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A random sample of 146 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. H0: p = 0.40 Ha: p < 0.40 H0: p ≠ 0.40 Ha: p = 0.40 H0: p = 0.40 Ha: p ≠ 0.40 H0: 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 = State the conclusion in the problem context. Do not reject the null hypothesis.

1. There is not sufficient evidence to conclude that the percentage of type A donations differs from 40%. Do not reject the null hypothesis.
2. There is sufficient evidence to conclude that the percentage of type A donations differs from 40%. Reject the null hypothesis.
3. There is sufficient evidence to conclude that the percentage of type A donations differs from 40%. Reject the null hypothesis.
4. There is not sufficient evidence to conclude that the percentage of type A donations differs from 40%.

Would your conclusion have been different if a significance level of 0.05 had been used?
a. Yes
b. No

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Answer:

There is sufficient evidence to conclude that the percentage of type A donations differs from 40%. Reject the null hypothesis.

Conclusion wouldn't be different if a significance level of 0.05 had been used.

Step-by-step explanation:

null and alternative hypotheses are

H0: p = 0.40

Ha: p ≠ 0.40

test statistic  can be calculated as:

z=[tex]\frac{p(s)-p}{\sqrt{\frac{p*(1-p)}{N} } }[/tex] where

  • p(s) is the sample proportion of having type A blood ([tex]\frac{84}{146} =0.575[/tex]
  • p is the proportion assumed under null hypothesis. (0.40)
  • N is the sample size (146)

then z=[tex]\frac{0.575-0.4}{\sqrt{\frac{0.4*0.6}{146} } }[/tex] ≈4.32

the p-value is ≈0.00002 <0.01

Conclusion:

There is sufficient evidence to conclude that the percentage of type A donations differs from 40%. Reject the null hypothesis.

Conclusion wouldn't be different if a significance level of 0.05 had been used since 0.00002 <0.05

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