Question

1. The results of a recent poll on the preference of shoppers regarding two products are shown below.

Product	Shoppers Surveyed	Shoppers Favoring This Product
A	800	560
B	900	612

​

At 95% confidence, the margin of error is

	a.	.0225.
	b.	.044.
	c.	.025.
	d.	.064.

2. The following information was obtained from independent random samples taken of two populations.
Assume normally distributed populations with equal variances.

	Sample 1	Sample 2
Sample Mean	45	42
Sample Variance	85	90
Sample Size	10	12

The degrees of freedom for the t distribution are

	a.	24.
	b.	20.
	c.	21.
	d.	22.

3. ​ For a sample size of 30, changing from using the standard normal distribution to using the t distribution in a hypothesis test,

	a.	​will result in the area corresponding to the critical value being larger.
	b.	​will have no effect on the area corresponding to the critical value.
	c.	​will result in the area corresponding to the critical value being smaller.
	d.	​Not enough information is given to answer this question.

Answer 1

1)

	product A		product B
x1                =	560	x2                =	612
p̂1=x1/n1 =	0.7000	p̂2=x2/n2 =	0.6800
n1                       =	800	n2                       =	900
estimated difference in proportion   =p̂1-p̂2   =			0.0200
std error Se =√(p̂1*(1-p̂1)/n1+p̂2*(1-p̂2)/n2) =			0.0225
for 95 % CI value of z=		1.960
margin of error E=z*std error =		0.0440

2) degrees of freedom for the t distribution are =n1+n2-2=10+12-2 =20

3)

will have no effect on the area corresponding to the critical value.