Write the null and alternative hypotheses in words and using symbols for each of

Question

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

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 diner at this restaurant?

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?

Explanation / Answer

Null Hypothesis H0: There is no difference in the average calorie intake of diners at a restaurant before and after calorie counts started to be displayed on menus. (average calorie intake of diners before calorie counts displayed on menus = average calorie intake of diners after calorie counts displayed on menus = 1100 calories). That is,

H0: Average calorie intake of diners at a restaurant after calorie counts started to be displayed on menus = 1100

Alternative Hypothesis H1 : The average calorie intake of diners at a restaurant after calorie counts started to be displayed on menus is less than the average calorie intake of diners at a restaurant befor calorie counts started to be displayed on menus. This is a one-sided alternative hypothesis.That is,

H1: Average calorie intake of diners at a restaurant after calorie counts started to be displayed on menus < 1100

Null Hypothesis H0: There is no difference in the average Verbal Reasoning score in GRE examination for the period 2004-2007 and period 2011. (average Verbal Reasoning score in GRE examination 2004-2007 = average Verbal Reasoning score in GRE examination 2011 = 462). That is,

H0: Average Verbal Reasoning score in GRE examination 2011 = 462

Alternative Hypothesis H1 : The average Verbal Reasoning score in GRE examination 2011 is higher than the average Verbal Reasoning score in GRE examination for period 2004-2007 . This is a one-sided alternative hypothesis.That is,

H1: Average Verbal Reasoning score in GRE examination 2011 > 462

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