Question

9.9. Is gender independent of education level? A random sample of people was surveyed and

each person was asked to report the highest education level they obtained. Perform a hypothesis

test. Include all 5 steps.

	High School	Bachelors	Masters
Female	30	60	54
Male	25	40	44

10.9. Compute and interpret the correlation coefficient for the following grades of 6 students

selected at random.

Mathematical Grade	70	92	80	74	65	83
English Grade	74	84	63	87	78	90

Answer 1

Null hypothesis: Ho: gender is independent of education level

Alternate hypothesis: HA: gender is dependent of education level

degree of freedom(df) =(rows-1)*(columns-1)=		2
for 2 df and 0.05 level of signifcance critical region       χ2=			5.991
Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	High school	Bachelors	Masters	Total
	female	31.30	56.92	55.78	144
	male	23.70	43.08	42.22	109
	total	55	100	98	253
chi square    χ2	=(Oi-Ei)2/Ei	High school	Bachelors	Masters	Total
	female	0.0543	0.1670	0.0567	0.2781
	male	0.0718	0.2206	0.0749	0.3673
	total	0.1261	0.3876	0.1316	0.6454
test statistic X2 =		0.645

Decision:as test statistic is not in critical region, we fail to reject null hypothesis

Conclusion: we can not conclude that gender is not independent of education level

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From the data,

X	Y	XY	X^2	Y^2
70	74	5180	4900	5476
92	84	7728	8464	7056
80	63	5040	6400	3969
74	87	6438	5476	7569
65	78	5070	4225	6084
83	90	7470	6889	8100

n	6
sum(XY)	36926.00
sum(X)	464.00
sum(Y)	476.00
sum(X^2)	36354.00
sum(Y^2)	38254.00
Numerator	692.00
Denominator	2887.38
r	0.2397
r square	0.0574
Xbar(mean)	77.3333
Ybar(mean)	79.3333
SD(X)	8.8632
SD(Y)	9.0492
b	0.2447
a	60.4102

The correlation coefficient = r = 0.2397

the correlation coefficient is 0.2397, indicate that weak linear relationship between X and Y