Question

1. Use the following information for the next three problems.  Suppose that  = 30% of the students at a large university must take a statistics course.  Suppose that a random sample of 50 students is selected.  Let  = the percent of students in the sample who must take statistics.

   Different samples will produce different values of .  In order for the values of  to vary according to a normal model, we need to check two conditions.  Which two of the following need to be checked?

   	a.	The sample size  is large ().
   	b.	The sample observations are independent of each other.
   	c.	and
   	d.	The population distribution is normal in shape.

QUESTION 4

1. 95% of all samples will produce a  between __________ and __________.

   	a.	0.235 and 0.365
   	b.	0.280 and 0.320
   	c.	0.105 and 0.495
   	d.	0.170 and 0.430

QUESTION 5

1. What is the chance that more than 38% of the students in a sample must take statistics (i.e. what is the chance that  > 0.38)?

   	a.	0.6480
   	b.	0.8907
   	c.	0.1093
   	d.	1.23

Answer 1

  

b.  
The sample observations are independent of each other.

d.  
The population distribution is normal in shape.

4)

Sample proportion (\hat{p}) = 0.30

Sample size (n) = 50

Confidence interval(in %) = 95

z @ 95% = 1.96

Since we know that

Required confidence interval = (0.3-0.127, 0.3+0.127)

Required confidence interval = (0.173, 0.427)

Option d 0.170 and 0.430

5)

Mean =0.35

S.d. =

P(x > 0.38)=?

The z-score at x = 0.38 is,

z = 0.38-0.3\0.0648

z = 1.2346

This implies that

P(x > 0.38) = P(z > 1.2346) = 1 - 0.8915102954927918

P(x > 0.38) = 0.1085

Option C