Question

A random sample of 169 recent donations at a certain blood bank reveals that 88 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.

a) What is the standard error for the sample proportion?

b) Computer the p-value of this test

Answer 1

Let p denotes the true proportion of type A donations.

To test against

Here

sample proportion

and sample size

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 5% level of significance if

Now,

standard error for sample proportion

The value of the test statistic

P-value

Since P-value = 0.590258 > 0.05, so we fail to reject H₀ at 5% level of significance and we can conclude that  the actual percentage of type A donations is not significantly different from 40%