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Chapter 8: Q6 (page 408)
Conclusions True or false: The conclusion of 鈥渇ail to reject the null hypothesis鈥� has exactly the same meaning as 鈥渁ccept the null hypothesis.鈥�
It is false that the meaning of 鈥渇ail to reject the null hypothesis鈥� is the same as 鈥渁ccept the null hypothesis鈥�.
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Testing Hypotheses. In Exercises 13鈥�24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.
Cans of Coke Data Set 26 鈥淐ola Weights and Volumes鈥� in Appendix B includes volumes (ounces) of a sample of cans of regular Coke. The summary statistics are n = 36, x = 12.19 oz, s = 0.11 oz. Use a 0.05 significance level to test the claim that cans of Coke have a mean volume of 12.00 ounces. Does it appear that consumers are being cheated?
Final Conclusions. In Exercises 25鈥�28, use a significance level of = 0.05 and use the given information for the following:
a. State a conclusion about the null hypothesis. (Reject or fail to reject .)
b. Without using technical terms or symbols, state a final conclusion that addresses the original claim.
Original claim: More than 58% of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of 0.3257.
Lead in Medicine Listed below are the lead concentrations (in ) measured in different Ayurveda medicines. Ayurveda is a traditional medical system commonly used in India. The lead concentrations listed here are from medicines manufactured in the United States (based on data from 鈥淟ead, Mercury, and Arsenic in US and Indian Manufactured Ayurvedic Medicines Sold via the Internet,鈥� by Saper et al., Journal of the American Medical Association,Vol. 300, No. 8). Use a 0.05 significance level to test the claim that the mean lead concentration for all such medicines is less than 14 .
3.0 6.5 6.0 5.5 20.5 7.5 12.0 20.5 11.5 17.5
Testing Hypotheses. In Exercises 13鈥�24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.
How Many English Words? A simple random sample of 10 pages from Merriam-Webster鈥檚 Collegiate Dictionary is obtained. The numbers of words defined on those pages are found, with these results: n = 10, x = 53.3 words, s = 15.7 words. Given that this dictionary has 1459 pages with defined words, the claim that there are more than 70,000 defined words is equivalent to the claim that the mean number of words per page is greater than 48.0 words. Assume a normally distributed population. Use a 0.01 significance level to test the claim that the mean number of words per page is greater than 48.0 words. What does the result suggest about the claim that there are more than 70,000 defined words?
Testing Claims About Proportions. In Exercises 9鈥�32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.
M&Ms Data Set 27 鈥淢&M Weights鈥� in Appendix B lists data from 100 M&Ms, and 27% of them are blue. The Mars candy company claims that the percentage of blue M&Ms is equal to 24%. Use a 0.05 significance level to test that claim. Should the Mars company take corrective action?
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