You Can Visit the Official Website of Any Large Restaurant $\alpha$

You can visit the official website of any large restaurant chain to examine the nutritional data for menu items. For fast-food restaurants, many menu items are high in fat, so most of their calorie content comes from fat (rather than from carbohydrates or protein) . Here we investigate the relationship between the amount of fat in a menu item (in grams) and the number of calories. To predict the number of calories in a menu item given its fat content, we use the simple linear regression model calories = $\alpha$ + $\beta$ (fat) , where the deviations are assumed to be independent and Normally distributed, with mean 0 and standard deviation $\sigma$ . At one major fast-food restaurant chain, there were 26 items listed under the heading of "Sandwiches" (which includes hamburgers, chicken sandwiches, and other sandwich selections) on the menu. We fit the model to the data using the method of least squares. We treat these 26 menu items (which came from one restaurant) as a sample from the population of all sandwich items at all fast-food restaurants. Suppose the researchers test the hypotheses H₀: $\beta$ = 0, H_a: $\beta$ > 0. The value of the t statistic for this test is greater than 5. The P-value corresponding to the test of the hypotheses is:

A) more than 0.02.
B) between 0.001 and 0.02.
C) between 0.0005 and 0.001.
D) less than 0.0005.