Question

Compute a 95% confidence interval for the expected price for a gallon of gas. Assume now that I tell you that the standard deviation of gas prices across different stations is 15 cents. How will this information change your 95% confidence interval? Explain.

a) The confidence interval will become narrower.

b) The confidence interval will become wider.

c) The confidence interval will remain unchanged.

d) The confidence interval cannot be determined with the given information.

Answer 1

The 95% confidence interval will become wider when the standard deviation of gas prices is given as 15 cents.

Step-by-step explanation:

A 95% confidence interval is used to estimate the range in which the true population mean lies with a 95% level of confidence. The width of the confidence interval is influenced by the standard deviation of the sample data. When the standard deviation is larger, it means that the data points are more spread out, causing the confidence interval to be wider. Conversely, when the standard deviation is smaller, the data points are more closely packed, resulting in a narrower confidence interval.

In this case, if the standard deviation of gas prices is given as 15 cents, which is larger than the standard deviation used to calculate the initial confidence interval, the 95% confidence interval will become wider. This is because the larger standard deviation suggests that the gas prices are more spread out, increasing the range of possible values for the population mean.

The correct answer is b) The confidence interval will become wider.