Assume that the average age at which students graduate high school is 17.6. Exum (2002) asked 84 male students at a large Mid-Atlantic University the age at which they had their first alcoholic drink. On average, these 84 students had their first alcoholic drink at 16.54 years of age (standard deviation

The null hypothesis is rejected. It can be concluded that the  average age of first drink is less that 17.6 years.

Step-by-step explanation:

A one-sample z-test can be used to determine whether the average age at which students graduate high school and had their first drink is less than 17.6 years.

The hypothesis can be defined as:

H₀: The average age of first drink is 17.6 years, i.e. μ = 17.6.

Hₐ: The average age of first drink is less that 17.6 years, i.e. μ < 17.6.

The information provided is:

We are using the z-test because the population standard deviation is known and the sample size is quite large, i.e. n = 84 > 30.

Compute the test statistic value as follows:

The test statistic value is -4.79.

Decision rule:

If the p-value of the test is less than the significance level (α) then the null hypothesis will be rejected and vice-versa.

Compute the p-value as follows:

*Use a z-table for the probability.

The p-value of the test is 0.

The p-value = 0 < α = 0.05.

Thus, the null hypothesis will be rejected at 5% level of significance.

Conclusion:

As the null hypothesis is rejected it can be concluded that the  average age of first drink is less that 17.6 years.

you need to show us the graph.

step-by-step explanation:

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1