One Sample Hypothesis Testing Review

Find the P-value and make a decision based on the given z-score and level of significance. Right tailed, z=1.98,  $\alpha$  =0.05.  

• P=0.239; Reject  $H_o$   

• P=0.239; Fail to reject  $H_o$  

• P=0.123; Reject  $H_o$  

• P=0.123; Fail to reject  $H_o$  

Find the critical value given the sample size and level of significance. Two-tailed, n=14,  $\alpha$  =0.01

• t*=-2.345 and t*=2.345

• t*=-3.012 and t*=3.012

• t*=3.012

• t*=-1.645 and t*=1.645

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 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 sufficient evidence to indicate that the average consumption of fresh citrus fruit by families in the US is at least 98 per year.

• 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.

Is this a z-test or t-test? 

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  $\alpha$  =0.05.

• 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.

•  Fail to reject $H_o$ 

• Reject  $H_o$  

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 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.

What is the difference between the way the t-test and the z-test work in this chapter?

• The difference is in the way you make a decision.

• The difference is in the way you write the null and alternate hypothesis.

• The difference is in the way you find the sample mean.

Contrast how you make a decision in the z-test versus making a decision in the t-test.

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