Question

A random sample of 149 recent donations at a certain blood bank reveals that 84 were type A blood. Does this suggest that the actual percentage of type A donations differs from 40%, the percentage of the population having type A blood? Carry out a test of the appropriate hypotheses using a significance level of 0.01.

State the appropriate null and alternative hypotheses.

H₀: p = 0.40
H_a: p < 0.40H₀: p = 0.40
H_a: p ≠ 0.40    H₀: p ≠ 0.40
H_a: p = 0.40H₀: p = 0.40
H_a: p > 0.40

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z = _______.

P-Value = _______.

State the conclusion in the problem context.

Reject the null hypothesis. There is sufficient evidence to conclude that the percentage of type A donations differs from 40%.Reject the null hypothesis. There is not sufficient evidence to conclude that the percentage of type A donations differs from 40%.    Do not reject the null hypothesis. There is sufficient evidence to conclude that the percentage of type A donations differs from 40%.Do not reject the null hypothesis. There is not sufficient evidence to conclude that the percentage of type A donations differs from 40%.

Would your conclusion have been different if a significance level of 0.05 had been used?

Answer 1

The null and alternative hypothesis are

H0: p = 0.40

Ha: p 0.40

Sample proportion = 84 / 149 = 0.5638

Test statistics

z = - p / sqrt( p (1 - p) / n)

= 0.5638 - 0.40 / sqrt(0.40 * ( 1 - 0.40) / 149)

= 4.08

p-value = 2 * P(Z > z) (Since this is two tailed test, p-value is double of probability)

= 2 * P(Z > 4.08)

= 2 * 0

= 0

Since p-value < 0.01 level reject H0.

Reject the null hypothesis. There is sufficient evidence to conclude that the percentage of type A

donations differs from 40%