Question

3. According to a recent article, 32% of drivers had driven drowsy in the past month. (Source: Thenationshealth.aphapublications.org/content/41/10/E52.fuII)

Suppose law enforcement officials are planning a survey of 1000 drivers to determine what proportion are driving drowsy.

A. Is whether a driver has driven drowsy in the past month qualitative or quantitative?

B. Would it be unusual if, in a random sample of 1000 drivers, 35% or more were driving drowsy in the last month? Include justifications for full credit.

C. What is the minimum number of drivers that must be sampled to be sure that the shape is approximately normal? Hint – use the formula

4.   The Graduate Management Admission Test (GMAT) is a test required for admission into many masters of business administration (MBA) programs. Suppose a random sample of 8 students took the test, and their scores are given below.

699, 560, 414, 570, 521, 663, 727, 413

A.Find a point estimate of the population mean.

B. Construct a 95% confidence interval for the true mean score for the population.

C. Interpret the interval you constructed above.

D. How many students should be surveyed to estimate the mean score within 25 points with 95% confidence? Hint – use the formula

Answer 1

A:

This is qualitative variable with possible values yes and no.

B:

Here we have

n=1000 and p=0.32

Number of drivers driving drowsy, let X, has a binomial distribution with parameters n=1000 and p=0.32.

The mean is

The standard deviation is

So usual range of values will be

The 35% of 1000 means 350.

Since 350 is not lie in the usual range of values so it is unusual that 35% or more were driving drowsy in the last month.

C:

For normal approximation following condition must be full fill:

That is sample size must be at least 46.