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 H_{0} follows a standard normal
distribution.

We reject H_{0} 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
H_{0} at 5% level of significance and we can conclude
that the actual percentage of type A donations is not
significantly different from 40%

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