Chapter 11: Q11-2-4BSC (page 533)
Is the hypothesis test described in Exercise 1 right tailed, left-tailed, or two-tailed? Explain your choice.
The hypothesis test is right-tailed.
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Cybersecurity The table below lists leading digits of 317 inter-arrival Internet traffic times for a computer, along with the frequencies of leading digits expected with Benford’s law (from Table 11-1 in the Chapter Problem).
a. Identify the notation used for observed and expected values.
b. Identify the observed and expected values for the leading digit of 2.
c. Use the results from part (b) to find the contribution to the\({\chi ^2}\)test statistic from the category representing the leading digit of 2.
Leading Digit | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Benford’s Law | 30.1% | 17.6% | 12.5% | 9.7% | 7.9% | 6.7% | 5.8% | 5.1% | 4.6% |
Leading Digits of Inter-Arrival Traffic Times | 76 | 62 | 29 | 33 | 19 | 27 | 28 | 21 | 22 |
Using Yates’s Correction for Continuity The chi-square distribution is continuous, whereas the test statistic used in this section is discrete. Some statisticians use Yates’s correction for continuity in cells with an expected frequency of less than 10 or in all cells of a contingency table with two rows and two columns. With Yates’s correction, we replace
\(\sum \frac{{{{\left( {O - E} \right)}^2}}}{E}\)with \(\sum \frac{{{{\left( {\left| {O - E} \right| - 0.5} \right)}^2}}}{E}\)
Given the contingency table in Exercise 9 “Four Quarters the Same as $1?” find the value of the test \({\chi ^2}\)statistic using Yates’s correction in all cells. What effect does Yates’s correction have?
Chocolate and Happiness Use the results from part (b) of Cumulative Review Exercise 2 to test the claim that when asked, more than 80% of women say that chocolate makes them happier. Use a 0.01 significance level.
The table below includes results from polygraph (lie detector) experiments conducted by researchers Charles R. Honts (Boise State University) and Gordon H. Barland (Department of Defense Polygraph Institute). In each case, it was known if the subject lied or did not lie, so the table indicates when the polygraph test was correct. Use a 0.05 significance level to test the claim that whether a subject lies is independent of the polygraph test indication. Do the results suggest that polygraphs are effective in distinguishing between truths and lies?
| |||
No (Did Not Lie) | Yes (Lied) | ||
| 15 | 42 | |
| 32 | 9 | |
Cybersecurity The accompanying Statdisk results shown in the margin are obtained from the data given in Exercise 1. What should be concluded when testing the claim that the leading digits have a distribution that fits well with Benford’s law?
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