## Related questions with answers

Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise.

A simple random sample of 50 adults is obtained, and each person's red blood cell count (in cells per microliter) is measured. The sample mean is $5.23$. The population standard deviation for red blood cell counts is $0.54$. Use a $0.01$ significance level to test the claim that the sample is from a population with a mean less than $5.4$, which is a value often used for the upper limit of the range of normal values. What do the results suggest about the sample group?

Solution

VerifiedP-VALUE METHOD

$H_0:\mu=54$

$H_1:\mu<54$

The value of the test statistic is then:

$z=\dfrac{\overline{x}-\mu}{\sigma/\sqrt{n}}=\dfrac{5.23-5.4}{5.4/\sqrt{50}}\approx -0.22$

The corresponding P-value (probability) can then be found using table A-2:

$P=P(Z<-0.22)=0.4129$

If the P-value is smaller than the significance level, reject the null hypothesis:

$P>0.01\Rightarrow \text{ Fail to reject } H_0$

There is no significant evidence to support the claim.

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