Question

9. Heights of male students are known to be normally distributed. One student in the class claims that
the mean height is 68 inches. Another student claims that the mean height is greater than 68 inches. A
SRS of 16 male students has x = 69.3 inches and s = 2.45 inches. Is this sufficient evidence at the 5%
level that the mean height of all male students is greater than 68 inches?

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 68

H_a : > 68

Test statistic = t

= ( - ) / s / n

= (69.3 - 68) / 2.45 / 16

= 2.12

Test statistic = 2.12

n = 16

df = 16 - 1 = 15

P-value = 0.1403

= 0.05  

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence t the 5% level that the mean height of all male students is greater than 68 inches .