Question

Practice question 6

A recent article reported that a job awaits only one in three (0.33) new college graduates. The major reasons given were an overabundance of college graduates and a weak economy. A survey of 200 recent graduates from your school revealed that 80 students had jobs. At the .01 significance level, can we conclude that a larger proportion of students at your school have jobs?

A     The Null Hypothesis is:

a    Job awaiting new college graduates is _______.

b    Job awaiting new college graduates is greater than _______.

c    Job awaiting new college graduates is less than         _______.

d Job awaiting new college graduates is not equal to      _______.

Answer the question by: Selecting the appropriate letter and then entering the correct number for the Null Hypothesis.
Enter numerical value of the Null Hypothesis as a fraction or a 2 place decimal with a 0 to the left of the decimal point..

B    The Alternate Hypothesis is:

a    Job awaiting new college graduates is equal to          ______.

b    Job awaiting new college graduates is greater than    ______.

c    Job awaiting new college graduates is less than        ______.

d    Job awaiting new college graduates is not equal to      ______.

Answer the question by:

Selecting the appropriate letter and then entering the correct number for the Alternate Hypothesis.
Enter numerical value of the Alternate Hypothesis as a fraction or a 2 place decimal with a 0 to the left of the decimal point..

Answer 1

1) The Null Hypothesis is -- Job awaiting new college graduates is equal to 33% of them.

(Option (a) is correct).

Justification: Since null hypothesis always takes into consideration the equality case, here the hypothesized population proportion is 0.33.

2) The Alternate Hypothesis is -- Job awaiting new college graduates is greater than 33% of them.

(Option (b) is correct).

Justification: Since in the alternative case we are to determine if the larger proportion of students at your school have jobs, which is an upper-tailed case.

The test statistic is Z= (p-p_hat)/(((p*(1-p)/n)^0.5); where p = sample proportion and p_hat is the hypothesized value of the population proportion, n = sample size. Z follows standard normal distribution under H0.

We reject H0 if Z(observed) > tau (alpha) where tau(alpha) is the upper alpha point of a standard normal distribution, alpha being the level of significance. Here alpha = 0.01.

Here Z(observed) =  1.278 and tau(alpha) = 2.326, thus, we do not reject H0 and conclude on the basis of the given sample measures at 1% level of significance that there is no significant evidence to support the claim that the Job awaiting new college graduates is greater than 0.33.

The answers are obtained using R-software. Code and output are attached below for verification.