Answer:
We reject the null hypothesis and fail to accept it and update that estimate that typical teenager sent does not 67 text messages per day.
Step-by-step explanation:
We are given the sample:
51, 175, 47, 49, 44, 54, 145, 203, 21, 59, 42, 100
Formula:
where
are data points,
is the mean and n is the number of observations.
![Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}](https://tex.z-dn.net/?f=Mean%20%3D%20%5Cdisplaystyle%5Cfrac%7B%5Ctext%7BSum%20of%20all%20observations%7D%7D%7B%5Ctext%7BTotal%20number%20of%20observation%7D%7D)
![Mean =\displaystyle\frac{990}{12} = 82.5](https://tex.z-dn.net/?f=Mean%20%3D%5Cdisplaystyle%5Cfrac%7B990%7D%7B12%7D%20%3D%2082.5)
Sum of squares of differences = 992.25 + 8556.25 + 1260.25 + 1122.25 + 1482.25 + 812.25 + 3906.25 + 14520.25 + 3782.25 + 552.25 + 1640.25 + 306.25 = 3539.363636
![S.D = \sqrt{\frac{3539.363636}{11}} = 59.5](https://tex.z-dn.net/?f=S.D%20%3D%20%5Csqrt%7B%5Cfrac%7B3539.363636%7D%7B11%7D%7D%20%3D%2059.5)
We are given the following in the question:
Population mean, μ =67
Sample mean,
= 82.5
Sample size, n = 12
Alpha, α = 0.05
Sample standard deviation, s = 59.5
First, we design the null and the alternate hypothesis
We use One-tailed t test to perform this hypothesis.
b) Formula:
Putting all the values, we have
Now,
a) Since,
![t_{stat} < t_{critical}](https://tex.z-dn.net/?f=t_%7Bstat%7D%20%3C%20t_%7Bcritical%7D)
We reject the null hypothesis and fail to accept it and update that estimate that typical teenager send more than 67 text messages per day.