Question

In a large clinical​ trial, 391 comma 407 children were randomly assigned to two groups. The treatment group consisted of 196 comma 153 children given a vaccine for a certain​ disease, and 26 of those children developed the disease. The other 195 comma 254 children were given a​ placebo, and 83 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 0.01 significance level will be used to test the claim that p 1less thanp 2. Which is​ better: A hypothesis test or a confidence​ interval? A hypothesis test 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? Upper P dash 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 the assumption that the two population proportions are equal, whereas the other method uses a standard deviation based on estimated values of the population proportions.

c. If a 0.01 significance level is to be used to test the claim that p 1less thanp 2​, what confidence level should be​ used? 98​% ​(Type an integer or a​ decimal.)

d. If the claim in part​ (c) is tested using this sample​ data, we get this confidence​ interval: negative 0.000417less thanp 1minusp 2less thannegative 0.000168. What does this confidence interval suggest about the​ claim? Because the confidence interval ___ (does not contain or contains) ___(0, the pooled sample proportion, the critical value, or the significance value) there _____ (appears to be or does not appear to be) a significant difference between the two proportions. Because the confidence interval consists ▼ ▼ ___ (only of values greater than, of values both less than and greater than, or only of values less than) _____ (0, the significance value, critical value, or the pooled sample proportion) it appears that the first proportion is ▼ ____ (greater than, less than, or not significantly different from the second proportion). There is ▼____( sufficient, or insufficient) 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.

Answer 1

(a)

A hypothesis test is better.

Confidence interval is used for estimating a population parameter from the sample statistic. Hypothesis test is used to compare one parameter with the other or with hypothesised value in order to determine if there is any significant difference.

However, confidence interval can also be used instead of hypothesis testing.

(b)

P-value method and critical value method are​ equivalent because they are two different approaches leading to the same conclusion in a hypothesis test.

(c)

99% confidence level is to be used in case of 0.01 significance level.

Confidence level = 1 - significance level =1 - 0.01 =0.99 =99%

(d)

The given confidence interval is:

(-0.000417 < p1 - p2 < -0.000168)

Because the confidence interval  does not contain 0, there appears to be a significant difference between the two proportions. Because the confidence interval consists only of values less than 0​​​​​​, it appears that the first proportion is less than the second proportion. There is 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.