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The results for the red blood cell count for 40 adult males in million cells per microlit\(s = 0.504\)er are summarized below.

Sample size\(n = 40\).

Sample mean\(\bar x = 4.932\).

Sample standard deviation .

Level of significance\(\alpha = 0.01\).

The claim states that the mean of the population is less than 5.4 million per microliter.

Null hypothesis: The sample is from the mean equal to 5.4 million cells per microliter.

Alternative hypothesis: The sample is from the mean below 5.4 million cells per microliter.

Mathematically,

\(\begin{array}{l}{H_0}:\mu = 5.4\\{H_1}:\mu < 5.4\end{array}\)

Here, \(\mu \)is the actual population mean red blood cell counts.

Assume that the simple random sample is taken from a normally distributed population. For an unknown measure of population standard deviation, the t-test applies.

The test statistic is given as follows.

\(\begin{array}{c}t = \frac{{\bar x - \mu }}{{\frac{s}{{\sqrt n }}}}\\ = \frac{{4.932 - 5.4}}{{\frac{{0.504}}{{\sqrt {40} }}}}\\ = - 5.873\end{array}\).

The degree of freedom is computed as follows.

\(\begin{array}{c}df = n - 1\\ = 40 - 1\\ = 39\end{array}\).

Refer to the t-table for the critical value corresponding to the row with degrees of freedom 39 and the level of significance 0.01 for the one-tailed test.

The critical value is \({t_{0.01}} = - 2.426\)

If the test statistic is lesser than the critical value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

The critical value is not lesser than the test statistic, and thus, the null hypothesis is rejected at a 0.01 level of significance.

Thus, there is sufficient evidence to support the claim that the mean of red blood cell count is lesser than 5.4 million cells per microliter.

The result suggests that the mean of the counts of cells for the population of adult males is lesser than 5.4 million per microliter. It does not infer anything about the count of cells for each male.