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Chapter 9: Q.23 (page 548)
You read that a statistical test at significance level=0.05 has power 0.78. What are the probabilities of Type I and Type II errors for this test?
The probabilities are Type I = and Type II error =
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The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures
students鈥� attitudes toward school and study habits. Scores range from 0 to 200. The mean score for U.S. college students is about 115. A teacher suspects that older students have better attitudes toward school. She gives the SSHA to an SRS of 45
of the over 1000 students at her college who are at least 30 years of age.
The design of controls and instruments affects how easily people can use them. A student project investigated this effect by asking right-handed students to turn a knob (with their right hands) that moved an indicator. There were two identical instruments, one with a right-hand thread (the knob turns clockwise) and the other with a left-hand thread (the knob must be turned counterclockwise). Each of the students used both instruments in a random order. The following table gives the times in seconds each subject took to move the indicator a fixed distance:
(a) Explain why it was important to randomly assign the order in which each subject used the two knobs.
(b) The project designers hoped to show that right-handed people find right-hand threads easier to use. Carry out a significance test at the significance level to investigate this claim
A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay for the upgrade. For the upgrade to be profitable, the company needs to sell it to more than of their customers. You contact a random sample of customers and find that 16 would be willing to pay for the upgrade.
(a) Do the sample data give good evidence that more than of the company鈥檚 customers are willing to purchase the upgrade? Carry out an appropriate test at the significance level.
(b) Which would be a more serious mistake in this setting鈥攁 Type I error or a Type II error? Justify your answer.
(c) Other than increasing the sample size, describe one way to increase the power of the test in (a).
For the study of Jordanian children in Exercise 4, the sample mean hemoglobin level was 11.3 g/dl and the sample standard deviation was 1.6 g/dl. A significance test yields a P-value of 0.0016.
(a) Interpret the P-value in context.
(b) What conclusion would you make if = 0.05? = 0.01? Justify your answer.
Hemoglobin is a protein in red blood cells that carries oxygen from the lungs to body tissues. People with fewer than 12 grams of hemoglobin per deciliter of blood (g/dl) are anemic. A public health official in Jordan suspects that Jordanian children are at risk of anemia. He measures a random sample of 50 children. Check the conditions for carrying out a significance test of the official鈥檚 suspicion.
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