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Chapter 9: Q. 1 (page 563)

Mr. Tabor believes that less than 75% of the students at his school completed their math homework last night. The math teachers inspect the homework assignments from a random sample of 50 students at the school.

Short Answer

Expert verified

H0:p=75%=0.75Ha:p<0.75

Step by step solution

01

Step 1. Given information

Claim is proportion is less than75%.

02

Step 2. Explanation

The null hypothesis statement is that the population is equal to the value mentioned in the claim:

H0:p=75%=0.75

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the population proportion is equal to the value given in the claim. If the null hypothesis is the claim, then the alternative hypothesis statement is the opposite of the null hypothesis.

Ha:p<0.75

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Most popular questions from this chapter

1 A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay \(100 for the upgrade. For the upgrade to be profitable, the company must sell it to more than 20% of their customers. You contact a random sample of 60 customers and find that 16 would be willing to pay \)100 for the upgrade.

a. Do the sample data give convincing evidence that more than 20% of the company’s customers are willing to purchase the upgrade? Carry out an appropriate test at the α=0.05significance level.

b. Which would be a more serious mistake in this setting—a Type I error or a Type II error? Justify your answer.

c. Suppose that 30% of the company’s customers would be willing to pay $100 for the upgrade. The power of the test to detect this fact is0.60. Interpret this value.

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.

Upscale restaurant You are thinking about opening a restaurant and are searching for a good location. From the 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 site. Based on the mean income of this sample, you will perform a test at the

α=0.05 significance level of H0:μ=\)85,000versus Ha:μ>\(85,000, where μ is the true mean income in the population of people who live near the restaurant. The power of the test to detect that μ=\)86,000is 0.64 Interpret this value.

Making conclusions A student performs a test of H0:μ=12versus Ha:μ≠12

at the α=0.05significance level and gets a P-value of 0.01. The

student writes: “Because the P-value is small, we reject H0. The data prove that Hais true.” Explain what is wrong with this conclusion.

Fair coin? You want to determine if a coin is fair. So you toss it 10times and record the proportion of tosses that land “heads.” You would like to perform a test of H0:p=0.5versus Ha:p≠0.5, where p= the proportion of all tosses of the

coin that would land “heads.” Check if the conditions for performing the significance test are met.
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