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free of colds. This difference is statistically significant (P *= 0.03)    <;■

the vitamin C group. Can we conclude that vitamin C has a strong efifect in preventing colds? Explain your answer.

6.74    Every user of statistics should understand the distinction betweejlMpeal

significance and practical importance. A sufficiently large sample will declare very smali effects statistically significant. Let us suppose wat SAT    |

mathematics (SATM) scores in the absence of coaching vary normally with mean /z = 475 and a = 100. Suppose further that coaching may change p but does not change <r. An increase in the SATM score from 475 to 478 is of no importance in seeking admission to college, but this unimportant change can be statistically very significant. To see this, calculate the P-value for the test of

H₀: il = 475 H_a: p >475

in each of the following situations:

(a)    A coaching service coaches 100 students; their SATM scores average ■^%t = 478.

(b)    By the next year, the service has coached 1000 students; their SATM scores average x = 478.

(c)    An advertising campaign brings the number of students coached fb 10,000; their average score is still x = 478.

6.75    Give a 99% confidence interval for the mean SATM score H after coaching in each part of the previous exercise. For large samples, the confidemK interval says, "Yes, the mean score is higher after coachingg but only by a smali amount.”

6.76    As in the previous exercises, suppose that SATM scores vary normaMpth a # 100. One hundred students go through a rigorous training program designed to raise their SATM scores by improving their mathematics skills. Carry out a test of

H₀: /i = 475 H_a'. /u. > 475

in each of the following situations:

(a) The students' average score is x — 491.4. Is this result signihca|fiH the 5% level?

/U\ TłiP awraap crnrp is F = 49I S Ts thic