Question

The 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 it is greater than 68 inches, and to support his claim takes an SRS of 16 male students and finds a sample mean of 69.3 inches and the standard deviation of his sample is 2.45 inches. Is this sufficient evidence 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

n = 16

df = 15

P-value = 0.0255

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence that the mean height of all male students is greater than 68 inches .