Question a~b,please help 8005A SEMESTER 2 2010 3. 15 marks Two measurements are

Question

Question a~b,please help

8005A SEMESTER 2 2010 3. 15 marks Two measurements are taken on each of 25 individuals, before(x) and after (y) a treatment. The x- and y-measurements are shown in the R output below, along with some other calculations and graphical output. Look over it carefully and then answer the questions which follow [1] 1.60312418 -2.06102544 -1.75647941 -0.22725671 0.08272729 1.00781044 7] -1.21937625 1.12035588 -0.38697633 2.24173252 0.52065991 2.73209367 13 0.12696252 1.43322231 0.71537482 0,86475981 0.53444080 0.70228742 [191 0.08754805 0.56305543 0.96900033 1.84191989 -0.06421617 -0.23076978 3 [25] 0.87202006 [1) 0.29211545 -2,24971175 -2.06651680 -1.20748167 -0.78238789 0.35618311 [7) -2.50129398 0,52543037-0.27436662 1.35137515 0.20490834 -0.02474893 [13] -0.57510685-0.30360414 0.20720438 0.20076354-0.44960451 1.63390683 [19) 0.07862053 -0,31208401 1.00054340 1.49314588 -0.31984030 1.48864988 [25) 0.92098992 x-y [1 1.895239631 0.188686317 0,310037393 0.980224958 0.865115179 [6] 0.651627330 1.281917730 0.594925507 0.112609708 0.890357371 [11] 0.315751566 2.756842599 0.702069366 1.736826453 0.508170438 [16] 0,66399627O 0.984045311 -0.931619410 0.008927522 0.8T5139447 [21 -0.031543067 0,348774014 0.255624131 -1.719419658 -0.048969864 > mean(x) [11 0.4829198 > mean (y) [11 -0.07588566 sd(x) 1] 1.125136 ad(y) [1] 1,114776 > length(x) [1] 25 >length y [1) 25 aun(x) 1] 12.07300 sun(y) 11.897142 sun(x2) [1] 36.21261 sun y 2) [1] 29.96938 u((x-y)"2) [1] 26.31768 > sun (x+y.) [1] 19.93216

Explanation / Answer

A statistical hypothesis is an assumption about a population parameter. This assumption may or may not be true. Hypothesis testing refers to the formal procedures used by statisticians to accept or reject statistical hypotheses.

Statistical Hypotheses

The best way to determine whether a statistical hypothesis is true would be to examine the entire population. Since that is often impractical, researchers typically examine a random sample from the population. If sample data are not consistent with the statistical hypothesis, the hypothesis is rejected.

There are two types of statistical hypotheses.

For example, suppose we wanted to determine whether a coin was fair and balanced. A null hypothesis might be that half the flips would result in Heads and half, in Tails. The alternative hypothesis might be that the number of Heads and Tails would be very different. Symbolically, these hypotheses would be expressed as

H0: P = 0.5
Ha: P 0.5

Suppose we flipped the coin 50 times, resulting in 40 Heads and 10 Tails. Given this result, we would be inclined to reject the null hypothesis. We would conclude, based on the evidence, that the coin was probably not fair and balanced.

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