Question

. In the 1980s, it was generally believed that congenital abnormalities affected about 5% of the nation’s children. Some 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 384 children and found that 46 of them showed signs of an abnormality. Is this strong evidence that the risk has increased?

a. Define the parameter and state the hypotheses.

b. Define the sampling distribution (mean and standard deviation).

c. Perform the test and calculate P-value

d. State your conclusion.

e. Explain what the p-value means in this context.

Answer 1

Explanation:

Reject null hypothesis

Answer 2

Reject null hypothesis

Explanation:

a)
`H_0: p =0.05\\H_a: p >0.05`

(Right tailed test at 5% level)

p = risk proportion

Sample proportion =
`(46)/(384) \\\\=0.1198`

Std error =
`\sqrt{(pq)/(n) } \\=\sqrt{(0.05(0.95))/(384) } \\=0.0111`

p difference =
`0.1198-0.05=0.0698`

b) Sampling proportion is Normal with mean = 0.05 and std error = 0.0698

c) Z = test statistic = p diff/std error

= 6.29

p value <0.05

d) Since p < alpha we reject null hypothesis.

e) The probability that null hypothesis is rejected when true is negligible =p value