Question

1. A pharmaceutical company claims that 52% of adult males living in a city in the Midwest get at least two colds per year. A random sample of 325 adult males in in the city of interest reported that 151 of them experienced two or more colds. Do these data indicate that the true proportion of adult males in the city who get two or more colds per year is less than 52%?

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.52

H_a : p < 0.52

$\hat p$ = x / n = 151 / 325 = 0.4646

Test statistic = z

= $\hat p$ - P₀ / [$\sqrt$P_{0 *} (1 - P₀ ) / n]

= 0.4646 - 0.52 / [$\sqrt$(0.52 * 0.48) / 325]

= -1.999

P-value = 0.0228

$\alpha$ = 0.05

P-value < $\alpha$

Reject the null hypothesis .

There is sufficient evidence to suggest that true proportion of adult males is less than 0.52 .