Question

In a large clinical trial, 398,890 children were randomly assigned to two groups. The treatment group consisted of 200,145 children given a vaccine for a certain disease, and 40 of those children developed the disease. The other 198,745 children were given a placebo, and 159 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Complete parts (a) through (d) below.

a. Assume that a 0.10 significance level will be used to test the claim that p1<p2. Which is better: A hypothesis test or a confidence interval?

(1)_____ is better.

b. In general, when dealing with inferences for two population proportions, which two of the following are equivalent: confidence interval method; P-value method; critical value method?

(2)_____ are equivalent, in that they will always lead to the same conclusion. Both of these methods use a standard deviation based on (3)_____ whereas the other method uses a standard deviation based on (4)_____

c. If a 0.10 significance level is to be used to test the claim that p1<p2, what confidence level should be used?

_____% (Type an integer or a decimal.)

d. If the claim in part (c) is tested using this sample data, we get this confidence interval:
-0.000691<p1-p2<-0.000509. What does this confidence interval suggest about the claim?

Because the confidence interval (5)_____ (6)_____ there (7)_____ a significant difference between the two proportions. Because the confidence interval consists (8)_____ (9)_____ it appears that the first proportion is (10)_____ the second proportion. There is (11)_____ evidence to support the claim that the rate of polio is less for children given the vaccine than it is for children given a placebo.
(1) A hypothesis test
A confidence interval

(2) Confidence interval method and P-value method
P-value method and critical value method
Confidence interval method and critical value method

(3) the assumption that the two population proportions are equal,
estimated values of the population proportions,

(4) estimated values of the population proportions.
the assumption that the two population proportions are equal.

(5) contains
does not contain

(6) the critical value,
0,
the pooled sample proportion,
the significance level,

(7) appears to be
does not appear to be

(8) only of values greater than
of values both less than and greater than
only of values less than

(9) 0,
the significance level,
the pooled sample proportion,
the critical value,

(10) greater than
less than
not significantly different from

(11) insufficient
sufficient

Answer 1

a) (1) A Hypothesis test is better.

b) (2) P-value method and critical value method are equivalent, in that they will always lead to the same conclusion. Both of these methods use a standard deviation based on (3) estimated values of the population proportions  whereas the other method uses a standard deviation based on (4) the assumption that the two population proportions are equal.

c) 90%

d) Because the confidence interval (5) does not contain (6) 0 there (7) appears to be a significant difference between the two proportions. Because the confidence interval consists (8) only of values less than (9) 0 it appears that the first proportion is (10) less than the second proportion. There is (11) sufficient evidence to support the claim that the rate of polio is less for children given the vaccine than it is for children given a placebo.