Question

In 1965, about 44% of the U.S. adult population had never smoked cigarettes. A national health survey of 1472 U.S. adults (presumably selected randomly) during 2010 revealed that 679 had never smoked cigarettes. Suppose you wished to test whether there has been a change since 1965 in the proportion of U.S. adults who have never smoked cigarettes. You test the hypotheses H₀: p = 0.44, H_a: p > 0.44.  The test statistic of the test is:

(Round to 2 decimal places.)

Answer 1

Solution :-

Given

The null and alternative hypothesis is

H0 : p = 0.44

Ha : p > 0.44

= x / n = 679 / 1472 = 0.461

P0 = 0.44

1 - P0 = 1 - 0.44 = 0.56

Test statistic = z

=

= 0.46 - 0.44/ [(0.44 * 0.56) /1472 ]

= 1.55

This is the right tailed test

P(z > 1.55) = 1 - P(z < 1.55) = 1 - 0.9394

P-value = 0.0606