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Chapter 7: Q66E (page 424)

A two-tailed test was conducted with the null and alternative hypotheses stated being \({H_0}:p = .69\) against \({H_a}:p \ne .69\), respectively, with a sample size of 150. The test results were z = -.98 and two-tailed p-value = .327

a. Determine the conditions required for a valid large sample test

Short Answer

Expert verified
  1. The sample is drawn from a binomial population. The sample size is large. These conditions are required for a valid large sample test.

Step by step solution

01

Given Information

The hypothesis are given by

\(\begin{aligned}{H_0}:p = .69\\{H_a}:p \ne .69\end{aligned}\)

The z-statistic is -.98..

The p-value is .327

02

Calculate np and nq

For \(n = 150\,and\,p = .69\)

\(\begin{aligned}np &= 150 \times 0.69\\ &= 103.5\\nq &= 150 \times 0.31\\ &= 46.5\end{aligned}\)

Here, np and nq both are greater than 15.

03

Step 3:

The sample is drawn from a binomial population. The sample size is large. These conditions are required for a valid large sample test.

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Most popular questions from this chapter

Producer's and consumer's risk. In quality-control applications of hypothesis testing, the null and alternative hypotheses are frequently specified as\({H_0}\)The production process is performing satisfactorily. \({H_a}\): The process is performing in an unsatisfactory manner. Accordingly, \(\alpha \) is sometimes referred to as the producer's risk, while \(\beta \)is called the consumer's risk (Stevenson, Operations Management, 2014). An injection molder produces plastic golf tees. The process is designed to produce tees with a mean weight of .250 ounce. To investigate whether the injection molder is operating satisfactorily 40 tees were randomly sampled from the last hour's production. Their weights (in ounces) are listed in the following table.

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