Include the null and alternative hypothesis, the test statistic and the p-value.
ID: 3267460 • Letter: I
Question
Include the null and alternative hypothesis, the test statistic and the p-value.
Complete the hypothesis test by typing the rejection decision and the conclusion.
7. I Medical: Red Blood Cell Count Letx be a random variable that represents red blood cell (RBC) count in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, the mean of the x distribution is about 4.8 (based on information from Diagnostic Tests with Nursing Implications, Springhouse Corporation). Suppose that a female patient has taken six labora tory blood tests over the past several months and that the RBC count data sent to the patient's doctor are 4.9 4.2 4.5 144.3 i Use a calculator with sample mean and sample standard deviation keys to verify that i = 4.40 and s r 0.28. ii. Do the given data indicate that the population mean RBC count for this patient is lower than 4.8? Use a = 0.05.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: >= 4.8
Alternative hypothesis: < 4.8
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) = 0.28 / sqrt(6) = 0.1143095
DF = n - 1 = 6 - 1 = 5
t = (x - ) / SE = (4.4 - 4.8)/0.1143095 = -3.4993
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 ( < 4.8), 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 -3.4993. We use the t Distribution Calculator to find P(t < -3.4993)
The P-Value is 0.008651.
The result is significant at p < 0.05
Interpret results. Since the P-value (0.008651) is less than the significance level (0.05), we cannot accept the null hypothesis.
Conclusion. Reject the null hypothesis. We have sufficient evidence to prove the claim that the population mean RBC count for this patient is lower than 4.8.