Question

The height of 10 students selected at a random from a school had a mean 116cm and SD 96cm.Is the group mean being different from the speculated population mean of 120cm?

need the answer {as early as possible}

Answer 1

The following null and alternative hypotheses need to be tested:

$H_0:\mu=120$

$H_1:\mu\not=120$

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.

Based on the information provided, the significance level is $\alpha = 0.05,$  $df=n-1=10-1=9$ degrees of freedom, and the critical value for a two-tailed test is $t_c =2.262156$

The rejection region for this two-tailed test is $R = \{t: |t| > 2.262156\}.$

The t-statistic is computed as follows:

$$t=\dfrac{\bar{x}-\mu}{s/\sqrt{n}}=\dfrac{116-120}{96/\sqrt{10}}=-0.131762$$

Since it is observed that$|t| = 0.131762< 2.262156=t_c,$ it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value for two-tailed, $\alpha=0.05, df=9$ degrees of freedom, $t=-0.131762$ is $p=0.898071,$ and since $p=0.898071>0.05=\alpha,$ it is concluded that the null hypothesis is not rejected.

Therefore, there is not enough evidence to claim that the population mean $\mu$ is different than $120,$ at the $\alpha = 0.05$ significance level.