Question

The mean annual tuition and fees in the 2013-2014 academic year for a sample of 13 private colleges in California was $33,000 with a standard deviation of $7300. A dotplot shows that it is reasonable to assume that the population is approximately normal. Can you conclude that the mean tuition and fees for private institutions in California is less than $35,000? Use the α=0.01 level of significance and the P-value method with the TI-84 Plus calculator.

a. state null and alternative hypothesis. what tail is the hypothesis test?

b. Compute the P-value of the test statistic.

c. Determine whether to reject H0. Use the =α0.05 level of significance.

d. State a conclusion

Answer 1

Given :-

Mean () = 33000

Standard deviation (sx) = 7300

Sample size (n) = 13

Alpha = 0.01

a)

Test Hypothesis -

Null : H0: u = 3500

Alternative : Ha: u < 3500

b)

Test statistic -

t = -0.988

P-value -

P = 0.1714

c) p-value is greater than alpha=0.05 then fail to reject null hypothesis (H0).

d)

Conclusion -

Therefore there is insufficient evidence to support the claim the mean tuition and fees for private institutions in California is less than $35,000.

# Note - I don't have TI-84 plus calculator but I have TI-83 plus calculator. I think both steps and answers are same.

step - STAT -> TESTS -> T-Test -> Stats.

​​​​put all value and calculate.