Question

We will use the prompt below for this and the next 4 questions.

In analyzing data from over 700 games in the National Football League, economist David Romer identified 1068 fourth-down situations in which, based on his analysis, the right call would have been to go for it and not to punt. Nonetheless, in 959 of those situations, the teams punted. Our goal is to find a 99% confidence interval for the proportion of times NFL teams punt on a fourth down when, statistically speaking, they shouldn’t be punting.¹ Assume the sample is reasonably representative of all such fourth down situations in the NFL.

The standard error of the sample statistic in this situation is 0.009.

¹Moskowitz, T. and Wertheim, J., Scorecasting, Crown Archetype, New York, 2011, p. 39.

What is the sample statistic? Round your answer to two decimal places.

Which distribution should we use when finding the multiplier?

The t-distribution with 958 degrees of freedom

The t-distribution with 1067 degrees of freedom

The standard normal distribution

The t-distribution with 699 degrees of freedom

What is the correct multiplier for our goal of finding a 99% confidence interval? Remember you can use StatKey or your notes to find this number.  

Round your answer to three decimal places.

Now compute the 99% confidence interval. What is the lower bound of your interval? Round your answer to three decimal places.

What is the upper bound of your interval? Round your answer to three decimal places.

Answer 1

a) Since the sample size is very large and more than 30 hence it is assumed that it is a normal distribution hence the sample statistic is 959/1068

=0.90

b) Since n>>>30 hence

It is assumed as standard normal distribution.

c) at 99% confidence level the Z score multiplier is 2.58 which can be computed using Z table shown in the last or by excel tool.

d) Since the standard error is 0.009 and Z critical is 2.58 hence margin of error= SE*Z

=0.009*2.58

=0.023

e) Since the margin of error is 0.023 and Sample proportion is 0.90 hence confidence interval will be

Proportion+/- margin of error

=0.90+/-0.023

={0.877,0. 923}

LOWER LIMIT=0.877 AND UPPER LIMIT=0.923

The Z table as