A random sample of 35 four-door passenger vehicles had a mean gas mileage, in miles per gallon ( mpg ), of 25.9mpg. The estimate had a margin of error of 2.6mpg at a 98% confidence level. Of the following, which is the most plausible value for the true mean gas mileage of all four-door passenger vehicles? Choose 1 answer: (A) 24mpg (B) 29mpg (C) 32mpg (D) 35mpg

Understand Given Information: Understand the given information and what is being asked. We have a sample mean of 25.9 mpg with a margin of error of 2.6 mpg at a 98% confidence level. We need to determine the most plausible value for the true mean gas mileage of all four-door passenger vehicles from the given options.Calculate Plausible Range: Calculate the range of plausible values for the true mean using the margin of error. The lower bound of the plausible range is the sample mean minus the margin of error: 25.9 mpg - 2.6 mpg = 23.3 mpg. The upper bound of the plausible range is the sample mean plus the margin of error: 25.9 mpg + 2.6 mpg = 28.5 mpg.Compare with Options: Compare the calculated range with the given options to determine the most plausible value. The range of plausible values for the true mean gas mileage is from 23.3 mpg to 28.5 mpg. We need to find which option falls within this range. (A) 24 mpg is within the range. (B) 29 mpg is outside the range. (C) 32 mpg is outside the range. (D) 35 mpg is outside the range.Select Correct Answer: Select the correct answer based on the comparison. The only option that falls within the plausible range is (A) 24 mpg.

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A random sample of 35 four-door passenger vehicles had a mean gas mileage, in miles per gallon (
mpg ), of
25.9mpg. The estimate had a margin of error of
2.6mpg at a
98% confidence level. Of the following, which is the most plausible value for the true mean gas mileage of all four-door passenger vehicles?
Choose 1 answer:
(A)
24mpg
(B)
29mpg
(C)
32mpg
(D)
35mpg

A random sample of $35$ four-door passenger vehicles had a mean gas mileage, in miles per gallon $(\mathrm{mpg})$ , of $25.9 \mathrm{mpg}$ . The estimate had a margin of error of $2.6 \mathrm{mpg}$ at a $98 \%$ confidence level. Of the following, which is the most plausible value for the true mean gas mileage of all four-door passenger vehicles? $\newline$ Choose $1$ answer: $\newline$ (A) $24 \mathrm{mpg}$ $\newline$ (B) $29 \mathrm{mpg}$ $\newline$ (C) $32 \mathrm{mpg}$ $\newline$ (D) $35 \mathrm{mpg}$

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Math Problems

Algebra 2

Interpret confidence intervals for population means

Full solution

Q. A random sample of

35

four-door passenger vehicles had a mean gas mileage, in miles per gallon

(\mathrm{mpg})

, of

25.9 \mathrm{mpg}

. The estimate had a margin of error of

2.6 \mathrm{mpg}

at a

98 \%

confidence level. Of the following, which is the most plausible value for the true mean gas mileage of all four-door passenger vehicles?

\newline

Choose

1

answer:

\newline

(A)

24 \mathrm{mpg}

\newline

(B)

29 \mathrm{mpg}

\newline

(C)

32 \mathrm{mpg}

\newline

(D)

35 \mathrm{mpg}

Understand Given Information: Understand the given information and what is being asked. $\newline$ We have a sample mean of $25.9$ mpg with a margin of error of $2.6$ mpg at a $98\%$ confidence level. We need to determine the most plausible value for the true mean gas mileage of all four-door passenger vehicles from the given options.
Calculate Plausible Range: Calculate the range of plausible values for the true mean using the margin of error. $\newline$ The lower bound of the plausible range is the sample mean minus the margin of error: $25.9 \, \text{mpg} - 2.6 \, \text{mpg} = 23.3 \, \text{mpg}$ . $\newline$ The upper bound of the plausible range is the sample mean plus the margin of error: $25.9 \, \text{mpg} + 2.6 \, \text{mpg} = 28.5 \, \text{mpg}$ .
Compare with Options: Compare the calculated range with the given options to determine the most plausible value. $\newline$ The range of plausible values for the true mean gas mileage is from $23.3$ mpg to $28.5$ mpg. We need to find which option falls within this range. $\newline$ (A) $24$ mpg is within the range. $\newline$ (B) $29$ mpg is outside the range. $\newline$ (C) $32$ mpg is outside the range. $\newline$ (D) $35$ mpg is outside the range.
Select Correct Answer: Select the correct answer based on the comparison. $\newline$ The only option that falls within the plausible range is (A) $24$ mpg.