Question

Use the results from a survey of a simple random sample of 2100 adults. Among the 2100 ​respondents, 1048 rated themselves as above average drivers. We want to test the claim that of the majority of adults rated themselves above average drivers. Complete parts​ (a) through​ (d).

a. Identify the sample proportion and use the symbol that represents it.
b. What is the best point estimate for the population proportion?
c. State the null and alternative hypotheses.
d. Write is the confidence interval for proportion of adults that rate themselves as above average drivers. (confidence level is 95%)

Answer 1

the 95% confidence interval for the proportion of adults who rate themselves as above-average drivers is:

(0.485, 0.523)

How can you write the confidence interval for the proportion of adults who rate themselves as above-average drivers?

The sample proportion of adults who rated themselves as above-average drivers is:

p = 1048 / 2100 ≈ 0.504

The symbol that represents the sample proportion is p.

b.The proportion of adults in the population who rate themselves as above-average drivers is unknown. However, the best point estimate for this proportion is the sample proportion, which is 0.504.

c. Null hypothesis (H 0): The majority of adults do not rate themselves as above-average drivers. Mathematically, H 0: p <= 0.5 (where p is the population proportion).

Alternative hypothesis (H a): The majority of adults do rate themselves as above-average drivers. Mathematically, H a: p > 0.5.

d.To estimate the range within which the true population proportion (p) likely falls, we can calculate a 95% confidence interval for p.

The margin of error: Calculate the margin of error using the formula:

ME = z *
`\sqrt`(p * (1 - p) / n)

ME ≈ 1.96 *
`\sqrt`(0.504 * (1 - 0.504) / 2100) ≈ 0.019

Confidence interval: The confidence interval is calculated as:

CI = p +/- ME

Therefore, the 95% confidence interval for the proportion of adults who rate themselves as above-average drivers is:

CI = 0.504 +/- 0.019 = (0.485, 0.523)

We are 95% confident that the true proportion of adults in the population who rate themselves as above-average drivers falls between 48.5% and 52.3%.