Assume we have a sample of size 16 from heights of students in a high school in
ID: 3149774 • Letter: A
Question
Assume we have a sample of size 16 from heights of students in a high school in cm. The data points are shown below:
167 173 156 198
176 187 164 189
163 176 157 196
197 145 162 177
t = 0.69
The null hypothesis cannot be rejected.
t = 0.69
The null hypothesis can be rejected.
Z = 1.69
The null hypothesis can be rejected.
Z = 1.69
The null hypothesis cannot be rejected.
t = 0.69
The null hypothesis cannot be rejected.
t = 0.69
The null hypothesis can be rejected.
Z = 1.69
The null hypothesis can be rejected.
Z = 1.69
The null hypothesis cannot be rejected.
Explanation / Answer
Assume we have a sample of size 16 from heights of students in a high school in cm.
Here the hypothesis for the test is,
H0 : mu = 173
Assume alpha = level of significance = 0.05
Here there are 16 observations
Sample size is small and population standard deviation is unknown so we use t-test statistic.
The test statistic formula is,
t = (Xbar - mu) / [ s/sqrt(n) ]
where Xbar is sample mean of 16 observations.
mu is the poppulation mean.
s is standard deviation of the data.
n is the sample size.
Xbar = sum of observations / total number of observations = 173.9375
s2 = 1/n-1 (x- Xbar)^2
= 1 / 16 -1 * 3868.938 = 1/15*3868.938 = 257.9292
s = sqrt(s2) = sqrt(257.9292) = 16.06
t = (173.9375 - 173) / (16.06 / sqrt(16)) = 0.9375 / 4.02 = 0.23
The null hypothesis cannot be rejected.
x (x-xbar)^2 167 48.12891 173 0.878906 156 321.7539 198 579.0039 176 4.253906 187 170.6289 164 98.75391 189 226.8789 163 119.6289 176 4.253906 157 286.8789 196 486.7539 197 531.8789 145 837.3789 162 142.5039 177 9.378906 2783 3868.938