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Anne reads that the average price of regular gas in her
state is $4.06 per gallon. To see if the average price of gas
is different in her city, she selects 10 gas stations at random
and records the price per gallon for regular gas at each sta-
hon. The data, along with the sample mean and standard
deviation, are listed in the table below.

Anne Reads That The Average Price Of Regular Gas In Her State Is 406 Per Gallon To See If The Average Price Of Gas Is Different In Her City She Selects 10 Gas S class=

Sagot :

Using the t-distribution, it is found that since the absolute value of the test statistic is less than the critical value for the two-tailed test, there is not enough evidence to conclude that the price of the gas in Anne's city is different of $4.06.

What are the hypothesis?

At the null hypothesis, we test if the average price is of $4.06 per gallon, hence:

[tex]H_0: \mu = 4.06[/tex]

At the alternative hypothesis, we test if the average is different of $4.06 per gallon, hence:

[tex]H_1: \mu \neq 4.06[/tex]

What is the test statistic?

We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

  • [tex]\overline{x}[/tex] is the sample mean.
  • [tex]\mu[/tex] is the value tested at the null hypothesis.
  • s is the standard deviation of the sample.
  • n is the sample size.

In this problem, considering the table, we have that the values of the parameters are: [tex]\overline{x} = 4.038, \mu = 4.06, s = 0.0533, n = 10[/tex].

Hence, the value of the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{4.038 - 4.06}{\frac{0.0533}{\sqrt{10}}}[/tex]

[tex]t = -1.31[/tex]

What is the decision?

Using a t-distribution calculator, considering a two-tailed test, as we are testing if the mean is different of a value, 10 - 1 = 9 df and a standard significance level of 0.05, the critical value is [tex]|t^{\ast}| = 2.2622[/tex]

Since the absolute value of the test statistic is less than the critical value for the two-tailed test, there is not enough evidence to conclude that the price of the gas in Anne's city is different of $4.06.

You can learn more about the t-distribution at https://brainly.com/question/13873630

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