Question

Suppose the mean height of women age 20 years or older in a certain country is 62.7 inches. One hundred randomly selected women in a certain city had a mean height of 61.5 inches. At the 10​% significance​ level, do the data provide sufficient evidence to conclude that the mean height of women in the city differs from the national​ mean? Assume that the population standard deviation of the heights of women in the city is 4.4 inches.

Answer 1

Answer: No, the data provided is not sufficient evidence to conclude that the mean height of women in the city differs from the national mean.

Step-by-step explanation:

Since we have given that

$H_0:\mu =62.7\\\\H_a:\mu \neq 62.7$

Mean height = 61.5 inches

Standard deviation = 4.4 inches

n = 100

So, test statistic value would be

$z=\dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\z=\dfrac{61.5-62.7}{\dfrac{4.4}{\sqrt{100}}}\\\\z=\dfrac{-1.2}{0.44}\\\\z=-2.727$

At 10% level of significance, in two tail test ,

z = 1.28

Since 1.28 > -2.727

So, we will accept the null hypothesis.

Hence, No, the data provided is not sufficient evidence to conclude that the mean height of women in the city differs from the national mean.