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 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.) CL = ?. (Left) α 2 =? (right) α 2 =? Lower Limit? Upper Limit? Mean?

Answer 1

Use the following information to answer the exercise: The data in Table 8.10 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.

The area covered in both the tails is given by

The confidence level is 95% or 0.95.

Then is calculated as shown below,

Hence the area covered by both tails is

What is estimating?

The sample mean is represented by.

The statistic is a measure on a sample that is used to estimate the mean of the population from which it is drawn, that is, . Here the population is the flags for different nations from various countries.

represents the population standard deviation. No. The population standard deviation is not known here.

=> mean = 3.2562 = 3.26 by using online calucaltion

sd = 1.0057 = 1.01

n = 39

=> 95% confidence interval :- X +/- t*sd/sqrt(n)

df = n - 1 = 38

t_{(0.025 , 38)} = 2.024

=> 3.26 +/- 2.024 * (1.01/sqrt(39))

= (2.93 , 3.59)

=> lower limit = 2.93

upper limt = 3.59

error = 0.33

midpoint = 3.26