An educator claims that the average salary of substitute teachers in school districts is less than $60 per day. A random sample of 8 school districts is selected, and the daily salaries are 60, 56, 60, 55, 70, 55, 60, and 55. Is there enough evidence to support the educator’s claim at 10% level of significance? (HELP: The sample mean is 58.88, and the sample standard deviation is 5.08)

The degrees of freedom are given by:

The p value would be given by:

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

Step-by-step explanation:

Information given

60, 56, 60, 55, 70, 55, 60, and 55.

We can calculate the mean and deviation with these formulas:

Replacing we got:

represent the mean

represent the sample standard deviation for the sample  

sample size  

represent the value that we want to test

represent the significance level

t would represent the statistic

represent the p value

Hypothesis to test

We want to test if the true mean is less than 60, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

The statistic would be given by:

 (1)  

Replacing the info we got:

The degrees of freedom are given by:

The p value would be given by:

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

you forgot an image

step-by-step explanation:

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.