For each of the following situations, give a definition of the population propor
ID: 3355179 • Letter: F
Question
For each of the following situations, give a definition of the population proportion, p , and state H o and H a (Remember H a is the research hypothesis).
(a) A politician wishes to conduct a poll to determine if more than 50% of the registere d voters in his district will vote for him.
(b) An editor of a magazine intends to show that fewer than 1.5% of the lines printed in his magazine have typographical errors.
(c) Medical researchers intend to conduct a study to determine if the mortality rate of individuals infected with a certain virus has fallen below 70%.
(d) In 1984 it was known that 15% of all California motorists had tampered with emission - control devices in order to save money by buying leaded rather than unleaded gas. The mayor of a particular city in California wants to find out if the proportion of tampered cars in his city differs from the statewide proportion.
(e) A graduate student intends to conduct a study to determine if fewer than 10% of the students in Nova Scotia universities come from outside the province.
(f) A coin is tossed 100 times to determine if the coin is unfair.
Explanation / Answer
Solution:-
(a) A politician wishes to conduct a poll to determine if more than 50% of the registere d voters in his district will vote for him.
Population - Registere d voters in politician district.
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P < 0.50
Alternative hypothesis: P > 0.50
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.
(b) An editor of a magazine intends to show that fewer than 1.5% of the lines printed in his magazine have typographical errors.
Population- Total lines printed in editor's magazine.
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P > 0.015
Alternative hypothesis: P < 0.015
Note that these hypotheses constitute a one-tailed test.
(c) Medical researchers intend to conduct a study to determine if the mortality rate of individuals infected with a certain virus has fallen below 70%.
Population- Individuals infected with a certain virus.
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P > 0.70
Alternative hypothesis: P < 0.70
Note that these hypotheses constitute a one-tailed test.
(d) In 1984 it was known that 15% of all California motorists had tampered with emission - control devices in order to save money by buying leaded rather than unleaded gas. The mayor of a particular city in California wants to find out if the proportion of tampered cars in his city differs from the statewide proportion.
Population - All California motorists
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P = 0.80
Alternative hypothesis: P 0.80
Note that these hypotheses constitute a two-tailed test.
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