Question

The average price of gasoline in the United States is $2.86. Californians believe that they pay more for gas than the national average. A sample of 100 gas stations in California has a mean price of $3.11 with a standard deviation of $0.89. Using a 0.05 significance level test the hypothesis that Califiornians pay more for gas. z=2.81 and a p-value of (1−9975) .0025<.05 So there is sufficient evidence to support the alternative hypothesis that the mean price of gasoline in California is greater than the national average of $2.86. z=−2.81 and a p-value of (1−.0025) .9974>.05 So there is not sufficient evidence to support the alternative hypothesis that the mean price of gasoline in California is greater than the national average of $2.86. z=2.50 and a p-value of (1−9938) .0062<.05 So there is sufficient evidence to support the alternative hypothesis that the mean price of gasoline in California is greater than the national average of $2.86. z=2.50 and a p-value of .9938 .9938>.05 So there is not sufficient evidence to support the alternative hypothesis that the mean amount of money spent on back to school supplies is greater than $606.40.

Answer 1

To test the hypothesis that Californians pay more for gas than the national average, a significance test is used. The test compares the sample mean price of gas in California with the national average price, using a 0.05 significance level. With a z-value of 2.81 and a p-value of (1-0.9975), there is sufficient evidence to support the alternative hypothesis that Californians pay more for gas.

Step-by-step explanation:

To test the hypothesis that Californians pay more for gas than the national average, we can use a significance test. Using a 0.05 significance level, we compare the sample mean price of gas in California ($3.11) with the national average price ($2.86). We calculate the test statistic z by subtracting the national average from the sample mean, and then dividing by the standard deviation ($0.89/√100). Comparing the z-value to the critical value and p-value, we determine whether there is sufficient evidence to support the alternative hypothesis that Californians pay more for gas.

In this case, we have z=2.81 and a p-value of (1-0.9975), which is less than 0.05. Therefore, there is sufficient evidence to support the alternative hypothesis that the mean price of gasoline in California is greater than the national average. Hence, Californians do pay more for gas.