Question

A random sample of 22 college​ men's basketball games during the last season had an average attendance of 5,166 with a sample standard deviation of 1,755. Complete parts a and b below.

a. Construct a 99​% confidence interval to estimate the average attendance of a college​ men's basketball game during the last season.

The 99​% confidence interval to estimate the average attendance of a college​ men's basketball game during the last season is from a lower limit of to an upper limit of . ​(Round to the nearest whole​ numbers.)

b. What assumptions need to be made about this​ population?

A. The only assumption needed is that the population follows the normal distribution.

B. The only assumption needed is that the population distribution is skewed to one side.

C. The only assumption needed is that the population size is larger than 30.

D. The only assumption needed is that the population follows the​ Student's t-distribution.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 5166

sample standard deviation = s = 1755

sample size = n = 22

Degrees of freedom = df = n - 1 = 22-1 =21

a) At 99% confidence level

= 1-0.99% =1-0.99 =0.01

/2 =0.01/ 2= 0.005

t/2,df = t0.005,21 = 2.83

t /2,df = 2.83

Margin of error = E = t/2,df * (s /n)

= 2.83 * (1755 / 22)

Margin of error = E = 1059.4

The 99% confidence interval estimate of the population mean is,

- E < <  + E

5166 -1059.4 < < 5166 + 1059.4

4107 < < 6225

(4107,6225)

A lower limit = 4107 an upper limit of = 6225

b) A. The only assumption needed is that the population follows the normal distribution.