In one of the studies, it was found that, in a random sample of 261 married persons, 135 were smokers while in a sample of 239 non-married persons there were 131 smokers. a) Find a 90% confidence interval for the true difference in proportion of smokers among the married and non-married populations. Interpret this confidence interval. b) Based on the above interval, can one conclude that there is a significant difference between the proportions of smokers in the two populations ? Justify your answer. c) Do a formal hypothesis testing to test whether the two populations’ proportions are significantly different. Use α = 0.10 and a p−value method. Set up the appropriate null and alternative hypotheses. Is the conclusion same as the one in part(b)?
In one of the studies, it was found that, in a random sample of 261 married persons, 135 were smokers while in a sample of 239 non-married persons there were 131 smokers.
a) Find a 90% confidence interval for the true difference in proportion of smokers among the married and non-married populations. Interpret this confidence interval.
b) Based on the above interval, can one conclude that there is a significant difference between the proportions of smokers in the two populations ? Justify your answer.
c) Do a formal hypothesis testing to test whether the two populations’ proportions are significantly different. Use α = 0.10 and a p−value method. Set up the appropriate null and alternative hypotheses. Is the conclusion same as the one in part(b)?
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