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Chapter 9: Q.10 (page 546)
In planning a study of the birth weights of babies whose mothers did not see a
doctor before delivery, a researcher states the hypotheses as
The problem is incorrect as the population mean value is as per the null hypothesis and is less than as per the alternative hypothesis.
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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).
Two-sided test The one-sample t statistic from a sample of observations for the two-sided test of has the value .
(a) Find the P-value for this test using (i) Table and (ii) your calculator. What conclusion would you draw at the significance level? At the significance level?
(b) Redo part (a) using an alternative hypothesis of .
The reason we use procedures instead of procedures when carrying out a test about a population mean is that
(a) can be used only for large samples.
(b)requires that you know the population standard deviation .
(c) requires you to regard your data as an SRS from the population.
(d) applies only if the population distribution is perfectly Normal.
(e) can be used only for confidence intervals.
You are testing against based on an SRS of observations from a Normal population. What values of the statistic are statistically significant at thelevel?
(a)
(b)
(c)
(d)
(c)
Bullies in middle school A University of Illinois study on aggressive behavior surveyed a random sample of 558 middle school students. When asked to describe their behavior in the last 30 days, 445 students said their behavior included physical aggression, social ridicule, teasing, name-calling, and issuing threats. This behavior was not defined as bullying in the questionnaire. Is this evidence that more than three-quarters of the students at that middle school engage in bullying behavior? To find out, Maurice decides to perform a significance test. Unfortunately, he made a few errors along the way. Your job is to spot the mistakes and correct them.
where p= the true mean proportion of middle school students who engaged in bullying.
- A random sample of 558 middle school students was surveyed.
- 558(0.797)=444.73 is at least 10.
The probability that the null hypothesis is true is only 0.0138, so we reject . This proves that more than three-quarters of the school engaged in bullying behavior.
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