Question

Question 2 (1 point) The mean annual tuition and fees for a sample of 7 private colleges was $28,179 with a standard deviation of $4,546. A dotplot shows that it is reasonable to assume that the population is approximately normal. A researcher wants to test to see if the mean tuition and fees for private institutions differs from $30,000. Compute the value of the test. Write down your P-value. You will need it for the next question. Write only a number as your answer. Round to four decimal places (for example: 0.3841). Your Answer: Answer Question 3 (1 point) In the last question, a researcher wanted to test to see if the mean tuition and fees for private institutions differs from $30,000. What is the conclusion at the 0.05 level of significance? There is evidence to conclude that the mean tuition and fees for private institutions differs from $30,000. There is not enough evidence to conclude that the mean tuition and fees for private institutions differs from $30,000 There is evidence to conclude that the mean tuition and fees for private institutions do not differ from $30,000 There is not enough evidence to conclude that the mean tution and fees for private institutions do not differ from $30,000.

Answer 1

Answer)

Null hypothesis Ho : u = 30000

Alternate hypothesis Ha : u not equal to 30000

As the population standard deviation is unknown here we will use t distribution to conduct the test

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

t = (28179 - 30000)/(4546/√7) = -1.06

Degrees of freedom is = n-1 = 6

For 6 dof and -1.06 test statistics

P-value from t distribution is = 0.3299

3)

As the obtained p-value is greater than the given significance 0.05

We fail to reject the null hypothesis Ho

There is not enough evidence to conclude that mean tution fee differs from 30000