Question

Q2)

(a). A recent article in the Daily Mirror newspaper reported that only one in three new college graduates are able to obtain a job. The reason stated is that there is an overabundance of college graduates and a weak economy.

A survey of 200 college graduates revealed that 80 had jobs. Using a significance level of α=0.02, conduct a hypothesis test to examine if a larger proportion of college graduates have jobs than the newspapers claim.

State all answers in this question to 2dp accuracy.

1. State the Null and Alternative hypotheses.

2. Write down the critical value.

3. Calculate the test statistic.  

4. Compare test statistic against critical value and make your decision.

5. State your conclusion.

(1 Mark)

Q2(b).

Executives at Toyota were given the new high-performance 3.5-litre V6 SUV automobile, they were asked to keep records of the number of miles travelled per gallon of petrol for this new vehicle using regular petrol versus high octane petrol.

Their results follow.

	Miles per gallon
Executive	Regular	High-Octane
Bowers	25	28
Smith	33	31
Grasser	31	35
Jones	45	44
King	42	47
Rau	38	40
James	29	29
Burns	42	37
Snow	41	44
Lawless	30	44

Perform a dependent samples t-test (paired t-test) to examine if there is a difference in the number of miles travelled per gallon. Use a 5% significance level.

1. State the null hypothesis and the alternate hypothesis.

2. Calculate the test statistic.  (state accurate to 2dp)

3. State the Degrees of Freedom for this test.

(1 Mark)

4. Look up the critical value.

(1 Mark)

5. Make your decision and write a conclusion.

Answer 1