Question

An economist studying fuel costs wants to estimate the mean price of gasoline in her state on a certain day. On that day, she takes an SRS of 121212 gas stations and finds the sample mean price (in dollars per gallon) is \bar x=\$2.29 x ˉ =$2.29x, with, \bar, on top, equals, dollar sign, 2, point, 29 with a standard deviation of s_x=\$0.20s x ​ =$0.20s, start subscript, x, end subscript, equals, dollar sign, 0, point, 20. The prices in the sample are roughly symmetric with no distinct outliers. Based on this sample, which of the following is closest to a 90\%90%90, percent confidence interval for the mean price of gasoline that day in her state?

Answer 1

Answer:

($2.19,$2.39)

Step-by-step explanation:

khan

Answer 2

Based on this sample, the confidence interval which is closest to a 90%, for the mean price of gasoline that day in her state is ($2.19, $2.39).

What is random sample?

Random sample is the way to choose a number or sample in such a manner that each of the sample of the group has an equal probability to be chosen.

When the sample size is less than 30, the formula which is used is,

$\overline x\pm t.\dfrac{s}{\sqrt n}$

Here, n is the sample size, $\overline x$ is the sample mean, s is the standard deviation.

Economist, takes an SRS of 12 gas stations. The sample size for the given problem is 12,

$n=12$

Thus, degree of freedom,

$df=12-1\\df=11$

In the t table, for df 11, the value of t is 1.796.

An economist studying fuel costs wants to estimate the mean price of gasoline in her state on a certain day.

On that day, she takes an SRS of 12 gas stations and finds the sample mean price (in dollars per gallon) is,

$\bar x=2.29$

With a standard deviation of

$s_x=0.20$

Put the values in the above formula,

$2.29\pm 1.796.\dfrac{0.20}{\sqrt 12}\\2.29\pm 0.1037\\2.29+0.1037=2.3937\\2.29- 0.1037=2.1863$

Thus, based on this sample, the confidence interval which is closest to a 90%, for the mean price of gasoline that day in her state is ($2.19, $2.39).

Learn more about the random sample here;

https://brainly.com/question/17831271