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Aplitude test are normally distributed with mean of 500 and standard Scores for & common standardized college Randomly selected men are given Test Preparation C...

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Aplitude test are normally distributed with mean of 500 and standard Scores for & common standardized college Randomly selected men are given Test Preparation Course before taking this test Assume , for sake deviation of 98. of argument that the preparation course has no effect randomly sclected, find the probability that his score at Icast 560.7. If ! of the men P(X > 560.7) = Enter your answer a5 number accurate t0 decimal places. If 15 of the men Jre randomly selected, find the probabi

aplitude test are normally distributed with mean of 500 and standard Scores for & common standardized college Randomly selected men are given Test Preparation Course before taking this test Assume , for sake deviation of 98. of argument that the preparation course has no effect randomly sclected, find the probability that his score at Icast 560.7. If ! of the men P(X > 560.7) = Enter your answer a5 number accurate t0 decimal places. If 15 of the men Jre randomly selected, find the probability that their mean score at least 560.7. P(M > 560.7) Enter your answer as number accurate t0 decimal places; Assume that any probability less than 5%/ sufficient cvidence conclude that the preparation course docs help men do better If the random sample of 15 men docs result in mean score of 560.7,is there strong evidence to support the claim that the course actually eflective? The probability indicates that it IS too possible by chance alone randomly select = group of students with [cam high as 560.7. Yes: The probability indicates that it Is (highly unlikely that by chance, randomly sclected group of students would get & mean as high as 560.7_



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At a large university, a mathematics placement exam is administered to all students. This exam has a history of producing scores with a mean of 77 Samples of 36 male students and 30 female students are randomly selected from this year's student body and the following scores recorded. a. Describe each set of data with a histogram (use the same class intervals on both histograms), mean, and standard deviation. b. Test the hypotheses, "Mean score for all males is $77 "$ and "Mean score for all females is 77 " using $\alpha=0.05$ c. Do the preceding results show that the mean scores for males and females are the same? Justify your answer. Be careful! d. Test the hypothesis, "There is no difference between the mean scores for male and female students" using $\alpha=0.05$ e. Do the results found in part d show that the mean scores for males and females are the same? Explain. f. Explain why the results found in part b cannot be used to conclude, "The two means are the same."

20 every day. The non hypothesis is that new one in smaller than or equal to Muto and the alternative high Busses that me one is bigger than mute. So the critical values are the values in Table four, corresponding to mobility on 1.9. So that is even toe 1.3. So the rejection reasons contain all very is larger than 1.28 So this tested statistics X one bar 162 minus mu one minus muto over squared off symbol on the square over anyone plus Sigma squared over and to which approximately equal to four point always so if the value of testing is within the rejection rating than not, have also rejected. So as UH, two point or seven is bigger than 1.28 So you reject the not hypothesis, so there is sufficient evidence to support that.

All right, were given some data about graduates and there salaries 10 years after graduation, and we've divided them into data for men and data from women. So for part A, given the statistics Ah, we're given a sample of 40 men, and we want to find the probability that our sample mean will be within 10,000 of our population. Means hold on. Gonna crack that notation. There we go on that might need his penmanship, but you get the general idea, right? So let's find our standard deviation of the sampling distribution. It's gonna be the standard deviation over sample size. So that's gonna be, uh, 40,000 divided by the square root of 40. That equals 6324 56 We're gonna find a Z lower and see upper like so. So for a C lower, uh, it's gonna be negative. 10,000 divided by our center deviation, uh, for the sample. Yeah, our sampling distribution, and then for upper, it's gonna be 10,000 positive. When you compute these out, you get negative 1.58 from 1.58 Comparing this to our normal probabilities table. This gives you probability. Lower 0.571 probability, upper 0.9429 Uh, this means our probability is gonna be probability upper minus probability, lower. Which is zero point 8858 Right party. Uh, this time we're looking at a sample of 40 women, and now we need to find the probability that our sample mean that we find is within 10,000 of the mean for the women. So once again, we're going to find our standard deviation sampling distribution. That's gonna be this time. We're looking at the statistics for the women. So this is going to be 25,000 over square root of 40. Calculate that out. That's 3952.47 are Sorry. 847 Anyway, let's find a Z lowers the upper. So the els you again. That's gonna be negative. 10,000 over our standard deviation of the sampling distribution for women. This one's gonna be 10,000 positive. So these are equal negative. 2.53 2.53 respectively. This is P. L. Looking at our table Once again, this lower probability is from zero point 0057 Upper probability 0.9943 Finding a probability, which is probability Oper minus probability, lower. You get, um, zero point 9886 part C s us two compared these to given explanation why one is higher than the other. And we see that part. He is greater. This is because standard deviation for men is greater then that for women I'm gonna have to move that up on. And because the standard deviation is greater, this means that this is a small This is smaller relative to our standard deviation, which means this let fewer standard deviations away from the mean, as opposed to this. All right, I'm gonna move to a different page party. Now we have sample of 100 men. We want to find the probability that air sample mean is within. Ah, I believe it is sorry. It's not within this time. We need to find a sample mean that is greater than our population mean minus 4000. All right, so let's find our sampling distribution. Ah, standard deviation. So that's referring back to hear. That's 40,000 square root of 100 square. 100 is tense. And this just 4000. All right, now we just see score for 4000 against 4000. So this could be because we are looking at 4000 less than the mean That's gonna be negative. 4000 top standard deviation is 4000. So this is negative 1.0 And if we look at our table, this corresponds to a probability is zero point 1587 and there you have it.

All right, We're getting some statistics about the population. Means score on the critical reading, math and writing sections of the S A T. And we're also given that the population standard deviation for all three of these categories is 100. Now, for each of these parts were goingto excuse me, we're giving a sample size a section, and then we're supposed to find the probability that our point estimate for the mean will fall under a certain interval. So for part A, our sample size is 90. We're looking at the creek reading section and our error, the error. We're trying to find the probability of its plus or minus 10. Really? Technically, none of this writing and math and critical reading stuff the scores don't matter because we're only looking at the error. So yeah, keep that in mind anyway. So let's start with our standard deviation of the sampling distribution. Ah, I I think it's safe to say that 90 is small enough compared to all the people who take the S a T that we can just assume better. Our population sizes relatively infinite, so we're just going to use that formula, so it's gonna be 100 over the square root of 90. This equals about 10.54 Now we're going to Z score the upper and lower bounds. So negative. 10. Get See. Score to approximately 0.95 on lowered snake. It's positive. 10. Not negative. Over 10.54 Okay. Looking at our table since by central limit their, um this is big enough that we can just assume it's normal. Billy, on the lower end of zero point 1711 Probability on the upper end is 0.82 uh, 89 We find our probability by subtracting the upper limit minus the lower limit. And this equals zero. Oops. 0.6578 All right, party sample sizes still 90. Now, we're looking at the math section and we're still looking for an air of 10. But you probably noticed, in part A. We never used this bit of information here. Like the population mean never came into it, so we don't need to worry about it. Fact, we don't even need to worry about it here or here. It's completely irrelevant to the question anyway, so let's do this. Our standard deviation of the sampling. Distribution is also 10.54 And you might notice this means literally. All the math is the same. So for a gravity sake, I'm not gonna write it out again. This probability is 0.6578 again. All right. We were looking at the writing section. Not that it matters. Our sample size is 100 we're still looking for an error of plus or minus 10. So let's find our standard deviation with the sampling distribution. This time, it will be different. Uh, well, this isn't even approximately. It's ah 100 divided by 10. So this is 10. All right, let's see. Score the upper and lower. But if the standard deviation is 10 and we're looking for an error of plus or minus 10 batches means not ours. E lower is negative one and ours ear upper is one. So this meat So what? Z equals negative one. Our probability is 0.1587 And when Z equals one, our probability is equal to 0.84 13 It's probability lower probability, upper so probably upper minus probability. Lower equals 0.8413 13 There we go, minus 0.1587 This equals 0.68 to 7. And this should make sense because of the 68 95 99.7 role that 68% uh, is congruent with what we know about the set of points between negative one and one standard deviation. That means now the problem asks us to analyze the standard deviation and compare it two parts A and B, and we notice it's larger. And this makes sense because we looked at a larger sample. So yeah, that means we're having more. We have a wider standard deviation here for four hour point estimate for the meat, so they don't lead to a larger probability, and there you have it.

Right, where will the population has mean new equals 14 From the following sample data, we want to calculate the sample mean X bar and the sample standard deviation S. To do so let's remember the definition of these terms X bar Is the some of the data divided by n or in this case 15.1, I'm a sample standard deviation S is the sum of deviations about the mean square divided by n minus one or 2.51 Next we want to implement a right tail test. That is we want to test whether or not the population mean should actually be greater than the no mean 14. With us using the sample data with a significance level alpha equals 140.1 Where we are noted that X is approximately normally distributed. So to implement this test, we have to answer the following questions in order First, what is the significance of hypotheses? We've alpha equals 0.1 H not is new equals 14 H. A. Is that I mean is greater than 14. What distribution will use computer associated test statistic? Since the population standard deviation sigma is unknown. We have to use a student's T distribution which we know is okay to use because the shape of the distribution is normal, which is both symmetrical amount shaped from this. We calculate the T stat Which is given by this formula and reduces down to 1.386 for this problem? Next compute the p interval and sketch it out so we have degree of freedom and minus 29. We use the one tailed T. Table to identify that this tea interval falls between a p interval of 10.75 point one. That is because our T statistic falls between associated T values for these p values. We can graph this as the area under the student's t distribution. To the right of our T stat 1.386 as is highlighted in yellow on the right. What can we conclude from this? Well, we can conclude that P is greater than alpha, so we have statistically insignificant findings and we fail to reject astronaut, which means that we lack sufficient evidence that suggests our population mean is greater than the No. Mean 14.


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