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Chapter 9: Q1 (page 423)

Verifying requirements in the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups. The treatment group considered of 201,229 children given the sulk vaccine for polio, and 33 of those children developed polio. The other 200,745 children were given a placebo, and 115 of those children developed polio. If we want to use the methods of this section to test the claim that the rate of polio is less for children given the sulk vaccine, are the requirements for a hypothesis test satisfied? Explain.

Short Answer

Expert verified

Yes, the requirement of the test is satisfied.

Step by step solution

01

Step-1: Given information

The study is conducted on 401974 children divided into two groups:

Treatment: of 201229, 33 developed polio.

Placebo: of 200,745, 115 developed polio.

02

Step-2: Express the claim

The claim to be tested is whether the rate of polio is less for children in the treatment group or not.

The test of proportions is expected to be conducted.

There are three requirements of the test.

03

Step-3: Verify the requirements

1. Simple random samples: The samples are selected randomly

2. Independence of group: One treatment group considered is 201,229 children given Salk vaccine for polio, and another treatment group of 200,745 children were given Placebo. These two groups are independent of each other, as there is no association between the children in each group.

3. Counts of successes or failures: From each sample, there are at least 5 number of successes and 5 number of failures.

In the treatment group of children, the successes and failures are larger than 5. In Placebo group of children, the successes and failures are larger than 5.

Thus, requirements are satisfied.

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Most popular questions from this chapter

In Exercises 5鈥�20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with 鈥淭able鈥� answers based on Table A-3 with df equal to the smaller of\({n_1} - 1\)and\({n_2} - 1\).)

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a. Use a 0.05 significance level to test the claim that females and males have the same mean BMI.

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Female BMI: n = 70, \(\bar x\) = 29.10, s = 7.39

Male BMI: n = 80, \(\bar x\) = 28.38, s = 5.37

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A sample size that will ensure a margin of error of at most the one specified.

Critical Thinking: Did the NFL Rule Change Have the Desired Effect? Among 460 overtime National Football League (NFL) games between 1974 and 2011, 252 of the teams that won the overtime coin toss went on to win the game. During those years, a team could win the coin toss and march down the field to win the game with a field goal, and the other team would never get possession of the ball. That just didn鈥檛 seem fair. Starting in 2012, the overtime rules were changed. In the first three years with the new overtime rules, 47 games were decided in overtime and the team that won the coin toss won 24 of those games. Analyzing the Results

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