A hot topic of debate is whether the legal driving age should be raised to eighteen. From a random sample of 400 Americans, 52% favored raising the legal driving age to eighteen. Based on the data, can you conclude that a majority of Americans believe the legal driving age should be raised to 18? Let alpha=2.5%

We fail to reject the null hypothesis and conclude that the claim of a majority of Americans believing the legal driving age should be raised to 18 is not supported

Step-by-step explanation

The hypothesis is:

H₀: P ≤ 0.50

H_a: P > 0.50

The test statistic is given by;

Z = (p - P)/√(P(1-P)/n)

p = 52% = 0.52

Z = (0.52 - 0.50)/√(0.50(1-0.50)/400)

= 0.8

The P-vale associated with the Z score will be;

P(Z > 0.8)

= P(Z < -0.8)

From the Z table;

P(Z < -0.8) = 0.2119

Since the P-value is greater than the significant level of 2.5% (0.025), we fail to reject the null hypothesis and the claim that a majority of Americans believe the legal driving age should be raised to 18 is not supported