Question

Z and P-Value needed. double-check answers thank you!

A random sample of 146 recent donations at a certain blood bank reveals that 83 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. TO Ho: p = 0.40 Ha: p < 0.40 Ho: P = 0.40 Ha: p > 0.40 O Ho: p = 0.40 Ha: p = 0.40 Ho: p = 0.40 Ha: 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 =

Answer 1

Solution :

Given that,

$p_{0}$ = 0.40

1 - $p_{0}$ = 0.60

n = 146

x = 83

Level of significance = $\alpha$ = 0.01

Point estimate = sample proportion = $\hat p$ = x / n = 0.569

This a two- tailed test.

The null and alternative hypothesis is,

Ho: p = 0.40

Ha: p $\neq$ 0.40

Test statistics

z = ($\hat p$ - $p_{0}$ ) / $\sqrt{}$ $p_{0}$*(1-$p_{0}$) / n

= ( 0.569 - 0.40) / $\sqrt{}$ (0.40*0.60) / 146

= 4.16

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

= 2 * ( 1 - P(Z < 4.16))

= 2 * ( 1 - 1 )

= 0