Fiber Density. In the article "Comparison of Fiber Counting by TV Screen and Eyepieces of Phase Contrast Microscopy" (American Industrial Hygiene Association Journal, Vol. 63, pp. 756-761), I. Moa et al. reported on determining fiber density by two different methods. The fiber density of 10 samples with varying fiber density was obtained by using both an eyepiece method and a TV-screen method. A hypothesis test is to be performed to decide whether, on average, the eyepiece method gives a greater fiber density reading than the TV-screen method.

Fiber Density. In the article "Comparison of Fiber Counting by TV Screen and Eyepieces of Phase Contrast Microscopy" (American Industrial Hygiene Association Journal, Vol. 63, pp. 756-761), I. Moa et al. reported on determining fiber density by two different methods. The fiber density of 10 samples with varying fiber density was obtained by using both an eyepiece method and a TV-screen method. A hypothesis test is to be performed to decide whether, on average, the eyepiece method gives a greater fiber density reading than the TV-screen method.

(a) We identify the variable is "fiber density" of two different methods, eyepiece method and TVscreen method.

We identify the two populations, which are eyepiece method and TV-screen method.

We identify the matched pairs are comparison of fiber counting methods.

We identify the paired-difference variable is the difference between the fiber counting methods.

(e) Let ${\mu }_1$and ${\mu }_2$denote the mean fiber density of eyepiece method and mean fiber density of TV-screen method, respectively. The null and alternative hypotheses are $H_0$: mean fiber density of eyepiece method is not greater than TV screen method

$\text{(or)}{H}_0:{\mu }_1={\mu }_2$

$H_{\mathrm{a}}$: mean fiber density of eyepiece method is greater than TV screen method

$\text{(or)}{H}_{\mathrm{a}}:{\mu }_1>{\mu }_2$

The alternative hypothesis states that

$H_{\mathrm{a}}$: mean fiber density of eyepiece method is greater than TV screen method

$\text{(or)}{H}_{\mathrm{a}}:{\mu }_1>{\mu }_2$

Mean fiber density of eyepiece method greater than the fiber density of TV screen method which confirms that it is a right -tailed test.