Question

Problem:      Construct and interpret a 90%, 95%, and 99% confidence interval for the mean heights of either adult females or the average height of adult males living in America. Do not mix genders in your sample as this will skew your results. Gather a random sample of size 30 of heights from your friends, family, church members, strangers, etc. by asking each individual in your sample his or her height. From your raw data convert individual heights to inches. Record your raw data and your conversions in the table on page 2 of this document. Construct and interpret the confidence interval based on the raw data from your random sample. In a word processed document, answer the reflections questions below. Use the equation editor to show your calculations for the percent difference indicated in 6) below.

Reflections: 1)            Summarize the characteristics of your sample – how many was in it, who was in it, from where did you get your sample, what would you estimate to be the average age of your sample, etc.?

2) What is x for your sample?

3) What is s for your sample?

3) State and interpret the 90% confidence interval for your sample.

4) State and interpret the 95% confidence interval for your sample.

5) State and interpret the 99% confidence interval for your sample.

6) Research from a credible source the average height in the population as a whole for the group you sampled. Make sure to credit your source. Calculate a percent difference between the average of your sample and the average in the population as a whole.   What was the percent difference of the average height in your sample and the population as a whole? Comment on your percent difference.

Table of Raw Data of womens heights

Sample Number	Height in Feet and Inches	Height Converted to Inches
1	5 feet	60
2	5 feet 3 inches	63
3	5 feet 5 inches	65
4	5 feet 5 inches	65
5	5 feet 9 inches	69
6	5 feet 11 inches	71
7	5 feet 1 inch	61
8	5 feet 2 inches	62
9	5 feet 3 inches	63
10	5 feet 6 inches	66
11	6 feet	72
12	5 feet 11 inches	71
13	5 feet 4 inches	64
14	5 feet 8 inches	68
15	5 feet 8 inches	68
16	5 feet 4 inches	64
17	5 feet 7 inches	67
18	5 feet 5 inches	65
19	5 feet 5 inches	65
20	5 feet 2 inches	62
21	5 feet 5 inches	65
22	5 feet 9 inches	69
23	5 feet 2 inches	62
24	5 feet 3 inches	63
25	5 feet 1 inches	61
26	5 feet 4 inches	64
27	5 feet 5 inches	65
28	5 feet 5 inches	65
29	5 feet 3 inches	63
30	5 feet 6 inches66	66

Answer 1

Solution1:

in excel  

install anlaysis tool pack then go to data>data analysis>descriptive statistics.

select the data range

you will get

Height Converted to Inches
Mean	65.13333
Standard Error	0.566768
Median	65
Mode	65
Standard Deviation	3.104317
Sample Variance	9.636782
Kurtosis	-0.21166
Skewness	0.600386
Range	12
Minimum	60
Maximum	72
Sum	1954
Count	30

mean=65.13333

median=65

mode=65

mean=median =mode

shape :symmetrical

follows normal distribution.

No outliers found

Solution2:

x of the sample is sample mean=xbar=65.1333

Solution3:

s of the sample is standard deviation=s=

3.104317

Solution4:

alpha=1-0.90=0.1

90% confidence interval for your sample.

xbar-MOE,xbar+MOE

MOE=margin of error=tcrit *s/sqrt(n)

MOE can be found in excel as

syntax is CONFIDENCE.T(alpha.samplesd,samplesize)

=CONFIDENCE.T(0.1;3.104317;30)

=0.963011079

90% lower limit=65.1333-0.963011079=64.17029

90% upper limit=65.1333+0.963011079=66.09631

we are 90% confident that the true population mean height of womens height lies in between

64.17029 and 66.09631 inches