Question

itl 5 LTE Confidence Interval for the P... DOCX -16 KB Close Confidence Interval for the Population Mean l. Determine the critical values for 80%, 90%, 95%, and 99%; 2. Construct 80%, 90%, 95%, and 99% confidence interval for the population mean given that the standard deviation of the population is 900 and the sample mean is 425 and the sample consist of 100 points of data 3. Find the T interval for the following: Construct 80% 90%. 95%, and 99% confidence interval for the population mean given that the standard deviation of the population is 900 and the sample mean is 425 and the sample consist of 10 points of data. 4. Given the following data drawn from a unknown normal population with unknown mean and variance construct a 95% confidence interval from the population mean. 25, 19, 37, 29, 40, 28, 3. This set of data has less than 30 data points. The Z interval will not work with this small of a data group. The T interval is used in the case where the number of data points is less than 30 e Email Word Isave

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Answer 1

1) answer)

Steps to find the confidence interval

First we divide the confidence level by 100

Then we subtract it from 1

Then we divide it by 2

Then we look into the z table for the required critical value

-80%

80/100 = 0.8

1-0.8

0.2/2

0.1

From z table 0.1 corresponds to -1.28

As the z(standard normal table) is symmetrical therefore, on the right tail critical value is 1.28

So the required critical values are -1.28, 1.28

Similarly we will find out the critical values of other confidence levels

-90%

Critical values are -1.645 and 1.645

-95%

Critical values are -1.96 and 1.96

-99%

Critical values are -2.58 and 2.58

2)

As here sample size is greater than 30 and population standard deviation is known, we will use z interval

Standard deviation = 900

Mean = 425

N(sample size) = 100

First we will find out the standard error

Standard error = standard deviation/√n

= 900/√100 = 90

- 80% confidence interval

Margin of error(MOE) = Z*standard error

Z is the critical value for 80% confidence interval

Which is 1.28

And confidence interval is given by

[Mean - MOE, Mean + MOE]

MOE = 1.28*90

Mean = 425

Required confidence interval is

[425-1.28*90, 425+1.28*90]

[ 309.8, 540.2]

-90

MOE = Z*standard error

Z = 1.645

Therefore required confidence interval is

[425-1.645*90, 425+1.645*90]

[ 276.95, 573.05]

-95%

Z = 1.96

[425-1.96*90, 425+1.96*90]

[ 248.6, 601.4]

-99%

Z = 2.58

[425-2.58*90, 425+2.58*90]

[ 192.8, 657.2]