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Chapter 11: Q.66 (page 658)

What is the test statistic?

Short Answer

Expert verified

The value of the test statistic is42.17.

Step by step solution

01

Given Information

The average waiting time in a doctor’s office varies. The standard deviation of waiting times in a doctor’s office is 3.4 minutes. A random sample of 30 patients in the doctor’s office has a standard deviation of waiting times of 4.1 minutes.

02

Explanation

We have to find the test statistic:

Here, we observed that

n=30

s=4.1

σ=3.4

Let's find the null hypothesis and alternative hypothesis

Null hypothesis: H0:σ2=3.42

Alternative hypothesis: Ha:σ2>3.42

Then, compute the degrees of freedom:

n-1

=30-1

=29

We can compute the test statistics by using the given formula

localid="1648703739753" Teststatistic=(n-1)s2σ2

=(29-1)(4.1)2(3.4)2

=29×16.8111.56

=42.17

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Most popular questions from this chapter

You want to buy a specific computer. A sales representative of the manufacturer claims that retail stores sell this computer at an average price of \(1,249 with a very narrow standard deviation of \)25. You find a website that has a price comparison for the same computer at a series of stores as follows: \(1,299;\)1,229.99;\(1,193.08;\)1,279;\(1,224.95;\)1,229.99;\(1,269.95;\)1,249. Can you argue that pricing has a larger standard deviation than claimed by the manufacturer? Use the 5% significance level. As a potential buyer, what would be the practical conclusion from your analysis?

Letα=0.05

Decision: ________

Conclusion (write out in a complete sentence.): ________

If df=2, the chi-square distribution has a shape that reminds us of the exponential.

The average waiting time in a doctor’s office varies. The standard deviation of waiting times in a doctor’s office is 3.4 minutes. A random sample of 30 patients in the doctor’s office has a standard deviation of waiting times of 4.1 minutes. One doctor believes the variance of waiting times is greater than originally thought.

What type of test should be used?

According to an avid aquarist, the average number of fish in a 20-gallon tank is 10, with a standard deviation of two. His friend, also an aquarist, does not believe that the standard deviation is two. She counts the number of fish in 15other 20-gallon tanks. Based on the results that follow, do you think that the standard deviation is different from two? Data:11;10;9;10;10;11;11;10;12;9;7;9;11;10;11
See all solutions

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