In each of the following cases, state the null hypothesis H_0 and the alternativ

Question

In each of the following cases, state the null hypothesis H_0 and the alternative hypothesis H_1 about the population proportion p under test. Interpret p in each instance. (a) The winner in the last congressional election received 54% of the vote. One year before the next election, the congressman hired a polling agency to conduct a sample survey of voters to determine if this proportion has changed. (b) The proportion of overdue books in a library is 5%. It is proposed to raise the line for overdue books from 5 cents to 10 cents per day. It is felt that this would reduce the proportion of overdue books. (c) The scrap rate in making of a composite material is as high as 40%. A new production process is proposed which is claimed to reduce the scrap rate. (d) Gatorade and All Sport are two drinks popular among athletes. A marketing firm wants to determine whether a greater proportion of people like the taste of Gatorade or All Sport. For this purpose, a blind test is conducted in which the two drinks are offered in a random order to a group of tasters, who are then asked to indicate preference for one or the other drink.

Explanation / Answer

Solution:-

a)

P = 54/100

P = 0.54

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P = 0.54
Alternative hypothesis: P 0.54

b)

P = 5/100

P = 0.05

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P > 0.05
Alternative hypothesis: P < 0.05

c)

P = 40/100

P = 0.40

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P > 0.40
Alternative hypothesis: P < 0.40

d)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: PGatorade< PAll sports
Alternative hypothesis: PGatorade > PAll sports

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.