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. Please show work

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.) Make a formal hypothesis testing to test whether the two populations' proportions are significantly different. Use = 0.10 and a pvalue method. Set up the appropriate null and alternative hypotheses. Is the conclusion same as the one in part(b)?