Question

Suppose the heights (in inches) of all college students follow a Normal distribution with standard deviation σ=3. A sample of 25 students is taken from the population; the average height of these students is 68.4 inches. Does this sample data provide strong evidence that the average height of all students is less than 70 inches?

Which test should be used?

What is the null hypothesis?

What is the alternative hypothesis?

What is the p-value?

Answer 1

Solution :

Given that,

Population mean = = 70

Sample mean = = 68.4

Population standard deviation = = 3

Sample size = n = 25

Z - test should be used.

This is a left (One) tailed test,

The null hypothesis is,  

Ho: 70

The alternative hypothesis is,  

Ha: 70

The test statistics,

Z =( - )/ (/n)

= ( 68.4 - 70 ) /( 3 / 25 )

= -2.67

P-value = P(Z < z )

= P(Z < -2.67 )

= 0.0038