question 4 A-E lial are lhè consequences of l. this type of error? 4. Billy\'s m

Question

question 4 A-E lial are lhè consequences of l. this type of error? 4. Billy's mother asks him, "Shouldn't you be studying for your spelling test instead of watching television?" Billy replies, "I already studied." "You know all of the words on this list?" his mother asked skeptically. "Well. maybe not all of them," he replies, "but I bet I know over 90% of them." "I am going to pick four words from this list at random. If you spell all four of them correctly, you can watch television. If not, you have to study for an hour."

Explanation / Answer

Part a

This is an alternative hypothesis.

Ha: P > 0.9

Part b

The competing hypothesis or null hypothesis for this test is given as below:

H0: P = 0.9

Part c

This would be type II error which is defined as the probability of do not rejecting the null hypothesis when actually the null hypothesis is false. The probability that Billy spells all four words correct is 1 – 0.9 = 0.1 or 10%.

Part d

This would be type II error.

The probability of he misses at least one word is given as below:

P(X1) = 1 – P(X=0)

P(X=0) = 4C0* 0.08^0 * (1 – 0.08)^(4 – 0)

P(X=0) = 4C0 * 0.08^0 * 0.92^4

P(X=0) = 1 * 1 * 0.92^4

P(X=0) = 0.92^4

P(X=0) = 0.99995904

P(X1) = 1 – P(X=0)

P(X1) = 1 – 0.99995904 = 0.00004096

Required probability = 0.00004096

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