(1 point) Prospective drivers who enrol in Smart Driver Driving School have always been taught by a conventional teaching method. The driving school has many branches across provinces. Last year, among all students that took driving lessons from the school in a certain province, 80% passed the provincial road test. This year, the teaching committee came up with a new teaching method. The committee randomly assigned half of its 2400 students enrolled this year to receive the conventional teaching method and the remaining half to receive the new teaching method. In a random sample of 100 students who received the conventional teaching method, 79% passed the road test

To test if the passing rate has decreased from last year for students who received the conventional teaching method, what will be the null hypothesis?

A. The proportion of 100 students who received the conventional teaching method and subsequently passed the road test this year is lower than 0.80.
B. The proportion of 1200 students who received the conventional teaching method and subsequently passed the road test this year is lower than 0.80.
C. The proportion of 1200 students who received the conventional teaching method and subsequently passed the road test this year equals 0.80.
D. The proportion of 100 students who received the conventional teaching method and subsequently passed the road test this year equals 0.80.
E. The proportion of 1200 students who received the conventional teaching method and subsequently passed the road test this year equals 0.78.
F. The proportion of 100 students who received the conventional teaching method and subsequently passed the road test this year equals 0.78.

Part ii) For the test mentioned in the previous part, what will be the alternative hypothesis?

From the hypothesis tested, we have that the null hypothesis is:

C. The proportion of 1200 students who received the conventional teaching method and subsequently passed the road test this year equals 0.80.

ii) The alternative hypothesis is

We are testing if the passing rate has decreased from last year for students who received the conventional teaching method.

At the null hypothesis, we test if the proportion has not decreased, that is, if it still is of 80%, hence:

Hence, option C is correct.

At the alternative hypothesis, it is tested if the proportion has decreased, that is:

A similar problem is given at link

(i) Correct option is (C).

(ii) The proportion of 1200 students who received the conventional teaching method and subsequently passed the road test this year is lower than 0.80.

Step-by-step explanation:

A new teaching method is implemented at the Smart Driver Driving School to teach students.

The passing rate of students using the conventional method is 0.80.

After implementing the new method half the students were taught using the conventional method and the other half using the new method.

The passing rate of students in the conventional method group was 0.79.

A hypothesis test for single proportion can be used to determine whether the passing rate has decreased from last year for students who received the conventional teaching method.

(i)

The hypothesis is defined as follows:

H₀: The passing rate has not decreased from last year for students who received the conventional teaching method, i.e p = 0.80.

Hₐ: The passing rate has decreased from last year for students who received the conventional teaching method, i.e p < 0.80.

Thus, the correct null hypothesis is given by the statement:

(C) The proportion of 1200 students who received the conventional teaching method and subsequently passed the road test this year equals 0.80.

(ii)

The alternate hypothesis is given by:

The proportion of 1200 students who received the conventional teaching method and subsequently passed the road test this year is lower than 0.80.

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