The U.S. Bureau of Labor Statistics released its Consumer Expenditures report in October 2008

annual-average

#1

The U.S. Bureau of Labor Statistics released its Consumer Expenditures report in October 2008. Among its findings is that average annual household spending on food at home was $3,624. Suppose a random sample of 137 households in Detroit was taken to determine whether the average annual expenditure on food at home was less for consumer units in Detroit than in the nation as a whole. The sample results are in the file Detroit Eats. Based on the sample results, can it be concluded at the ? = 0.02 level of significance that average consumer-unit spending for food at home in Detroit is less than the national average.

a. Because t = -15.7648 is less than the critical t value of -2.0736, do not reject H0.
The annual average consumer unit spending for food at home in Detroit is not less than the 2006 national consumer unit average.

b. Because t = -15.7648 is less than the critical t value of -2.0736, reject H0.
The annual average consumer unit spending for food at home in Detroit is less than the 2006 national consumer unit average.

c. Because t = -13.2314 is less than the critical t value of -1.4126, reject H0.
The annual average consumer unit spending for food at home in Detroit is less than the 2006 national consumer unit average

d. Because t = -13.2314 is less than the critical t value of -1.4126, do not reject H0.
The annual average consumer unit spending for food at home in Detroit is not less than the 2006 national consumer unit average

please tell why? thanks

Answer:

Critical value of t at 0.02 sig level and Degrees of Freedom (n - 1 = 136) is -2.0736
Since this is a left tailed test we reject any t score less than the critical value

right option is

b. Because t = -15.7648 is less than the critical t value of -2.0736, reject H0.
The annual average consumer unit spending for food at home in Detroit is less than the 2006 national consumer unit average.