A random sample of 100 people was taken.Eighty-five of the people in the sample favored Candidate A.We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%.The p-value is

A) .2112.
B) .05.
C) .025.
D) .1056.

Question

thurgashini nadaraja · Accepted Answer

Final Answer : D, Explanation :  The p-value in hypothesis testing represents the probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct. In this case, the null hypothesis would likely be that the proportion of the population in favor of Candidate A is 80% (or 0.8). Given that 85 out of 100 people favored Candidate A, which is an observed proportion of 0.85, the p-value would be calculated based on the standard error of the proportion and the difference between the observed proportion and the hypothesized proportion (0.85 - 0.8). The exact p-value would depend on the use of a normal approximation to the binomial distribution, which is appropriate here given the large sample size (n=100). Without performing the exact calculation here, the correct answer is provided as D) .1056, which suggests that there is a 10.56% chance of observing a sample proportion of 0.85 or more in favor of Candidate A if the true population proportion is 0.8. This p-value is relatively high, indicating that the evidence is not strong enough to reject the null hypothesis at common significance levels (e.g., 0.05 or 0.01).

A random sample of 100 people was taken.Eighty-five of the people in the sample favored Candidate A.We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%.The p-value is

A) .2112.
B) .05.
C) .025.
D) .1056.

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Learning Objectives

Related questions

A random sample of 100 people was taken.Eighty-five of the people in the sample favored Candidate A.We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%.The p-value isA) .2112.B) .05.C) .025.D) .1056.

Definitions

Learning Objectives

Learning Objectives

Related questions

A random sample of 100 people was taken.Eighty-five of the people in the sample favored Candidate A.We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%.The p-value is

A) .2112.
B) .05.
C) .025.
D) .1056.