# Is there good evidence that the proportion of smokers has decreased over these 10 years?

Younger people use their cell phones to text more often than older people. A random sample of 625 teens aged 12 to 17 who use their cell phones to text found that 475 sent more than 10 text messages in a typical day. In a random sample of 1917 adults aged 18 and over who use their cell phones to text, 786 sent more than 10 text messages a day.

(A) What is the standard error (SE) of the sample estimate of p1 – p2 (where p1 is the proportion for teens aged 12 to 17 and p2 is the proportion for adults 18 and older) ?

(B) Give a 90% confidence interval for p1 – p2 (where p1 is the proportion for teens aged 12 to 17 and p2 is the proportion for adults 18 and older)?

2. Consider a sample of 148 small businesses. During a three-year period, 15 of 106 headed by men and 7 of the 42 headed by women failed. Let p1 be the proportion of businesses headed by women that failed. Let p2 be the proportion of businesses headed by men that failed.

(A) Find the pooled proportion of businesses that failed.

(B) Find the test statistic for a significance test to see if this is evidence the proportion of businesses failed is higher for women than for men.

3. We have two samples. The first sample taken in Alaska in 1999 involved 2100 adults, of which 600 were current smokers. The second sample taken in Alaska in 2009 involved 2400 adults, of which 500 were smokers. The samples are to be compared to determine if the proportion of adults in Alaska who smoke has decreased since 1999. Take p1 to be the proportion of smokers in the 1999 sample, and p2 to be the proportion of smokers in the 2009 sample.

(A) What is the pooled sample estimate of adult smokers in Alaska?

(B) What is the z test statistic for comparing the proportions of smokers in Alaska in 1999 and 2009?

(C) Is there good evidence that the proportion of smokers has decreased over these 10 years?

(D) What is the Margin of error for the 90% (large-sample) confidence interval for p1-p2?

Note: We do not do plus-four confidence intervals.