Question

Let x be a random variable that represents the hemoglobin count (HC) in human blood (measured in grams per milliliter). In healthy female adults, x has an approximatelynormal distribution with a population mean of u = 14.4 and population standard deviation of a = 2.5. Suppose a female patient had several blood tests over the past year and a random sample of 10 tests showed her sample mean HC to be x = 15.6.At a significance level of alpha = 5% = 0.05, does the sample data indicate that the patient's

Answer 1

We have to perform an hypothesis test for the mean.

The claim is that the patient's mean HC is greater than the population average.

Then, the null and alternative hypothesis are:

`\begin{gathered} H_0:\mu=14.4 \\ H_a:\mu>14.4 \end{gathered}`

The significance level is 0.05.

The sample has a size n = 10.

The sample mean is M = 15.6.

The standard deviation of the population is known and has a value of σ = 2.5.

We can calculate the standard error as:

`\sigma_M=(\sigma)/(√(n))=(2.5)/(√(10))\approx0.7906`

Then, we can calculate the z-statistic as:

`z=(M-\mu)/(\sigma_M)=(15.6-14.4)/(0.7906)=(1.2)/(0.7906)\approx1.52`

This test is a right-tailed test, so the P-value for this test is calculated as:

`P-value=P(z>1.52)=0.064`

As the P-value (0.06) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.05, there is not enough evidence to support the claim that the patient's mean HC is greater than the population average.

Answer:

z = 1.52

P-value = 0.064

Conclusion: fail to reject the null hypothesis.