Question

A random sample of 158 recent donations at a certain blood bank reveals that 86 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.)

Find z and P value

Answer 1

Solution :

Given that,

= 0.40

1 - = 0.60

n = 158

x = 86

Level of significance = = 0.01

Point estimate = sample proportion = = x / n = 0.544

This a two tailed test.

Ho: p = 0.40

Ha: p 0.40

Test statistics

z = ( - ) / *(1-) / n

= ( 0.544 - 0.40) / (0.40*0.60) / 158

= 3.69

P-value = 2 * P(Z>z)

= 2*(1 - P(Z <z ))

= 2*(1- P(Z < 3.69))

= 2* (1 - 0.9999)

= 2* 0.0001

= 0.0002

The p-value is p = 0.0002, and since p = 0.0002 < 0.01, it is concluded that the null hypothesis is rejected.

Conclusion:

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population

proportion p is different than at = 0.01 significance level.

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