Several years ago, the mean height of women 20 years of age or older was 63.7 inches. suppose that a random sample of 45 women who are 20 years of age or older today results in a mean height of 65.1 inches. (a) state the appropriate null and alternative hypotheses to assess whether women are taller today. (b) suppose the p-value for this test is 0.16. explain what this value represents. (c) write a conclusion for this hypothesis test assuming an alphaequals0.10 level of significance.

(a) State the appropriate null and alternative hypotheses to assess whether women are taller today.

Solution:

Definition of null hypothesis : The null hypothesis attempts to show that no variation exists between variables or that a single variable is no different than its mean. it is denoted

Alternative Hypothesis: In statistical hypothesis testing, the alternative hypothesis is a position that states something is happening, a new theory is true instead of an old one (null hypothesis).

We are given that The mean height of women 20 years of age or older was 63.7 inches.

So, null hypothesis :

Alternative Hypothesis :

b)The P-value for this test is 0.16.

Solution: The p-value represents the probability of getting a sample mean height of 65.1 inches.

c) Write a conclusion for this hypothesis test assuming an alpha equals 0.10 level of significance.

Solution:

p- value = 0.16

Since the p - value is high .

So, we will accept the null hypothesis

So,  

Hence The mean height is 63.7 inches

D because a unit vectored is a vectored with a unit of magnitude.

we use a unit vector when we only interested in the direction of the vector rather than the magnitude