Question 13 Marks
Ten individuals are chosen at random from the population and their heights are found to be in inches 63, 63, 64, 65, 66, 69, 69, 70, 70, 71. Discuss the freedom value of Student's-t and 5% level of significance is 2.62.
Answer
$\begin{aligned} \bar{x} & =\text { mean } \\ & =\frac{\sum x}{n} \\ & =\frac{670}{10}=67\end{aligned}$
Now, compute the standard deviation using formula as.
$\begin{aligned} \sigma & =\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}} \\ & =\sqrt{\frac{88}{9}} \\ & =3.13 \text { inches }\end{aligned}$
View full question & answer→| x | $x-\bar{x}$ | $(x-\bar{x})^2$ |
| 63 | -4 | 16 |
| 63 | -4 | 16 |
| 64 | -3 | 9 |
| 65 | -2 | 4 |
| 66 | -1 | 1 |
| 69 | 2 | 4 |
| 69 | 2 | 4 |
| 70 | 3 | 9 |
| 70 | 3 | 9 |
| 71 | 4 | 16 |
| $\sum x=670$ | $\sum(x-\bar{x})^2=88$ |
$\begin{aligned} \bar{x} & =\text { mean } \\ & =\frac{\sum x}{n} \\ & =\frac{670}{10}=67\end{aligned}$
Now, compute the standard deviation using formula as.
$\begin{aligned} \sigma & =\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}} \\ & =\sqrt{\frac{88}{9}} \\ & =3.13 \text { inches }\end{aligned}$