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Mathematics

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2) In 1990, about 40% of U.S. adult population had never smoked cigarettes. A national health survey of 1200 U.S. adults (presumably selected randomly) during 2010 revealed that 540 had never smoked cigarettes. a) Construct 95% confidence interval for the true proportion of U.S. adults in 2010 that have never smoked cigarettes and interpret this interval. b) Suppose you wished to test whether there has been a change since 1990 in the proportion of U.S. adults that have never smoked cigarettes. Use 0.01 significance level to test this belief. (i) Ho: vs. Ha: (ii) Value of the test statistic: 1 (iii) p-value: (iv) Conclusion: 3) A manufacturer of watches would like to examine the preference for digital versus analog watches. A sample of n = 200 people is selected, and these individuals are classified by age and preference. The manufacture would like to know whether there is a relationship between the age and watch preference. The observed frequencies are shown below: Digital 90 Analog 40 Undecided 10 Under 30 30 or over 10 40 10 a) State the null and alternative hypotheses. Ho: Ha: b) What are the degrees of freedom of the Chi square distribution for this test? c) What is the expected frequency for individuals under 30 and prefer analog watches? d) The value of the test statistic is calculated and it is 38.09. What is the p-value? P
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