It the 1980s, it was generally believed that congenital abnormalities affected a

Question

It the 1980s, it was generally believed that congenital abnormalities affected about 7% of a large nation's children. So people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 402 randomly selected children and found that 42 of them showed signs of an abnormality. Is this strong evidence that the risk has increased? (We consider a P-value of around 5% to represent reasonable evidence.) Complete parts a through f a) Write appropriate hypotheses. Let p be the proportion of children with genetic abnormal es. Choose the comect answer below O B. Ho p 0.1045 vs. HA: p 0.1045 O A. Ho: p 0.07 vs. HA: p

Explanation / Answer

(a) Null Hypothesis : H0 : p = 0.07

Alternative Hypothesis : Ha : p> 0.07

Option f is right

(b) (i) The sample is random . YES

(ii) The data are indepenedent : YEs

(iii) THere are more than 10 successes and 10 failures . : Yes [ successes = 42 and failures = 360]

(iv) less than 10% population is sampled : Yes [ as population is of large naton's children, must be in millions]

so all 4 are correct.

(c) p0 = 0.07 and p = 42/402 = 0.1045

Z = ( p - p0)/ sqrt [ p0 ( 1- p0)/n] = ( 0.1045 - 0.07)/ sqrt ( 0.07 * 0.93/ 402)

Z = 0.0345/ 0.01272 = 2.71

P-Value is 0.003364

(d) What is P - value in this case: In this case, P - value is the chance of observing 42 or more children with genetic abnormalities in a random sample of 402 children if 7% of children have genetic abnormalities. Option A is correct.

(e) We can reject the null hypothesis. THere is significanct evidence that more than 7% of the nation's childen have genetic abnormalities. Option C is correct.

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