Question

Discussion Assignment #7 To be able to earn full credit you must post your own response (respond to all questions below) and respond to another student's post. 1. If a distribution is normal with u = 60 and a = 15, what is the z-score of 75? 2. If a distribution is normal with u = 60 and a = 15, what is the 2 score of 40? 3. How can the normal distribution be used to test hypotheses about populations? Also, how might you surmise that you can use this logic to test a hypothesis such as caffeine improves memory in the caffeine study that I reference in my lectures?

Answer 1

1)

Z = (x-mean)/s.d

Given info

X = 75

Mean = 60

S.d = 15

Z = (75-60)/15 = 1

2)

Z = (40-60)/15 = -1.33

3)

When the population standard deviation is mentioned

We can use standard normal distribution to conduct the test

Where

Test statistic z = (sample mean - claimed mean)/(s.d/√n)

And then we can estimate the p-value by looking for the z obtained in the z table

In your example let's say memory score for the population was 60

We need to test if caffeine increase this score

Null hypothesis Ho : u = 60

Alternate Hypothesis Ha : u > 60

Now we will calculate the test statistics z and then p-value

If p-value is small generally less than 0.05

Then we will reject the null hypothesis and will conclude that yes we have enough evidence to conclude that caffeine improves the memory

If p-value is greater than 0.05

We will fail to reject the null hypothesis

In this case we will conclude that we do not have enough evidence to conclude that the caffeine improve the memory