Dean Halverson recently read that full-time college students study 20 hours each week. She decides to do a study at her university to see if there is evidence that students study an average of more than 20 hours each week. A random sample of 35 students were asked to keep a diary of their activities over a period of several weeks. It was found that the average number of hours that the 35 students studied each week was 21.1 hours. The sample standard deviation of 4.3 hours.
Find the p-value.
The p-value should be rounded to 4-decimal places.

It is given that students study an average of more than 20 hours each week and the random sample of 35 students was asked to keep a diary of their activities over a period of several weeks.

The average number of hours that the 35 students was 21.1 hours.

The sample standard deviation is 4.3 hours.

It is required to find the p-value.

What is the standard deviation?

It is defined as the measure of data dispersement, It gives an idea about how much is the data spread out.

We can test the hypothesis using the Z test, the formula for the Z-test is given below:

[tex]\rm Z= \frac{(x-u)}{\frac{S}{\sqrt{n} } }[/tex]

Where x is the sample mean

u is the population mean

s is the standard deviation

n is the sample size.

The hypothesis are: H0 : μ = 20 V/s H1 : μ > 20

We have x = 21.1

u = 20

s = 4.3

n = 35

Putting these values in the above formula, we get:

[tex]\rm Z= \frac{(21.1-20)}{\frac{4.3}{\sqrt{35} } }\\\\\rm Z= \frac{(1.1)}{\frac{4.3}{\sqrt{35} } }\\\\[/tex]

Z = 1.513

difference or df = n -1 ⇒ 35-1 ⇒ 34

P-value at (1.513, 34) = 0.06976 (From the p-value calculator)

P-value = 0.0698 (Rounded to 4-decimal places)

Thus, the p-value is 0.0698 if rounded to 4-decimal places.

Learn more about the standard deviation here:

brainly.com/question/12402189