Question

A female patient has had her red blood cell count tested on 6 occasions. A mean of 4.4 with sample standard deviation, s, of 0.28 was found. Generally, healthy, female adults have a red blood cell count of 4.8. Conduct a hypothesis test to determine if the red blood cell count for this patient is lower than normal. (Use a = 0.05.) (15 points)

Answer 1

Null Hypothesis H0:   = 4.8

Altenative Hypothesis Ha: < 4.8

Sample mean, = 4.4

Sample standard deviation s = 0.28

Since we do not know the true population standard deviation we will conduct one sample t test.

Standard error of mean, SE = s / = 0.28 / = 0.1143095

Test statistic, t = ( - ) / SE =  (4.4 - 4.8) / 0.1143095 = -3.50

Degree of freedom = n-1 = 6-1 = 5

p-value = p(t < -3.50, df = 5) =  0.0086

Since, p-value is less than 0.05 significance level, we reject null hypothesis H0.

There is sufficient evidence at 5% significance level to conclude that the true mean red blood cell count for this patient is lower than normal count of 4.8