Question

Two professors at a local college developed a new teaching curriculum designed to increase​ students' grades in math classes. In a typical developmental math​ course, 55​% of the students complete the course with a letter grade of​ A, B, or C. In the experimental​ course, of the 15 students​ enrolled, 12 completed the course with a letter grade of​ A, B, or C. Is the experimental course effective at the alpha equals 0.025 level of​ significance? Complete parts ​(a) through​ (g).

​(a) State the appropriate null and alternative hypotheses.

Upper H 0​:

versus

Upper H 1​:

​(Type integers or decimals. Do not​ round.)

​(b) Verify that the normal model may not be used to estimate the​ P-value.

Because np 0 left ( 1 minus p 0 right )= ___, ___ 10, the normal model may not be used to approximate the​ P-value.

​(Round to one decimal place as​ needed.)

​(c) Explain why this is a binomial experiment.

There is a fixed number of trials with two mutually exclusive outcomes. The trials are independent and the probability of success is fixed at

_____?____ for each trial.

​(Type an integer or a decimal. Do not​ round.)

​(d) Determine the​ P-value using the binomial probability distribution. State your conclusion to the hypothesis test.

First determine the​ P-value.

​P-value =

​(Round to three decimal places as​ needed.)

Is there sufficient evidence to support the research that the experimental course is​ effective?

A.

Yes​, do not reject the null hypothesis because the​ P-value is greater than alpha. There is sufficient evidence to conclude that the experimental course is effective.

B.

No​, do not reject the null hypothesis because the​ P-value is greater than alpha. There is insufficient evidence to conclude that the experimental course is effective.

.C.

No​, reject the null hypothesis because the​ P-value is less than alpha. There is insufficient evidence to conclude that the experimental course is effective.

D.

Yes​, reject the null hypothesis because the​ P-value is less than alpha. There is sufficient evidence to conclude that the experimental course is effective.

​(e) Suppose the course is taught with 45 students and 30 complete the course with a letter grade of​ A, B, or C. Verify whether the normal model may now be used to estimate the​ P-value.

Because np 0 left ( 1 minus p 0 right )= ___, _____ ? ​10, the sample size is less than ​5% of the population​ size, and the sample can be reasonably

assumed to be random, the normal model may be used to approximate the​ P-value.

​(Round to one decimal place as​ needed.)

​(f) Use the normal model to obtain and interpret the​ P-value. State your conclusion to the hypothesis test.

First find the test​ statistic, z 0.

z 0=

​(Round to two decimal places as​ needed.)

Now determine the​ P-value.

​P-value=

​(Round to three decimal places as​ needed.)

Is there sufficient evidence to support the research that the experimental course is​ effective?

A.

Yes​, reject the null hypothesis because the​ P-value is greater than alpha. There is sufficient evidence to conclude that the experimental course is effective.

B.

No​, do not reject the null hypothesis because the​ P-value is less than alpha. There is insufficient evidence to conclude that the experimental course is effective.

Your answer is not correct.C.

Yes​, reject the null hypothesis because the​ P-value is less than alpha. There is sufficient evidence to conclude that the experimental course is effective.

.D.

No​, do not reject the null hypothesis because the​ P-value is greater than alpha. There is insufficient evidence to conclude that the experimental course is effective.

Answer 1

(a)

(b)

Here we have

n=15 and p=0.55

So is less than 10 so  the normal model may not be used to approximate the​ P-value.

(c)

There is a fixed number of trials with two mutually exclusive outcomes. The trials are independent and the probability of success is fixed at 0.55 for each trial.

(d)

B.

No​, do not reject the null hypothesis because the​ P-value is greater than alpha. There is insufficient evidence to conclude that the experimental course is effective.

---------------------------------

(e)

Here we have

n=45 and p=0.55

So   is greater than 10 so  the normal model can be used to approximate the​ P-value.

Conclusion:

D.

No​, do not reject the null hypothesis because the​ P-value is greater than alpha. There is insufficient evidence to conclude that the experimental course is effective.