Basic Hypothesis Testing: 1

Transcription

1 Basic Hypothesis Testing: 1 The number of cell phone users has grown exponentially since The increase in cell phone use should bring a reduction in customer local phone bills because of the heightened competition. According to The World of Wireless Communications, in 1996, the mean local monthly bill for cell phone users in the U.S. was $ A hypothesis test is to be performed to determine whether last year s mean local monthly bill for cell phone users has decreased from the 1996 mean of $ State the null and alternative and if this is two- or onetailed test. Page 1

2 Basic Hypothesis Testing: 2 According to The Beer Institute, the mean annual consumption of beer per person in the U.S gallons (roughly 235 twelve-ounce bottles). A random sample of 300 Washington, D.C., residents yielded a mean annual beer consumption of 27.8 gallons. You want to perform a hypothesis test to decide whether the mean for the nation s capital differs from the national mean. State the null and alternative and if this is two- or onetailed test. Page 2

3 Basic Hypothesis Testing: 3 The American Hospital Association reports in Hospital Stats that the mean cost to community hospitals per patient per day in U.S. hospitals was $1033 in In that same year, a random sample was obtained of 30 daily costs in Ohio hospitals. A hypothesis test was then performed to decide whether the mean cost in Ohio hospitals exceeded the national mean. State the null and alternative and if this is two- or onetailed test. Page 3

4 Z-test: 1 Recall the cell phone problem The number of cell phone users has grown exponentially since The increase in cell phone use should bring a reduction in customer local phone bills because of the heightened competition. According to The World of Wireless Communications, in 1996, the mean local monthly bill for cell phone users in the U.S. was $ A hypothesis test is to be performed to determine whether last year s mean local monthly bill for cell phone users has decreased from the 1996 mean of $ Page 4

5 Z-test: 1 Recall the cell phone problem The following are last year s local monthly bills, in dollars, for a random sample of 50 cell phone users At the 5% significance level, do the data provide sufficient evidence to conclude that last year s mean local monthly bill for cell phone users has decreased from the 1996 mean of $47.70? Assume thatσ = $25 The sum of the 50 phone bills is $2, Page 5

6 Page 6 Econometrics 322 Z-test:

7 Z-test: 1 Coding Sheet for Monthly Local Phone Bills Data Variable Possible Values Source Mnemonic Monthly Local Phone Bills Dollars, nominal Random sample, 2002, of cell phone users bills Page 7

8 Z-test: 1 Econometrics 322 Page 8

9 Z-test: 1 Page 9

10 Z-test: 1 Econometrics 322 Page 10

11 Z-test: 1 From EViews Documentation: The reported probability value is the p-value, or marginal significance level, against a twosided alternative. If this probability value is less than the size of the test, say 0.05, we reject the null hypothesis. The probability value for a one-sided alternative is one half the p-value of the two-sided test. (Emphasis added.) Conclusion: Reject H o Reason: p-value = (0.0747)/2 < 0.05 Conclusion: Mean local phone bills are statistically lower than last year s bills Note: < so also conclude reject Page 11

12 Z-test: 2 Recall the beer example According to The Beer Institute, the mean annual consumption of beer per person in the U.S gallons (roughly 235 twelve-ounce bottles). A random sample of 300 Washington, D.C., residents yielded a mean annual beer consumption of 27.8 gallons. You want to perform a hypothesis test to decide whether the mean for the nation s capital differs from the national mean. Page 12

13 Z-test: 2 Recall the beer example At the 10% level of significance, do the data provide sufficient evidence to conclude a difference exists? Test the null hypothesis. Assume gallons σ = 55 Page 13

14 Z-test: 3 Recall the hospital cost problem The American Hospital Association reports in Hospital Stats that the mean cost to community hospitals per patient per day in U.S. hospitals was $1033 in In that same year, a random sample was obtained of 30 daily costs in Ohio hospitals. The mean cost was $1123. Assuming a population standard deviation of $350 for Ohio hospitals, do the data provide sufficient evidence to conclude that, in 1997, the mean cost in Ohio hospitals exceeded the national mean of $1033? Use a 5% significance level. Page 14