Height |
162.5 |
175.5 |
160 |
175 |
158 |
163 |
186 |
165 |
155 |
165 |
172 |
168 |
175.5 |
158 |
188.5 |
162.5 |
183 |
162.5 |
180.5 |
171 |
180.5 |
180.5 |
176 |
175 |
173 |
165.5 |
160 |
161.5 |
174 |
165 |
178 |
164 |
153 |
183 |
162.5 |
178 |
178 |
168.5 |
162.5 |
185.5 |
176.5 |
188 |
167 |
155 |
160.5 |
173 |
177.5 |
180 |
178 |
171.5 |
168 |
164.5 |
170.5 |
168 |
160.5 |
165 |
157 |
161.5 |
157.5 |
173 |
Lastly, although the procedure in #3 above was convenient, in most cases if we are trying to predict the population mean from a sample mean, we will most likely not know the population standard deviation, sigma. Thus, our next best statistic to use is the sample standard deviation in its place. However, when using the sample standard deviation, we are no longer able to use a normal distribution, and must use the t-distribution instead. a. Determine the margin of error in estimating the population mean height from this one sample’s mean based upon a 95% level of confidence. Do NOT USE our earlier assumption of sigma = 10.2 cm, but use the sample standard deviation value you calculated in 3a, along with appropriate t-score instead of a z-score. b. Using your margin of error value from (5a), give the 95% confidence interval for the population mean height measure as predicted from this one sample's results. State this interval below within an interpretive sentence.
Solution:-
a)
Mean = 169.7167
Median = 168.25
Mode = 162.5
Variance = 82.96921
Height | |
Mean | 169.7167 |
Standard Error | 1.175934 |
Median | 168.25 |
Mode | 162.5 |
Standard Deviation | 9.108744 |
Sample Variance | 82.96921 |
Kurtosis | -0.88965 |
Skewness | 0.209291 |
Range | 35.5 |
Minimum | 153 |
Maximum | 188.5 |
Sum | 10183 |
Count | 60 |
b)
M.E = 2.353
c) 95% confidence interval for the mean is C.I = (
167.364, 172.069).
C.I = 169.7167 + 2.353
C.I = ( 167.364, 172.069)
If repeated samples were taken and the 95% confidence
interval was computed for each sample, 95% of the intervals
(167.364, 172.069) would contain the population
mean.
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