Questions: In one month, the national mean price per gallon (in dollars) of gasoline was 3.105. The data table here represents a random sample of 20 gas stations in city A. Is gas in city A more expensive than the nation? Assume the data come from a normal population with no outliers. Complete parts (a) through (d) below. 3.01 3.09 3.08 3.08 3.15 3.12 3.14 3.17 3.14 3.17 3.16 3.18 3.21 3.23 3.19 3.23 3.24 3.21 3.23 3.28 (a) What type of test should be used? - A hypothesis test regarding two population standard deviations - A hypothesis test regarding the difference between two population proportions from independent samples using the standard normal test statistic - A hypothesis test regarding the difference of two means using a matched-pairs design - A hypothesis test regarding a single population mean using Student's approximate t

In one month, the national mean price per gallon (in dollars) of gasoline was 3.105. The data table here represents a random sample of 20 gas stations in city A. Is gas in city A more expensive than the nation? Assume the data come from a normal population with no outliers. Complete parts (a) through (d) below. 3.01 3.09 3.08 3.08 3.15 3.12 3.14 3.17 3.14 3.17 3.16 3.18 3.21 3.23 3.19 3.23 3.24 3.21 3.23 3.28 (a) What type of test should be used? - A hypothesis test regarding two population standard deviations - A hypothesis test regarding the difference between two population proportions from independent samples using the standard normal test statistic - A hypothesis test regarding the difference of two means using a matched-pairs design - A hypothesis test regarding a single population mean using Student's approximate t
Transcript text: In one month, the national mean price per gallon (in dollars) of gasoline was 3.105. The data table here represents a random sample of 20 gas stations in city A. Is gas in city A more expensive than the nation? Assume the data come from a normal population with no outliers. Complete parts (a) through (d) below. \begin{tabular}{lll|l|l|} 3.01 & 3.09 & 3.08 & 3.08 \\ 3.15 & 3.12 & 3.14 & 3.17 \\ 3.14 & 3.17 & 3.16 & 3.18 \\ 3.21 & 3.23 & 3.19 & 3.23 \\ 3.24 & 3.21 & 3.23 & 3.28 \end{tabular} (a) What type of test should be used? A hypothesis test regarding two population standard deviations A hypothesis test regarding the difference between two population proportions from independent samples using the standard normal test statistic A hypothesis test regarding the difference of two means using a matched-pairs design A hypothesis test regarding a single population mean using Student's approximate t
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Solution

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Solution Steps

Step 1: Calculate Sample Mean and Standard Deviation

The sample mean (\(\bar{x}\)) of the gasoline prices from the 20 gas stations in city A is calculated as follows:

\[ \bar{x} = \frac{3.01 + 3.09 + 3.08 + 3.08 + 3.15 + 3.12 + 3.14 + 3.17 + 3.14 + 3.17 + 3.16 + 3.18 + 3.21 + 3.23 + 3.19 + 3.23 + 3.24 + 3.21 + 3.23 + 3.28}{20} = 3.1655 \]

The sample standard deviation (\(s\)) is calculated to be:

\[ s \approx 0.0665 \]

Step 2: Determine the Type of Test

Since we are comparing the sample mean to a known population mean (the national mean price of gasoline), we will use:

A hypothesis test regarding a single population mean using Student's approximate \(t\).

Step 3: Perform the Hypothesis Test

We will conduct a right-tailed test to determine if the mean price in city A is significantly greater than the national mean price of gasoline (\(\mu_0 = 3.105\)).

The standard error (\(SE\)) is calculated as:

\[ SE = \frac{s}{\sqrt{n}} = \frac{0.0665}{\sqrt{20}} \approx 0.0149 \]

The test statistic (\(t_{test}\)) is calculated using the formula:

\[ t_{test} = \frac{\bar{x} - \mu_0}{SE} = \frac{3.1655 - 3.105}{0.0149} \approx 4.0669 \]

The p-value for this right-tailed test is:

\[ P \approx 0.0003 \]

Final Answer

Based on the results of the hypothesis test, we conclude that the mean price of gasoline in city A is significantly higher than the national mean price. The test statistic is \(t_{test} \approx 4.0669\) and the p-value is \(P \approx 0.0003\).

Thus, the answer is:

\(\boxed{\text{Gas in city A is more expensive than the national mean.}}\)

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