a Formulate appropriate hypotheses to test whether the perce

(a)       Formulate appropriate hypotheses to test whether the percentage of debit card shoppers increased by more than 5 percent. Choose the correct null and alternative hypotheses (a, b, or c).

(b)      Calculate zcalc and the p-value. (Round your intermediate values and final answers to 4 decimal places.)

Solution

Answer to the question)

Claim is : P2 -P1 > 0.05 , that is the proportion has increased by more than 5% or 0.05

this claim becomes the alternate hypothesis

Thus the null hypothesis would be : P1 - P2 < = .05 [ this implies that the difference between the two proportions is less than 0.05]

Thus the correct option is the first option.

.

p1 = 42/200 = 0.21

p2= 62 / 200 = 31

p = (42+62) / (200+200) = 0.26

.

The formula of statistic is:

z = ((p1 - p2) - 0.05 ) / sqrt(P * q *(1/n1 + 1/n2)

.

On plugging the values we get

z = (0.21 -0.31 - 0.05) / sqrt(0.26 *0.74 *2 /200)

z = -3.42

.

P value = 0.0003

.

Decision: Since the P value 0.0003 < alpha 0.05 , we reject the null hypothesis and conclude that the increase in the proportion is more than 5%