A data set includes data from student evaluations of courses. The summary statistics are nequals83, x overbarequals3.32, sequals0.56. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 3.50. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

Hypothesis

Null hypothesis:    

Alternative hypothesis:    

Statistic

P value

The degrees of freedom are given by:

And the p value would be given by:

Conclusion

Since the p value is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 3.5

Step-by-step explanation:

Information given

represent the sample mean

represent the sample deviation

sample size    

represent the value to test

t would represent the statistic

represent the p value

System of hypothesis

We want to verify if the true mean is equal to 3.5, the system of hypothesis are:    

Null hypothesis:    

Alternative hypothesis:    

Statistic

The statistic would be given by:

(1)    

Replacing we got:

P value

The degrees of freedom are given by:

And the p value would be given by:

Conclusion

Since the p value is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 3.5

the answer is 96 degrees

step-by-step explanation:

you have to realize that a line equals 180 degrees

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: