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3_ The output of a radio signal detection system is a normal random variable N(p,1) with unknown mean /. Consider the binary simple hypotheses Ho pL = 0 VS Hi p = 0...

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3_ The output of a radio signal detection system is a normal random variable N(p,1) with unknown mean /. Consider the binary simple hypotheses Ho pL = 0 VS Hi p = 0.34_A sample mean of 0.5 was obtained from n = 16 independent measurements_ At significance level 2.5%, find the rejection region of the Neyman- Pearson test and determine the outcome.Find the pvalue of the above test and determine the outcome_Find the probability of the Type II error of the test in part

3_ The output of a radio signal detection system is a normal random variable N(p,1) with unknown mean /. Consider the binary simple hypotheses Ho pL = 0 VS Hi p = 0.34_ A sample mean of 0.5 was obtained from n = 16 independent measurements_ At significance level 2.5%, find the rejection region of the Neyman- Pearson test and determine the outcome. Find the pvalue of the above test and determine the outcome_ Find the probability of the Type II error of the test in part



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Health Insurance: Administrative Cost The following data are based on information from Domestic Affairs. Let $x$ be the average number of employees in a group health insurance plan, and let $y$ be the average administrative cost as a percentage of claims. $$ \begin{array}{l|rrrrr} \hline x & 3 & 7 & 15 & 35 & 75 \\ \hline y & 40 & 35 & 30 & 25 & 18 \\ \hline \end{array} $$ (a) Make a scatter diagram and draw the line you think best fits the data. (b) Would you say the correlation is low, moderate, or strong? positive or negative? (c) Use a calculator to verify that $\Sigma x=135, \Sigma x^{2}=7133, \Sigma y=148$, $\Sigma y^{2}=4674$, and $\Sigma x y=3040$. Compute $r$. As $x$ increases from 3 to 75 , does the value of $r$ imply that $y$ should tend to increase or decrease? Explain.

Number 15 Christian E. Given the population distribution X is normal. If the population distribution X is normal, then the sampling distribution off off the sample mean X stage is also normal, so the answer will be yes. Question number be given it snowed to immune, equal 6.3 and X stage equal 4.5 and Zita equal three. Unequal 16. Does it? Value is a sample mean decreased boy. The population mean divide, divided by the standard deviation so that equal export minus new over zita over square root and equal 4.5 minus 6.3 over three over square root. 16. It almost equal minus point toe. Four. Question Number C. Given it snowed new equal 6.3 in each one in the tomb, you is less than 6.3 x dash equal 4.5. Zita equal three and unequal 16. Does it? Value is a sample mean decreased by the population mean divided by the standard deviation. The equal export minus mu minus New over. Zita over square root in equal 4.5, minus 6.3 over. See over square roots 16. It equal minus 2.4 the value is the probability off obtaining a value more extreme or equal to the standard standards. The test statics that did remind the probability using table five. So probability equal probability off that is less than minus 2.4 equals four point oh 82 with your number the given each node two new equal 6.3 and each one to mute is less than 6.3. Extension equal 4.5 Data equal three in equal 16. Goma Equal point is very Alfa equal points you one does it a value Is the sample mean decreased by the population being divided boy the standard deviation So the equal explore minus new over zita over a square square root in equal 4.5 minus 6.3 over three over squared 16 equal minus two points. Four. The B value is the probability off obtaining a value more extreme or equal to the standard Just static said did remind the probability. Using a table five. So probability equal probability off the is listen minus 2.4 equal 0.0 eat to If the if the value is smaller than the significance level Alfa, then the null hypothesis is rejected. Toe P is lesson 0.1 So a rejected reject h no

Question number 13. Given the population distribution X is normal. If the population distribution X is normal, then the sampling distribution off the sample mean X dash is also normal. Question number be given it snowed two new equal seven Extension equal eight and in equal 20 and zika equal full. So does that. Value is the sample mean decreased boy. The population mean divide by divided by the standard division standard division so that equal export minus mu over zita over square root in equal eight minus seven over full over square root, 20 is equal. Almost 1.12 Christian and proceed women It snowed two new equal seven and H E to mu not equal. Seven. Export equal Eat Zita equal four and in equal 20. That value is a sample me increased by the population mean divided by the standard deviation. So then equal stash minus mu over zita over square root and equal eight minus 7/4 over square root. 20 is equal 1.12 The B value is the population off obtaining a value more extreme or equal to the A standards? Um, standards. The test static that did remind the probability using table five So probability equal be off is it is less than minus 1.12 or two is or our century, or that is bigger than minus 1.12 Equal to multiply boy, be off. That is less than minus 1.12 equal to multiply. Boy 0.1314 equal 0.26 to 8. Question number D given each node two new equal seven and h A to mu not equal seven. Extension equal. Eat Zita equal full in equal 20 Alfa equal or point or five. Does it value is a sample mean decreased by the population mean divided by the standard deviation. So then equal backstage minus mu over. Zita over a square. Root in equals eight minus seven over four minus square root 20 is equal 1.12 Yeah, the P the P value is the probability off obtaining a value more extreme or equal to the standard. A standard test Statics. Uh, that did your mind the probability using table five. So prosperity equal probability of scent is listening minus 1.12 or they he's bigger than minus one 0.12 equal to multiply boy be off. That is less than minus 1.12 equal to multiply boy 0.1314 equal 0.26 to 8. If the If the value is smaller than the significance level Alfa, then the null hypothesis is rejected. So be is bigger than 0.5 and this will feel toe eject each note.

We have n equals 25 values, transformers, symmetric, mound shaped distribution sample mean is equal to 10 and the sample standard deviation is equal to two. Using a significant level of alpha equals 20.5 conducted to tail test of new equals 9.5 on the stand for the population. Me first, you have to answer A. Is it appropriate to use a distribution for hypothesis test for this? Yes. It's the distribution of symmetric and mount shape so we can use a student's T distribution. Note that the degrees of freedom is equal to end minus one is equal to 24 in this case, next one of the hypotheses, the hypotheses are h not mu equals 9.5. An alternative hypothesis. You does not equal 9.5. Next let's compute t remember the formula for tea, which is given here. This computes out the T value 1.25 Next let's compute the p p interval using a T interval. We see that P falls between 0.2 and 0.25 for this T statistic. Next we deserve and whether or not we reject asian art. No, the entire P interval is greater than our significant level alpha. So we do not reject a chart, and we interpret this to mean that we lack evidence that suggest new. It's not equal to 9.5.


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