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In: Statistics and Probability

(10) The average tuition and room and board cost at a small private liberal arts college...

(10) The average tuition and room and board cost at a small private liberal arts college is reported to be $20,000 per term. A study of 400 small liberal arts colleges find that the average cost per term is $20,100. The population standard deviation is $1,500. If α = 0.05, what is the critical Z value for the test: Ho: µ= 20,000?

Solutions

Expert Solution

Solution :

Given that,

Population mean = = 20000

Sample mean = = 20100

Population standard deviation = = 1500

Sample size = n = 400

Level of significance = = 0.05

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 20000

Ha: 20000

The test statistics,

Z =( - )/ (/n)

= ( 20100 - 20000 ) / ( 1500 / 400)

= 1.133

Critical value of  the significance level is α = 0.05, and the critical value for a two-tailed test is

= 1.96

The critical value is 1.96

Since it is observed that | z |= 1.133 = 1.96, it is then concluded that the null hypothesis is fail to reject.

orchestra answered 2 years ago
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