Question

Which hypothesis test you believe you should use and why.

• One Sample Proportion Z-test

• Two Sample Proportion Z-test

• One Mean t-test

• Pooled t-test

• Non-Pooled t-test

• Paired t-test

• ANOVA F-test

• Bootstrapping is also an option

Questions:

4. The NOAA National Climatic Data Center of the United States provides data on the average annual temperature for every state in the United States. The average annual temperatures are based on data collected by weather stations throughout each state during the years 1971 to 2000. Is there strong evidence that the mean average annual temperature in the United States is greater than 50 degrees Fahrenheit? Explain. Use a significance level of 5%.

5. As gas prices continue to rise, more customers are beginning to take into account miles per gallon (a measure of the average distance traveled per unit of energy consumed) when determining which type of car to purchase. Do cars made in Japan typically get more miles per gallon than cars made in the United States? A random sample of 79 cars made in Japan had a mean of 30.48 and a standard deviation of 6.11 miles per gallon. A random sample of 249 cars made in the United States produced a mean of 20.14 and a standard deviation of 6.41 miles per gallon. Use a significance level of 0.10.

6. The U.S. Census Bureau reports that 26% of all U.S. businesses are owned by women. A Colorado consulting firm surveys a random sample of 410 businesses in the Denver area and finds that 115 of them have women owners. Should the firm conclude that its area is unusual? Test an appropriate hypothesis and state your conclusion. Use =0.05.

Answer 1

1) The NOAA National Climatic Data Center of the United States provides data on the average annual temperature for every state in the United States. The average annual temperatures are based on data collected by weather stations throughout each state during the years 1971 to 2000. Is there strong evidence that the mean average annual temperature in the United States is greater than 50 degrees Fahrenheit? Explain. Use a significance level of 5%.

For this problem, we are trying to test whether the mean average annual temperature in the United States is greater than 50 degrees Fahrenheit

So we will use the One Mean t-test here.

2) As gas prices continue to rise, more customers are beginning to take into account miles per gallon (a measure of the average distance traveled per unit of energy consumed) when determining which type of car to purchase. Do cars made in Japan typically get more miles per gallon than cars made in the United States? A random sample of 79 cars made in Japan had a mean of 30.48 and a standard deviation of 6.11 miles per gallon. A random sample of 249 cars made in the United States produced a mean of 20.14 and a standard deviation of 6.41 miles per gallon. Use a significance level of 0.10.

Here we are comparing whether cars made in Japan typically get more miles per gallon than cars made in the United States

So these two populations have separate variances and we are comparing means

So we should use Non-Pooled t-test

3) The U.S. Census Bureau reports that 26% of all U.S. businesses are owned by women. A Colorado consulting firm surveys a random sample of 410 businesses in the Denver area and finds that 115 of them have women owners. Should the firm conclude that its area is unusual? Test an appropriate hypothesis and state your conclusion. Use =0.05.

Here we are testing proportion of U.S. businesses are owned by women .

So we will use One Sample Proportion Z-test