector space, determine the dimension and find a basis;
Check whether the set of all 2x3 matrices with first row any multiple of (2 =] 31. a vector space or not. If it is a vector space, determine the dimension and find a basis;...
5 answers
~SJXAieJyJJtLTLa]poant Paarticle with charg" q Is at the centerGaussn "uracethe formcuba . The electric flux through any one faca of the cube is:[email protected]
~SJX Aie JyJJt LTL a] poant Paarticle with charg" q Is at the center Gaussn "urace the form cuba . The electric flux through any one faca of the cube is:. QE0 Vineo qJeo q6e0 m [email protected]
2 answers
Sialateihe crculation of the flow v (22,y) around the closed material curve z + 9v29Eaaigne D2 DDEE(0,0}.EEEl 12xANone of these
Sialateihe crculation of the flow v (22,y) around the closed material curve z + 9v29 Eaaigne D2 DDEE(0,0}. EEEl 12x ANone of these...
5 answers
Chapter 5, Section 5.3, Question P24 Use the Multiplication Rule to find the probability that if you draw two cards from a standard 52-card deck without replacing the first before drawing the second, both cards will be hearts_ Give the exact answers in the form of fraction_ The probabilityWhat is the probability if you replace the first card before drawing the second?The probability
Chapter 5, Section 5.3, Question P24 Use the Multiplication Rule to find the probability that if you draw two cards from a standard 52-card deck without replacing the first before drawing the second, both cards will be hearts_ Give the exact answers in the form of fraction_ The probability What is t...
5 answers
[-/4 Points]DETAILSLARPCALC1O 5.4.040.Find the exact value of the expression_ tan 259 tan 1108 tan 250 tan 1100Show My Work (Optional)Submit AnswerView Previous Question Question 9 of 25 View Next Qu
[-/4 Points] DETAILS LARPCALC1O 5.4.040. Find the exact value of the expression_ tan 259 tan 1108 tan 250 tan 1100 Show My Work (Optional) Submit Answer View Previous Question Question 9 of 25 View Next Qu...
5 answers
Given the matrix28 Fl6 A = eR": 13 21find all eigenvalues of A2. find the corresponding eigenvectors of A3. show that A is diagonalizable; that is find an invertible matnx A" € RSS anda diagonal matrix D € RS: such thatK-'AK = D,NO NEED TO VERIFY THIS IDENTITY Wfind Ihe maltx A*
Given the matrix 28 Fl6 A = eR": 13 21 find all eigenvalues of A 2. find the corresponding eigenvectors of A 3. show that A is diagonalizable; that is find an invertible matnx A" € RSS anda diagonal matrix D € RS: such that K-'AK = D, NO NEED TO VERIFY THIS IDENTITY W find...
5 answers
13) ( ICpts) IC sin $ and is in quadrnt [L find 14) ( [Opts) For Y = cos(4x) the exact values of the other five trigonometric functions of 8. (Decimal approximations will NOT be accepted ) Find the amplitude_Find thc pcriodSketch the graph of one cycle ofy 2cos(4x) and labcl the scalc on thc _- and )-axcs .
13) ( ICpts) IC sin $ and is in quadrnt [L find 14) ( [Opts) For Y = cos(4x) the exact values of the other five trigonometric functions of 8. (Decimal approximations will NOT be accepted ) Find the amplitude_ Find thc pcriod Sketch the graph of one cycle ofy 2cos(4x) and labcl the scalc on thc _- an...
5 answers
Hint: Adapt the proof of the dominated convergence theorem in [SS]: Theorem 2. Let ( fn_ be a sequence of measurable functions on Rd and let (gn , be a sequence of nonnegative integrable functions: Suppose that Ifn(x) < gn(x) for a.e. x (ii) fn + f a.e and gn 7 g [email protected] (iii) lim f 9 = | 9 < o n+O Then f is integrable and lim f s = f f n-00 Hint: Apply Fatou's lemma to suitable sequences of nonnegative functions.
Hint: Adapt the proof of the dominated convergence theorem in [SS]: Theorem 2. Let ( fn_ be a sequence of measurable functions on Rd and let (gn , be a sequence of nonnegative integrable functions: Suppose that Ifn(x) < gn(x) for a.e. x (ii) fn + f a.e and gn 7 g [email protected] (iii) lim f 9 = | 9 < o ...

-- 0.022046--