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# Q10 - vote for the Progressive Party Is there any...

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EXERCISES IN STATISTICS Series A, No. 10 1. A horticulturist considers that a batch of seeds is worth sowing if 50% of the resulting flowers are going to be pure white. To test the worth of a particular batch, he sows eight seeds with the intention of sowing the remainder if at least four of the eight plants have white flowers. Find the probability of his making a wrong decision (a) if 25% of the seeds are of the white variety, and (b) if 75% of the seeds are of the white variety. 2. In the previous election, 65% of the poll voted for the Progressive Party. In a recent opinion survey, 280 out of 400 people have said that they intend to
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Unformatted text preview: vote for the Progressive Party. Is there any substantial evidence to suggest that the party has increased its support? Hint: use the fact that ≥ x n − p ¥ ¡r pq n is distributed approximately as a standard normal variate. 3. Imagine that a random sample of size 160 is drawn from a normal popula-tion where the standard deviation is 25 in order to test the null hypothesis that the mean is 104 against the alternative that it is 100. Calculate the probability of a Type II error in a one-tailed test with a 5% signiﬁcance level. What sample size is required for the probability of the Type II error to be 0.05?...
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