In 1960, census results indicated that the age at which men in a certain region first married had a mean of 24.5 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has increased since then. We plan to test our hypothesis by selecting a random sample of 40 men who married for the first time last year.
The men in our sample married at an average age of 25.3 years, with a standard deviation of 5.4 years. That results in a t-statistic of 0.937 What is the P-value for this?

The degrees of freedom are given by:

And the p value would be given by:

Step-by-step explanation:

Information given

represent the sample mean

represent the sample standard deviation

sample size  

represent the value to verify

t would represent the statistic  

represent the p value

Hypothesis to test

We want to test if the true mean is higher than 24.5, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

The statistic is given by:

 (1)  

Replacing the info given we got:

The degrees of freedom are given by:

And the p value would be given by:

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c

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%