health insurance companies. A recent study cxamined 35randomly selected children

Question

health insurance companies. A recent study cxamined 35randomly selected children and round that 28 of thom showed signs of genedc abnormality. (a) Which hypothescs should be used to to if the proportion of genetic abnormalitics has increazed in recent years? Ho: -0.06 vs. Ha: p > 0.06 Ho: -0.06 vs. Hg: P 0.06 Ho: -0.0784 vs. Ha: p 0.0784 Ho: p-0.0784 vs. Ha: p + 0.0784 Ho: p 0.06 vs. Ha: p0.06 (b) Are thc conditions met tor doing the hypothesis test? The sample was randamly chosen. The 15 sxcesses and faiures condition is met. The chidren taking part in the study were independent of cach other. None of the conditions are met. (c) What is the -value? Use 3 decimals.) (d) what does this p-value mean? The p value is the chance of abserving 28 or more dildren with genetic abnorm eRies e dom sample of 357 children, r the true proportion of children with genetic abnormalties is 7.8496. The p-vaiue is the chance of observing 28 cr mere ildren with genetic 8bnormelties ra endarn sample of 357 children, rthetrue proportion of children wth genetic ebnorme ities is 6%, The p-value is the chance of observing 6% or ch dren with genetic abnormalities. The p-value gves te actual percentage of chidran who have ganetic abnormalitea. (e) What is the conclusion ofthe hypotneas test, tor -0.05? Do not reject H0. There is insufficient evidence that more than 6% of this nation's children have genetic abnormalities. Reject HO, Thore is sfficient evidence that more than 6% of this nation's children havo genetic aenormaite Reject Ho-There is insufficient evidence that more than 6% of this nstion's children have genetic bnormalties. Do not reject M0, There 's sufficient evidenc that more than 6% of this nation's children h ve genete abnormalres, (F) Do this study show thet environmental chemicals cause congenital abnormelities? Yes, the hypothesia teat shows that ervironmental chemicals cause the ganotic abnormality. Thia study docs not addresa what causc the genetc atnonmality. No, the hypothesis teat shows that environmentel chemicels do not cause the genetie abrnermality.

Explanation / Answer

Answer in details with explanations and calculation wherever required:

a. Claim comes in the alternative hypothesis
The claim is that increase in number of chemicals has led to increase in no. of abnormalities

Ho: p = .0784, Ha: p> .0784

4th option is right

b.One must also check that any assumptions (conditions) needed to run the test have been satisfied e.g. normality of data, independence, and number of success and failure outcomes
Here, in our case - The sample must be reasonably random.

So, 1st option - the sameple was randomly choosen is met

c.p-value?

p = x/n = 28/357 = .0784

Z = p-p0/sqrt(p0*p0'/n) = (.0784-.06)/sqrt(.0784*.9216/357) = 1.29

The p-value is therefore P(Z>1.29) = .0985

d. 2nd option is right interpretation. Please remember that true propotion is 6%

e. Since our p-value is .0985 and is more than .05 we conclude that we do not reject Ho.
There is insufficient evidence that more than 6% of this nation' children have gen.ab.
Option 1 is right

f. Options 3 is right. Since there is no statistically significant increase in the proportion with genetic abnormalities we can conclude the hypothesis and say that ' envirnomnrtal chemicals do not cause the genetic abnormalities'.

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