The press release “Luxury or Necessity? The Public Makes a U-Turn” (Pew Research Center, April 23, 2009) summarizes results from a survey of a nationally representative sample of n = 1003 adult Americans.
a. One question in the survey asked participants if they think of a landline phone as a necessity or as a luxury that they could do without. Sixty-eight percent said they thought a landline phone was a necessity. Estimate the proportion of adult Americans who view a landline phone as a necessity using a 95% confidence interval.
b. In the same survey, 52% said they viewed a television set as a necessity. Is there convincing evidence that a majority of adult Americans view a television set as a necessity? Test the relevant hypotheses using a = .05.
c. The press release also described a survey conducted in 2003. When asked about a microwave oven, 68% of the 2003 sample regarded a microwave oven as a necessity, whereas only 47% of the 2009 sample said they thought a microwave oven was a necessity. Assume that the sample size for the 2003 survey was also 1003. Is there convincing evidence that the proportion of adult Americans who regard a microwave oven as a necessity decreased between 2003 and 2009? Test the appropriate hypotheses using a = .01.