use the contingency table to the right to calculate the marginal frequencies and find the expected frequency…

Explanation:

Step1: Recall the formula for expected frequency

The formula for the expected frequency $E_{ij}$ in a contingency - table is $E_{ij}=\frac{R_i\times C_j}{n}$, where $R_i$ is the row total, $C_j$ is the column total, and $n$ is the sample size.

Step2: Calculate expected frequencies for male - compact

$R_1 = 88$, $C_1=40$, $n = 190$. So $E_{11}=\frac{88\times40}{190}=\frac{3520}{190}\approx18.53$.

Step3: Calculate expected frequencies for male - full - size

$R_1 = 88$, $C_2 = 42$, $n = 190$. So $E_{12}=\frac{88\times42}{190}=\frac{3696}{190}\approx19.45$.

Step4: Calculate expected frequencies for male - SUV

$R_1 = 88$, $C_3 = 70$, $n = 190$. So $E_{13}=\frac{88\times70}{190}=\frac{6160}{190}\approx32.42$.

Step5: Calculate expected frequencies for male - van

$R_1 = 88$, $C_4 = 38$, $n = 190$. So $E_{14}=\frac{88\times38}{190}=\frac{3344}{190}=17.60$.

Step6: Calculate expected frequencies for female - compact

$R_2 = 102$, $C_1 = 40$, $n = 190$. So $E_{21}=\frac{102\times40}{190}=\frac{4080}{190}\approx21.47$.

Step7: Calculate expected frequencies for female - full - size

$R_2 = 102$, $C_2 = 42$, $n = 190$. So $E_{22}=\frac{102\times42}{190}=\frac{4284}{190}\approx22.55$.

Step8: Calculate expected frequencies for female - SUV

$R_2 = 102$, $C_3 = 70$, $n = 190$. So $E_{23}=\frac{102\times70}{190}=\frac{7140}{190}\approx37.58$.

Step9: Calculate expected frequencies for female - van

$R_2 = 102$, $C_4 = 38$, $n = 190$. So $E_{24}=\frac{102\times38}{190}=\frac{3876}{190}=20.40$.

Answer:

Gender	Compact	Full - size	SUV	Van
Male	18.53	19.45	32.42	17.60
Female	21.47	22.55	37.58	20.40