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Chapter 9: Q.94 (page 592)
Significance and sample size A study with subjects reported a result that was statistically significant at the level. Explain why this result might not be particularly large or important.
The sample size is too much large and for such large samples the value of the test statistic
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Attitudes In the study of older students’ attitudes from Exercise , the sample mean SSHA score was and the sample standard deviation was .
(a) Calculate the test statistic.
(b) Find the P-value using Table . Then obtain a more precise P-value from your calculator.
Eye black Athletes performing in bright sunlight often smear black grease under their eyes to reduce glare. Does cye black work? In one experiment, 16 randomly selected student subjects took a test of sensitivity to contrast after 3 hours facing into bright sun, both with and without eye black. Here are the differences in sensitivity, with eye black mines without eye black:
| 0.07 | 0.64 | -0.12 | -0.05 | -0.18 | 0.14 | -0.16 | 0.03 |
| 0.05 | 0.02 | 0.43 | 0.24 | -0.11 | 0.28 | 0.05 | 0.29 |
We want to know whether cye black increases sensitivity an the average.
(a) State hypotheses, Be sure to define the parameter.
(b) Check conditions for carrying out a significance test.
(c) Theof the test is . Interpet this value in context.
- Interpret a Type l error and a Type ll error in context, and give the consequences of each.
- Understand the relationsonship between the significance level at a test P(Type li error), and power.
Tests and CIs The P-value for a one-sided test of the null hypothesisis .
(a) Does the confidence interval for include ? Why or why not?
(b) Does the confidence interval for include ? Why or why not?
Paying high prices? A retailer entered into an exclusive agreement with a supplier who guaranteed to provide all products at competitive prices. The retailer eventually began to purchase supplies from other vendors who offered better prices. The original supplier filed a lawsuit claiming violation of the agreement. In defense, the retailer had an audit performed on a random sample of invoices. For each audited invoice, all purchases made from other suppliers were examined and compared with those offered by the original supplier. The percent of purchases on each invoice for which an alternative supplier offered a lower price than the original supplier was recorded.For example, a data value of means that the price would be lower with a different supplier for of the items on the invoice. A histogram and some computer output
for these data are shown below. Explain why we should not carry out a one-sample t-test in this setting.
During the winter months, the temperatures at the Colorado cabin owned by the Starnes family can stay well below freezing (32°F or 0°C) for weeks at a time. To prevent the pipes from freezing, Mrs Starnes sets the thermostat at 50°F. The manufacturer claims that the thermostat allows variation in-home temperature of S 3°F. Mrs Starnes suspects that the manufacturer is overstating how well the thermostat works.
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