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

Respuesta :

Answer:

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

[tex] df = n-1= 15-1 =14[/tex]

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

[tex] t_{cric}= \pm 1.761[/tex]

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: [tex]\mu =\mu_o [/tex]

Alternative hypothesis: [tex]\mu \neq \mu_o [/tex]

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

[tex] df = n-1= 15-1 =14[/tex]

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

[tex] t_{cric}= \pm 1.761[/tex]

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

d. ​Between -1.761 and 1.761

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