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

$3,200 x 7.25% = $3,200 x .0725 = $232 interest monthly

$232 monthly x 12 annual = $2, 784

step-by-step explanation:

the diagram shows you   triangle def with de=4, df=9 and de≠df≠ef.

the sum of the lengths of two triangles' sides are always greater than the length of the third side:

substitute sides lengths:

then 5< ef< 13 (option 3 is true).

def is a scalene triangle with all sides of different lengths (option 5 is true, option 2 is false).

answer: correct choices are 1, 3 and 5