Question

Identify hypotheses, Part II. Write the null and alternative hypotheses in words and using symbols for each of the following situations.

(a) Since 2008, chain restaurants in California have been required to display calorie counts of each menu item. Prior to menus displaying calorie counts, the average calorie intake of diners at a restaurant was 1100 calories. After calorie counts started to be displayed on menus, a nutritionist collected data on the number of calories consumed at this restaurant from a random sample of diners. Do these data provide convincing evidence of a difference in the average calorie intake of a diners at this restaurant?

(b) Based on the performance of those who took the GRE exam between July 1, 2004 and June 30, 2007, the average Verbal Reasoning score was calculated to be 462. In 2011 the average verbal score was slightly higher. Do these data provide convincing evidence that the average GRE Verbal Reasoning score has changed since 2004?

Answer 1

Part (A)
`H_0:\mu=1100` and
`H_a:\mu\\eq1100`

Part (B)
`H_0:\mu=462` and
`H_a:\mu>462`

Explanation:

Consider the provided statement.

Part (A)

Prior to menus displaying calorie counts, the average calorie intake of diners at a restaurant was 1100 calories. After calorie counts started to be displayed on menus, a nutritionist collected data on the number of calories consumed at this restaurant from a random sample of diners.

If there is no statistical significance in the test then it is know as the null which is denoted by
`H_0`, otherwise it is known as alternative hypothesis which denoted by
`H_a`.

`H_0`: There is no change in the average calorie intake for diners.

`H_a`: There is a difference in calorie intake for diners.

`H_0:\mu=1100`

`H_a:\mu\\eq1100`

Part (B)

the average Verbal Reasoning score was calculated to be 462. In 2011 the average verbal score was slightly higher.

If there is no statistical significance in the test then it is know as the null which is denoted by
`H_0`, otherwise it is known as alternative hypothesis which denoted by
`H_a`.

`H_0`: There is no change in the average VRS.

`H_a`: There is an increase in the average VRS.

`H_0:\mu=462`

`H_a:\mu>462`