Question

More hypotheses Write the null and alternative hypotheses you would use to test each situation.

a) In the 1950s, only about 40% of high school graduates went on to college. Has the percentage changed?
b) Twenty percent of cars of a certain model have needed costly transmission work after being driven between 50,000 and 100,000 miles. The manufacturer hopes that a redesign of a transmission component has solved this problem.
c) We field-test a new-flavor soft drink, planning to market it only if we are sure that over 60% of the people like the flavor.

Answer 1

Answer:

The null and alternative hypotheses are shown below:

Part (a) $H_0: p=0.40\\H_a: p\neq 0.40$

Part (b) $H_0: p=0.20\\H_a: p< 0.20$

Part (c) $H_0: p=0.60\\H_a: p> 0.60$

Step-by-step explanation:

Consider the provided information.

We need to write the null and alternative hypotheses.

Part (a) In the 1950s, only about 40% of high school graduates went on to college.

The null hypotheses is 0.40 and alternative hypotheses is about 0.40 but not equal to 0.40.

$H_0: p=0.40\\H_a: p\neq 0.40$

Part (b) Twenty percent of cars of a certain model have needed costly transmission work after being driven between 50,000 and 100,000 miles. The manufacturer hopes that a redesign of a transmission component has solved this problem.

20% Cars need costly transmission and manufacture hopes that redesign of a transmission component solved this problem.

Thus, the null hypotheses is 0.20 and alternative hypotheses less than 0.20 because after redesign less than 0.20 cars needs transmission.

$H_0: p=0.20\\H_a: p< 0.20$

Part (c): We field-test a new-flavor soft drink, planning to market it only if we are sure that over 60% of the people like the flavor.

We planning to market it only if 0.60 of the people like the flavor.

Thus, the null hypotheses is 0.60 and alternative hypotheses greater than 0.60.

$H_0: p=0.60\\H_a: p> 0.60$