Question

The average cost of tuition and room and board at a small private liberal arts college is reported to be $8,500 per term. A financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. Based on the computed test statistic or p-value, what is our decision about the average cost?

• Equal to $8,500

• Greater than $8,500

• Less than $8,500

• Not equal to $8,500

Answer 1

Solution :

Given that ,

= 8500  

= 87455

= 1200

n = 350

The null and alternative hypothesis is ,

H₀ :   = 8500

H_a : > 8500

This is the right tailed test .

Test statistic = z

= ( - ) / / n

= ( 8745 - 8500) / 1200 / 350

= 3.82

The test statistic = 3.82

P - value = P(Z > 3.82 ) = 1- P (Z < 3.82 )

= 1 - 0.9999

= 0.0001

P-value = 0.0001

= 0.05  

0.0001 < 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to test the claim.