Question

42. Fresh coffee People of taste are supposed to prefer fresh-brewed coffee to the instant variety. On the other hand, perhaps many coffee drinkers just want their caffeine fix. A skeptic claims that only half of all coffee drinkers prefer fresh-brewed coffee. To test this claim, we ask a random sample of 50 coffee drinkers in a small city to take part in a study. Each person tastes two unmarked cups - one containing instant coffee and one containing fresh-brewed coffee-and says which he or she prefers. We find that 36 of the 50 choose the fresh coffee. t = Do these results give convincing evidence that coffee drinkers favor fresh-brewed over instant coffee?

Answer 1

H0: Null Hypothesis: P $\leq$ 0 50 (Coffee drinkers do not prefer fresh - brewed over instant coffee

HA: Alternative Hypothesis: P >0 50 (Coffee drinkers prefer fresh - brewed over instant coffee (Claim)

n = 50

$\hat{p}$ = 36/50 = 0.72

Take $\alpha$ = 0.05

From Table, critical value of Z = 1.64

Test Statistic is given by:

$Z=\frac{\hat{p}-p_{0}}{\sqrt{p_{0}\times (1-p_{0})/n}}=\frac{0.72-0.50}{\sqrt{0.50\times (1-0.50)/50}}=3.111$

Since calculated value of Z = 3.111 is greater than critical value of Z= 1.64 the difference is significant. Reject null Hypothesis.

Conclusion:

The data support the claim that Coffee drinkers prefer fresh - brewed over instant coffee.