Question

When a scientist conducted a genetics experiments with​ peas, one sample of offspring consisted of 903 ​peas, with 702 of them having red flowers. If we​ assume, as the scientist​ did, that under these​ circumstances, there is a 3 divided by 4 probability that a pea will have a red​ flower, we would expect that 677.25 ​(or about 677​) of the peas would have red​ flowers, so the result of 702 peas with red flowers is more than expected. a. If the​ scientist's assumed probability is​ correct, find the probability of getting 702 or more peas with red flowers. b. Is 702 peas with red flowers significantly​ high? c. What do these results suggest about the​ scientist's assumption that 3 divided by 4 of peas will have red​ flowers? a. If the​ scientist's assumed probability is​ correct, the probability of getting 702 or more peas with red flowers is nothing. ​(Round to four decimal places as​ needed.) b. Is 702 peas with red flowers significantly​ high? ▼ No, Yes, because the probability of this event is ▼ less greater than the probability cutoff that corresponds to a significant​ event, which is ▼ 0.95. 0.05. 0.5. c. What do these results suggest about the​ scientist's assumption that 3 divided by 4 of peas will have red​ flowers? A. Since the result of 702 peas with red flowers is significantly​ high, it is not strong evidence against the​ scientist's assumption that 3 divided by 4 of peas will have red flowers. B. Since the result of 702 peas with red flowers is not significantly​ high, it is strong evidence against the​ scientist's assumption that 3 divided by 4 of peas will have red flowers. C. Since the result of 702 peas with red flowers is significantly​ high, it is strong evidence supporting the​ scientist's assumption that 3 divided by 4 of peas will have red flowers. D. Since the result of 702 peas with red flowers is not significantly​ high, it is not strong evidence against the​ scientist's assumption that 3 divided by 4 of peas will have red flowers. E. The results do not indicate anything about the​ scientist's assumption. F. Since the result of 702 peas with red flowers is significantly​ high, it is strong evidence against the​ scientist's assumption that 3 divided by 4 of peas will have red flowers.

Answer 1

A.

This becomes a case of the binomial distribution with the event of success being that a pea will have a red​ flower with probability p. Let X be the random variable which denotes the presence of red flowers in n peas.

we know that, p = 3/4

= 0.75

P(X=x) = (nCx)*p^x*(1-p)^n-x

With n = 903 and using the above formula:

P(X702) = 0.030

B.

Definition of an unusual no. of success in a binomial experiment :

If,

P(Xx) < 0.05

and P(Xx) < 0.05 then x is an unusual no. of successes in that experiment.

Since P(X702) = 0.03 < 0.05

then we can say that X = 702 is a significantly high no. given the p and n.

C.

As we can see that 702 successes with p = 0.75 are an unusual no. of success thus probability need to be a bit high so that 702 does not remain a significantly high no. of successes.

Hence we can say that,

Scientist's null hypothesis that p = 0.75 will be rejected and thus,

F. Since the result of 702 peas with red flowers is significantly​ high, it is strong evidence against the​ scientist's assumption that 3 divided by 4 of peas will have red flowers.

is the correct answer.

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