Question

Height: 62, 67, 62, 63, 67, 74, 63, 73, 63

Weight: 130, 140, 102, 140, 145, 157, 130, 190, 135

2. (CLO 1) Construct a confidence interval to estimate the mean height and the mean weight by completing the following:

a. Find the sample mean and the sample standard deviation of the height.

b. Find the sample mean and the sample standard deviation of the weight.

c. Construct and interpret a confidence interval to estimate the mean height.

d. Construct and interpret a confidence interval to estimate the mean weight.

3. (CLO 2) Test a claim that the mean height of people you know is not equal to 64 inches using the p-value method or the traditional method by completing the following:

a. State H0 and H1.

b. Find the p value or critical value(s).

c. Draw a conclusion in context of the situation.

4. (CLO 3) Create a scatterplot with the height on the x-axis and the weight on the y-axis. Find the correlation coefficient between the height and the weight. What does the correlation coefficient tell you about your data? Construct the equation of the regression line and use it to predict the weight of a person who is 68 inches tall.

5. Write a paragraph or two about what you have learned from this process. When you read, see, or hear a statistic in the future, what skills will you apply to know whether you can trust the result?

Answer 1

We assume that both the given data (Height and Weight ) have been taken from a Normal Distribution.

In both cases, the Mean and Standard Deviation of the Distribution is unknown.

Answer 2:

Answer a:

The sample mean of height = sum of all observations / Number of observations

= 594/9 = 66 = (Say)

Here , Number of observations = 9 (in both the variables)

The following table shows the calculations-

Height (Xi)	( Xi - )	( Xi - )2
62	-4	16
67	1	1
62	-4	16
63	-3	9
67	1	1
74	8	64
63	-3	9
73	7	49
63	-3	9
Total	0	174

Answer b:

The sample mean of weight = sum of all observations / Number of observations

= 1269/9 = 141 = (say)

The following table shows the calculations-

Weight (Yi)	( Yi - )	( Yi - )2
130	-11	121
140	-1	1
102	-39	1521
140	-1	1
145	4	16
157	16	256
130	-11	121
190	49	2401
135	-6	36
Total	0	4474

The t-distribution table is given below-

All the answers of Question 2-

• Answer a: Sample Mean of height is 66 and sample Standard Deviation is 4.6637
• Answer b: Sample Mean of weight is 141 and sample Standard Deviation is 23.6485
• Answer c: The confidence limits to estimate the mean height

	Lower Limit	Upper Limit
=1%	60.7844	71.2156
=5%	62.4152	69.5848

• Answer d: The confidence limits to estimate the mean weight

	Lower Limit	Upper Limit
=1%	114.5531	167.4469
=5%	122.8222	159.1778

(NOTE THAT : Question 2 / The first four questions are attempted )