One Sample Hypothesis Testing Review

A citrus grower's association believes that the mean consumption of fresh citrus fruits by families in the U.S. is at least 98 pounds per year. A random sample of 13 families in the US has a mean consumption of 89.5 pounds per year with a standard deviation of 11 pounds. Test the validity of this claim at α=0.01. Calculate t to the hundredths place. t= (a)  

A citrus grower's association believes that the mean consumption of fresh citrus fruits by families in the U.S. is at least 98 pounds per year. A random sample of 13 families in the US has a mean consumption of 89.5 pounds per year with a standard deviation of 11 pounds. Test the validity of this claim at α =0.01. (Use your t from the last question.) What is the correct decision and conclusion?

• Reject $H_o$ . There is not sufficient evidence to indicate that the average consumption of fresh citrus fruit by families in the US is at least 98 per year.

• Fail to reject $H_o$ . There is sufficient evidence to indicate that the average consumption of fresh citrus fruit by families in the US is at least 98 per year.

• Fail to reject $H_o$ . There is not sufficient evidence to indicate that the average consumption of fresh citrus fruit by families in the US is at least 98 per year.

• z-test

• t-test

Calculate the P value. An auto maker estimates that the mean gas mileage of its luxury sedan is at least 25 miles per gallon. A random sample of eight such cars had a mean of 23 miles per gallon. The United Autoworkers have studied all cars of this type and found that the population standard deviation is 5 miles per gallon. Test the validity of this claim at α =0.05.

• P=.1786

• P=.897

• P=.5698

• P=.1292

Make a decision if P=.1292. 

An auto maker estimates that the mean gas mileage of its luxury sedan is at least 25 miles per gallon. A random sample of eight such cars had a mean of 23 miles per gallon. The United Autoworkers have studied all cars of this type and found that the population standard deviation is 5 miles per gallon. Test the validity of this claim at α =0.05.

Write a conclusion. An auto maker estimates that the mean gas mileage of its luxury sedan is at least 25 miles per gallon. A random sample of eight such cars had a mean of 23 miles per gallon. The United Autoworkers have studied all cars of this type and found that the population standard deviation is 5 miles per gallon. Test the validity of this claim at α =0.05.

• Since P=.1292 is greater than α =0.05, we must reject $H_o$ . There is sufficient evidence to indicate that the average gas mileage for this luxury sedan is at least 25 mpg.

• Since P=.1292 is greater than α =0.05, we must reject $H_o$ . There is not sufficient evidence to indicate that the average gas mileage for this luxury sedan is at least 25 mpg.

• Since P=.1292 is greater than α =0.05, we must fail to reject $H_o$ . There is not sufficient evidence to indicate that the average gas mileage for this luxury sedan is at least 25 mpg.

• Reject Ho, there is a significant difference

• Fail to reject Ho, there is NOT a significant difference

• Reject Ho, there is NOT a significant difference

• Accept Ho, there is a significant difference

The weight of the average 6th grade boy is 89 lbs. The principal of the school feeds them steak for first semester to see if their weight changes. What are the null and alternate hypotheses?

• H₀: μ = 89

  H₁: μ = 89

• H₀: μ = 89

  H₁: μ > 89

• H₀: μ = 89

  H₁: μ < 89

• H₀: μ = 89

  H₁: μ ≠ 89