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Chapter 9: Q. 10 (page 564)

In the study of older students’ attitudes, the sample mean SSHA score was 125.7and the sample standard deviation was 29.8. A significance test yields a P-value of 0.0101.

a. Explain what it would mean for the null hypothesis to be true in this setting.

b. Interpret the P-value.

Short Answer

Expert verified

Part a. The correct mean score for the students who are at least 30years of age is 115.

Part b. The P-value is if the population mean is equal to115, then there is possibility of 1.01%of getting a random sample with a sample mean of 125.7or more.

Step by step solution

01

Part a. Step 1. Given information

From the previous exercise

H0:μ=115Ha:μ>115

02

Part a. Step 2. Explanation

μis the population mean score of students who are at least 30years of age.

If the null hypothesis H0:μ=115is true, then this means that the true mean score for students who are at least 30years of age is115.

03

Part b. Step 1. Given information

n=45x¯=125.7s=29.8P=0.0101=1.01%

Result previous exercise:

H0:μ=115Ha:μ>115

04

Part b. Step 2. Explanation

The P-value is if the population mean is equal to 115, then there is possibility of 1.01%of getting a random sample with a sample mean of125.7 or more.

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Most popular questions from this chapter

How much juice? Refer to Exercise 3. The mean amount of liquid in the bottles is 179.6ml and the standard deviation is 1.3ml. A significance test yields a P-value of 0.0589. Interpret the P-value.

Opening a restaurant You are thinking about opening a restaurant and are

searching for a good location. From research you have done, you know that the mean income of those living near the restaurant must be over \(85,000to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50people living near one potential location. Based on the mean income of this sample, you will perform a test of

H0:μ=\)85,000

Ha:μ>$85,000

where μis the true mean income in the population of people who live near the restaurant. Describe a Type I error and a Type II error in this setting, and give a possible consequence of each.

Powerful potatoes Refer to Exercise 85. Determine if each of the following

changes would increase or decrease the power of the test. Explain your answers.

a. Change the significance level to α=0.10

b. Take a random sample of 250 potatoes instead of 500 potatoes.

c. The true proportion is p=0.10 instead of p=0.11

Which of choices (a) through (d) is not a condition for performing a significance test about a population proportion p?

a. The data should come from a random sample from the population of interest.

b. Both np0and n(1-p0)should be at least 10.

c. If you are sampling without replacement from a finite population, then you should sample less than 10%of the population.

d. The population distribution should be approximately Normal unless the sample size is large.

e. All of the above are conditions for performing a significance test about a population proportion.

The reason we use t procedures instead of z procedures when carrying out a test about a population mean is that

a. z requires that the sample size be large.

b. z requires that you know the population standard deviation σ

c. z requires that the data come from a random sample.

d. z requires that the population distribution be Normal.

e. z can only be used for proportions.
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