Question

A random sample of 154 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.

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	=

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.40

Ha : p 0.40

n = 154

x =84

= x / n = 84 / 154 =0.54

P0 = 0.40

1 - P0 = 1 - 0.40 =0.60

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.54 - 0.40/ [(0.40*0.60) / 154]

= 3.55

Test statistic = z = 3.55

P(z >3.55 ) = 1 - P(z <3.55 ) = 1 - 0.9998

P-value = 2 *0.0002 =0.0004

= 0.01

P-value <

0.0004 < 0.01

Reject the null hypothesis .

There is sufficient evidence to suggest that