Question

Find the mean price of gasoline in the State of Ohio. Set up a null and alternative hypothesis to see if your sample for Dayton is enough to prove that the population mean gasoline price in Dayton is different than the mean price in Ohio. Test the hypotheses. Show your work. Using a significance level of 0.05, what is your conclusion?

Dayton Mean=2.217 Standard Dev. 0.070711 Sample size 30 Confidence Interval .95 ME 0.0262150

5 CITIES IN OHIO mean 2.21 Standard Deviation 0.0707

Answer 1

Solution:-

The mean price of gasoline in the state of Ohio is 2.21.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u = 2.21
Alternative hypothesis: u 2.21

Note that these hypotheses constitute a two-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.0129

DF = n - 1

D.F = 29
t = (x - u) / SE

t = 0.5422

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the t statistic having 29 degrees of freedom is less than -0.5422 or greater than 0.5422.

P-value = P(t < - 0.5422) + P(t > 0.5422)

Use the calculator to determine the p-values.

P-value = 0.2959 + 0.2959

Thus, the P-value = 0.5918

Interpret results. Since the P-value (0.2959) is greater than the significance level (0.05), we cannot reject the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that the population mean gasoline price in Dayton is different than the mean price in Ohio.