Question

A random sample of size 15 is selected from a normal population. The population standard deviation is unknown. Assume the null hypothesis indicates a two-tailed test and the researcher decided to use the 0.10 significance level. For what values of t will the null hypothesis not be rejected?

a. ​To the left of -1.645 or to the right of 1.645
b. To the left of -1.345 or to the right of 1.345
c. ​To the left of -1.282 or to the right of 1.282
d. ​Between -1.761 and 1.761

Answer 1

Answer:

Since we don't know the population deviation $\sigma$ we need to use a t statistic, and the degrees of freedom are given by:

$df = n-1= 15-1 =14$

The significance level is $\alpha=0.1$ so we need to look in the t distribution with df =14 a value who accumulates $\alpha/2=0.05$ of the area on each tail and we got:

$t_{cric}= \pm 1.761$

And the non rejection zone of the null hypothesis would be:

d. ​Between -1.761 and 1.761

Step-by-step explanation:

For this case the sample size is n =15. We want to conduct a two tailed test in order to check if the true mean is equal to a specified value

Null hypothesis: $\mu =\mu_o$

Alternative hypothesis: $\mu \neq \mu_o$

Since we don't know the population deviation $\sigma$ we need to use a t statistic, and the degrees of freedom are given by:

$df = n-1= 15-1 =14$

The significance level is $\alpha=0.1$ so we need to look in the t distribution with df =14 a value who accumulates $\alpha/2=0.05$ of the area on each tail and we got:

$t_{cric}= \pm 1.761$

And the non rejection zone of the null hypothesis would be:

d. ​Between -1.761 and 1.761