Question

QUESTION 1

Using the t-table found HERE find find the t critical value for:

Degrees of Freedom = 5

Upper-tail probability = 0.10

3 points   

QUESTION 2

Using the t-table found HERE find find the t critical value for:

Degrees of Freedom = 11

Upper-tail probability = 0.005

3 points   

QUESTION 3

Using the t-table found HERE find find the t critical value for:

Degrees of Freedom = 23

Upper-tail probability = 0.05

3 points   

QUESTION 4

Using the t-table found HERE find find the t critical value for:

Degrees of Freedom = 20

Upper-tail probability = 0.15

3 points   

QUESTION 5

A group of 10 foot surgery patients had a mean weight of 240 pounds. The sample standard deviation was 25 pounds. Find a 95% confidence interval for a sample for the true mean weight of all foot surgery patients. Select the correct confidence interval from below.

Feel free to use: https://www.easycalculation.com/statistics/confidence-limits-mean.php

		(222.133, 257.867)
		(0, 50)
		(220.255, 258.127)
		(-10.456, 12.893)

5 points   

QUESTION 6

Construct a 98% Confidence Interval for the mean based on the following data: 45, 55, 67, 45, 68, 79, 98, 87, 84, 82.

Hint: You'll need to somehow find the mean and sample standard deviation for this data set.

Note: You can use the website https://www.easycalculation.com/statistics/confidence-limits-mean.php

What is the LOWER BOUND of the confidence interval? Round to two decimal places.

4 points   

QUESTION 7

Construct a 98% Confidence Interval for the mean based on the following data: 45, 55, 67, 45, 68, 79, 98, 87, 84, 82.

Hint: You'll need to somehow find the mean and sample standard deviation for this data set.

Note: You can use the website https://www.easycalculation.com/statistics/confidence-limits-mean.php

What is the UPPER BOUND of the confidence interval? Round to two decimal places.

Answer 1

T TABLE:

c

QUESTION 1:

GIVEN:

Degrees of Freedom = 5

Upper-tail probability = 0.10

From the above t table, the critical value is the value corresponding to row value (degrees of freedom) of 5 and the column value (one tail ​) is ​.

QUESTION 2:

GIVEN:

Degrees of Freedom = 11

Upper-tail probability = 0.005

From the above t table, the critical value is the value corresponding to row value (degrees of freedom) of 11 and the column value (one tail ) is .

QUESTION 3:

GIVEN:

Degrees of Freedom = 23

Upper-tail probability = 0.05

From the above t table, the critical value is the value corresponding to row value (degrees of freedom) of 23 and the column value (one tail ) is ​.

QUESTION 4:

GIVEN:

Degrees of Freedom = 20

Upper-tail probability = 0.15

From the above t table, the critical value is the value corresponding to row value (degrees of freedom) of 20 and the column value (one tail ) is .

GENERAL FORMULA FOR CONFIDENCE INTERVAL:

The 100(1-​) confidence interval for population mean is given by:

   Sample mean ​ (t critical value * standard error)

QUESTION 5:

GIVEN:

Sample size

Sample standard deviation

Sample mean

CALCULATION:

DEGREES OF FREEDOM:

Degrees of freedom

LEVEL OF SIGNIFICANCE:

CRITICAL VALUE:

The t critical value with 9 degrees of freedom and level of significance 0.025 is .

STANDARD ERROR:

Standard Error = Sample standard deviation / Square root of Sample size

Thus the 95% confidence interval for the true mean weight of all foot surgery patients is,

   Sample mean ​ (t critical value * standard error)

​   

​   

​   

Thus the 95% confidence interval for the true mean weight of all foot surgery patients is ​. Thus

Thus we are 95% confident that the interval captured the true mean weight of all foot surgery patients​.

QUESTION 6:

GIVEN:

The sample 45, 55, 67, 45, 68, 79, 98, 87, 84, 82.

Sample size

SAMPLE MEAN:

Sample mean = (45+ 55+ 67+ 45+ 68+ 79+ 98+ 87+ 84+ 82)/10

   = 71

SAMPLE STANDARD DEVIATION:

45	-26	676
55	-16	256
67	-4	16
45	-26	676
68	-3	9
79	8	64
98	27	729
87	16	256
84	13	169
82	11	121

Sample Standard deviation

DEGREES OF FREEDOM:

Degrees of freedom

LEVEL OF SIGNIFICANCE:

CRITICAL VALUE:

The t critical value with 9 degrees of freedom and level of significance 0.01 is ​.

STANDARD ERROR:

Standard Error = Sample standard deviation / Square root of Sample size

Thus the 98% confidence interval for the true mean is,

   Sample mean ​ (t critical value * standard error)

​   

​   

​   

​Thus the lower bound for confidence interval for the true mean ​is ​.

QUESTION 7:

GIVEN:

The sample 45, 55, 67, 45, 68, 79, 98, 87, 84, 82.

Sample size

SAMPLE MEAN:

Sample mean = (45+ 55+ 67+ 45+ 68+ 79+ 98+ 87+ 84+ 82)/10

   = 71

SAMPLE STANDARD DEVIATION:

45	-26	676
55	-16	256
67	-4	16
45	-26	676
68	-3	9
79	8	64
98	27	729
87	16	256
84	13	169
82	11	121

Sample Standard deviation

DEGREES OF FREEDOM:

Degrees of freedom

LEVEL OF SIGNIFICANCE:

CRITICAL VALUE:

The t critical value with 9 degrees of freedom and level of significance 0.01 is ​.

STANDARD ERROR:

Standard Error = Sample standard deviation / Square root of Sample size

Thus the 98% confidence interval for the true mean is,

   Sample mean ​ (t critical value * standard error)

​   

​   

​   

​Thus the upper bound for confidence interval for the true mean ​is ​.