Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteer be at the rghit pclae. The rset can be a toatl mses and you can sitll raed it wouthit porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe.

(Or rather...

According to a researcher at Cambridge University, it doesn't matter in what order the letters in a word are, the only important thing is that the first and last letter be at the right place. The rest can be a total mess and you can still read it without problem. This is because the human mind does not read every letter by itself but the word as a whole.)

According to a follow-up research at the University of Durham, however, there is a cost in relation to normal text.Whereas the base reading rate for normal sentences was 255 wpm, when the transpositions occurred to the internal letters, average reading rate was 227 wpm (a 12% decrement in reading speed (DRS)), when the transpositions involved the final or ending letters of words, average reading rate was 189 wpm (a 26% decrement) and when the transpositions were at the beginning of the words, average reading rate was 163 wpm (a 36% decrement).

We will assume that the distribution of DRS (decrement in reading speed) is approximately normal with mean 12% and standard deviation 6% for pages with internal letters of the words transposed, and it is approximately normal with mean 36% and standard deviation 9% for pages with beginnings of the words transposed.

After reading this article, Jim decided to play a joke on his friend David, whose normal reading rate is known to be the regular 255 wpm.Jim printed a number of pages of text, some with internal letters of the words transposed, and some with letters at the beginning of the words transposed.Jim decided, he would ask David to pick a page at random and to read it to the end, and (while enjoying the reaction) would measure David's DRS.Not knowing which typeof page David would pick (internal letters transposed or beginning letters transposed), Jim decided that if David's measured DRS turns out to beless than 24%, then Jimwill conclude that David must be reading a page with only internal letters of the words transposed, and if David's measured DRS turns out to be 24% or higher, then Jimwill conclude that David must be reading a page with letters at the beginning of the words transposed.

Statistically speaking, Jim will be deciding between the following hypotheses:

H0: Davidis reading a page with internal lettersof the words transposed; that is, DRS measurements follow a N(0.12, 0.06) distribution;

Ha: Davidis reading a page with beginning lettersof the words transposed; that is, DRS measurements follow a N(0.36, 0.09) distribution.

And Jim's decision rule for deciding between these two possible hypotheses will be:

Reject H0if Dave's measured DRS 0.24, and thus fail to reject H0if Dave's measured DRS <0.24.

For this situation, what is the value of, the significance level (also known as the probability of incorrectly rejecting the null hypothesis)?

For this situation, what is the value of (also known as the probability of type II error, that is, the probability of incorrectly failing to reject H0)?

For this situation, what is the power of the test (also known as the probability of correctly rejecting the null hypothesis)?