Question

The data in the table below are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag.

X	Freq.
1	1
2	7
3	18
4	7
5	6

A. Construct a 95% confidence interval for the true mean number of colors on national flags.

Fill in the blanks on the graph with the areas, the upper and lower limits of the Confidence Interval and the sample mean. (Round your answers to two decimal places.)

a/2=

C.L.=

B. Construct a 95% confidence interval for the true mean number of colors on national flags.

How much area is in both tails (combined)? (Enter an exact number as an integer, fraction, or decimal.)

C. Define the random variable X in words.

Answer 1

a)

/2 = 0.05 / 2 = 0.025

Confidence level = 0.95

b)

Mean = xf / n = 3.2564

Standard deviation S = sqrt [ X²f - n * mean²/ n-1 ] = 1.019

t critical values at 38 df with 0.05 significance level = 2.024

95% confidence interval is

- t * S / sqrt(n) < < + t * S / sqrt(n)

3.2564 - 2.024 * 1.019 / sqrt(38) < < 3.2564 + 2.024 * 1.019 / sqrt(38)

2.92 < < 3.59

95% CI is ( 2.92 , 3.59 )

c)

Random variable X is mean number of colors on a national flag are between 2.92 and 3.59