Hemoglobin is a protein in red blood cells that carries oxygen from the lungs to

Question

Hemoglobin is a protein in red blood cells that carries oxygen from the lungs to body tissues. People with less than 12 grams of hemoglobin per deciliter of blood qre anemic. A public health official in Jordan suspects that the mean for all children in Jordan is less than 12. He measures a sample of 50 children. Suppose that the "simple conditions" hold: the 50 children are an SRS from all Jordanian children, and the hemoglobin level in this population follows a Normal Distribution with the standard deviation 1.6 g/dL. The sample mean is in fact 11.3 g/dL.

1. State the null and alternative hypotheses.

2. Calculate the P-Value for this study.

3. Is this outcome statistically significant at the a = 0.05 level? At the a = 0.01 level?

Explanation / Answer

Solution:-

The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: >= 11.3
Alternative hypothesis: < 11.3

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n) = 1.6 / sqrt(50) = 1.6/7.071 = 0.226
DF = n - 1 = 50 - 1 = 49
t = (x - ) / SE = (12 - 11.3)/0.226 = 3.139

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

Here is the logic of the analysis: Given the alternative hypothesis ( < 11.3), we want to know whether the observed sample mean is small enough to cause us to reject the null hypothesis.

The observed sample mean produced a t statistic test statistic of 3.139. We use the t Distribution Calculator to find P(t < 3.139)

The P-Value is 0.001435.

The result is significant at p < .05

Interpret results. Since the P-value (0.001435) is less than the significance level (0.05), we reject the null hypothesis.

Now, for a = 0.01,

The P-Value is 0.001435.

The result is significant at p < 0.01

Interpret results. Since the P-value (0.001435) is less than the significance level (0.01), we reject the null hypothesis.

That is in both the cases, sample mean is less than 11.3g/dL

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.