Question

You would like to know whether forwards in a basketball league average the same (or different) numbers of points than the overall league average of 7.5 points. Drawing a random sample of 10 forwards from the league, their averages were: 10, 9, 6, 11, 13, 14, 9, 9, 9, and 10 points. If you were going to compare the obtained average of scoring by the sampled forwards with the population value of 7.5.
Required:
What is the critical t-value for such a test given an alpha level of 0.05?

Answer 1

Answer:

The critical t-value for such a test given an alpha level of 0.05 is 2.26

Step-by-step explanation:

Null hypothesis : $H_0:\mu = 7.5$

Alternate hypothesis :$H_a:\mu \neq 7.5$

Population mean = $\mu = 7.5$

Data : 10, 9, 6, 11, 13, 14, 9, 9, 9, and 10

Mean = $\bar{x}=\frac{\text{Sum of all observations}}{\text{no. of observations}}$

Mean =$\frac{10+9+6+11+13+14+9+9+ 9+ 10}{10}$

Mean =10

Standard deviation : $\sqrt{\frac{\sum(x-\bar{x})^2}{n}}$

Standard deviation :$\sqrt{\frac{(10-10)^2+(9-10)^2+(6-10)^2+(11-10)^2+(13-10)^2+(14-10)^2+(9-10)^2+(9-10)^2+(9-10)^2+(10-10)^2}{10}}$

Standard deviation s :2.144

$t = \frac{x-\mu}{\frac{s}{\sqrt{n}}}t = \frac{10-7.5}{\frac{2.144}{\sqrt{10}}}t=3.687$

Df = n-1 = 10-1 = 9

T critical =$t_{(df,\alpha)}=t_(9,0.05)=2.26$

T calculated > T critical

So, We failed to accept null hypothesis

Hence the critical t-value for such a test given an alpha level of 0.05 is 2.26