Chapter 10.3, Problem 22E

To determine

To construct: The two way table for the number of students who were surveyed.

Answer to Problem 22E

Two-way table for number of students in each category if 350 students were surveyed :

Preferred subject
	Math	Science	Total
Role	Male	$\frac{93}{350}=0.26$	$\frac{57}{350}=0.16$	$\frac{150}{350}=0.42$
	Female	$\frac{148}{350}=0.42$	$\frac{52}{350}=0.14$	$\frac{200}{350}=0.57$
total	$\frac{241}{350}=0.68$	$\frac{109}{350}=0.31$	$0.99\approx 1$

Explanation of Solution

Given:

150 male students surveyed,

62% prefer math class over science class.

74% of female prefer math.

Calculation:

Consider the total number of students in survey is $350$ .

Number of male students in survey is $150$ .

Number of female students in survey is,

  $350-150=200$ .

  $62\%$male students in the survey prefer math is,

  $\frac{62}{100}\times 150=93$

  $74\%$female students in the survey prefer math is,

  $\frac{74}{100}\times 200=148$ .

Compute the flowing two-way table:

Preferred subject
	Math	Science	Total
Role	Male	$\frac{93}{350}=0.26$	$\frac{57}{350}=0.16$	$\frac{150}{350}=0.42$
	Female	$\frac{148}{350}=0.42$	$\frac{52}{350}=0.14$	$\frac{200}{350}=0.57$
total	$\frac{241}{350}=0.68$	$\frac{109}{350}=0.31$	$0.99\approx 1$

Conclusion:

Two-way table for number of students in each category if 350 students were surveyed :

Preferred subject
	Math	Science	Total
Role	Male	$\frac{93}{350}=0.26$	$\frac{57}{350}=0.16$	$\frac{150}{350}=0.42$
	Female	$\frac{148}{350}=0.42$	$\frac{52}{350}=0.14$	$\frac{200}{350}=0.57$
total	$\frac{241}{350}=0.68$	$\frac{109}{350}=0.31$	$0.99\approx 1$