A researcher studying a memory enhancing technique had participants memorize nonsense words and definitions. Out of a list of 10 words, 57 participants were able to quickly learn 6.24 words on average with a standard deviation of 1.24. If it is known the mean number of words memorized in general is 5.65, is there sufficient evidence at that the memory enhancing technique helped participants learn more words? a. What are the null and alternative hypotheses?
b. What is the value of the test statistic?
c. What is the critical value?
d. What is the decision?
e. What is the conclusion?

A.

Null:

H0: u= 5.65

Alternative:

H1: u > 5.65

B.

The test statistic

Xbar = 6.24

u = 5.65

S = 1.24

N = 57

T = 6.24-5.65/(1.24/√57)

= 0.59/(1.24/7.5498)

= 0.59/0.1642

Test statistic = 3.593

C.

With alpha = 0.05

Df = n-1 = 57-1 = 56

T critical = 1.673

D.

If t test > 1.673 reject the null hypothesis

3.593>1.673, reject the null hypothesis

We conclude that there is enough evidence that the technique helped the participants to learn more.

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%