Question

Section 9.4 Practice Problems:

2. How many CSUN students would have to be polled to determine the percentage that hopes to transfer to UCLA to within 3.5% at

a. 95% confidence

b. 92% confidence

3. Suppose that a randomly chosen sample of 1024 airline travelers indicated that 624 checked a bag.

a. Check that this meets the conditions to find the 95% confidence interval.

b. What is the point estimate of the proportion of airline travelers that check a bag?

c. Find the 95% confidence interval for the proportion of all airline travelers that checked a bag.

i. Using the appropriate formula.

ii. Using the appropriate calculator function.

d. Interpret the interval in a sentence.

e. Can you say that a majority of airline travelers check a bag? Why or why not?

Answer 1

2.a)

Where,

Let  

Now,

b)

3. Suppose that a randomly chosen sample of 1024 airline travelers indicated that 624 checked a bag.

a.

The necessary conditions for a confidence interval are,

1. Randomization: The samples should be chosen randomly

2. Normal condition: The expected success/failure should be at least 10 each

3. Independent condition: The sample size should be no more than 10% of the population.

All the conditions are satisfied.

b.

c. Find the 95% confidence interval for the proportion of all airline travelers that checked a bag.

The confidence interval for the proportion is obtained using the formula,

(in excel use function =NORM.S.INV(0.975)

Interpretation: There is a 95% chance that the population proportion of all airline travelers that checked a bag lie between 0.579 to 0.639.

e)

.Since the 95% confidence interval for the proportion is greater than 0.50 we can say that the majority of airline travelers check a bag