Question

1. Average Senior High School annual cost of tuition fee for all private schools in Cavite last year was 46,300 a random sample of costs this year for 45 private schools indicated that the sample mean was 47,800 and a sample standard deviation was 5600 at the 0.10 level of significance, is there sufficient evidence to conclude that the cost has increased?

Solution:

1. State of hypotheses

2. The level of significance, critical region, and df if any

3. Compute for the value of one sample z-test or t-test

4. Decision rule

5. conclusion

Answer 1

Explanation:

H0 : μ = 46300

H1 : μ > 46300

α = 0.05

df = n - 1 = 45 - 1 = 44

Critical value for a one tailed t-test(since population standard deviation is not given).

Tcritical = 1.30

The test statistic :(xbar - μ) ÷ (s/sqrt(n))

The test statistic, t= (47800-46300) ÷ (5600√45)

t = 1500

t = 1500 / 834.79871

t = 1.797

The decision region :

Reject H0: if t value > critical value

1. 797 > 1.30

Tvalue > critical value ; We reject H0

Hence, there is sufficient evidence to conclude that cost has increased.