Question

1. 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? C. It is believed that nearsightedness affects about 8% of all children. In a random sample of 194 children, 21 are nearsighted. Do these data provide evidence that the 8% value is inaccurate? d. According to the NICTD, Agoraphobia affects about 12% of all people, but in a random sample of 300 people, 26 are agoraphobic. Do the data from the sample provide evidence to say that percentage of agoraphobic people is less than 10%?

Answer 1

(a) The key word is to find if there is a difference in the intake of calories. Also, this is a test of the mean as we are testing the average calorie intake.

H0: $\mu$ = 1000 : The average calorie intake is equal to 1100.

Ha: $\mu$ $\neq$ 1100 : The average calorie intake is different 1100.

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(b) The key word here is if the scores have changed since 2004. Also it is a test of the mean as we are talking about average scores.

H0: $\mu$ = 462 : The SAT score in 2012 intake is equal to 462.

Ha: $\mu$ $\neq$ 462 : The SAT score in 2012 intake is not equal to 462.

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(c) We see that there is no direction to the hypothesis, whether it is lesser than or greater than. In this case we use a two tailed test, and the test is for proportions, as we are finding out how many people agree or disagree.

H0: p = 0.08 : The proportion of children who are nearsighted is equal to 0.08.

Ha: p $\neq$ 0.08 : The proportion of children who are nearsighted is different from 0.08.

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(d) In this case, we have a direction (lesser than) and therefore conduct a left tailed test. Here again we use a test for proportions as we are finding out how many of a total sample have that condition.

H0: p = 0.10 : The proportion of people who are agoraphobic is equal to 0.10.

Ha: p < 0.10 :The proportion of people who are agoraphobic is less than 0.10.

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