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.)

Answer 1

Solution :

Given that,

Population mean = = 4.8

Sample mean = = 4.4

Sample standard deviation = s = 0.28

Sample size = n = 6

Level of significance = = 0.05

This is a left (One) tailed test,

The null and alternative hypothesis is,  

Ho: 4.8

Ha: 4.8

The test statistics,

t = ( - )/ (s/)

=( 4.4 - 4.8 ) / ( 0.28 / 6 )

= -3.499

Critical value of  the significance level is α = 0.05, and the critical value for a left-tailed test is

= -2.015

Since it is observed that t = -3.499 < = -2.015 , it is then concluded that the null hypothesis is rejected.

P- Value = 0.0086   

The p-value is p =0.0086 < 0.05, it is concluded that the null hypothesis is rejected.

Conclusion :

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the red blood cell count for this patient is lower than normal, at the 0.05 significance level.