Question

If a new survey were to be done with 500 Americans, would the standard error of the estimate be larger, smaller, or about the same. Assume the standard deviation has remained constant since 2010.

• about the same since the standard deviation has remained constant, so we shouldn't expect different results
• larger since we can be less sure of our estimate with a smaller sample size
• smaller since we can collect more accurate results from fewer individuals

Write the null and alternative hypotheses in words and then 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?
In symbols, the hypotheses are:

• Ho: μ = 1100
  Ha: μ < 1100
• Ho: μ = 1100
  Ha: μ = 1100
• Ho: μ = 1100
  Ha: μ ≠ 1100
• Ho: μ < 1100
  Ha: μ = 1100

(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?
In symbols, the hypotheses are:

• Ho: μ_{July, 2004} = μ_{June, 2007}
  Ha: μ_{July, 2004} ≠ μ_{June, 2007}
• Ho: μ_{July, 2004} = μ_{June, 2007}
  Ha: μ_{July 2004} > μ_{June, 2007}
• Ho: μ_{July, 2004} = μ_{June, 2007}
  Ha: μ_{July, 2004} < μ_{June, 2007}
• Ho: μ_{July, 2004} < μ_{June, 2007}
  Ha: μ_{July, 2004} = μ_{June, 2007}

Answer 1