Parametric Hypothesis Tests: Situational problems
17. From a recent nationwide study it is known that the typical American watches 25 hours of television per week (with a population standard deviation of 5.6 hours). Suppose 50 New Orleans residents are randomly selected and their viewing hours are calculated (both average and standard deviation). What technique should be used to determine whether New Orleans television viewing habits differ from the nationwide viewing habits?
One-sample difference of means—Z
20. Geographic consultant Pierre Portage is studying visitor activity patterns in the provincial park system of Quebec. Administrators of the park system want to know if park attendance levels differ from May to August, using the same set of parks in each case. What technique should Pierre advise them to apply?
Matched-pairs t
27. A random sample exit pool of Jefferson County voters resulted in the following opinions regarding a commercial-retail blue law that would prohibit businesses from being open on Sunday. In Drumlintown, 48 percent were in favor of such a law, while outside Drumlintown, 54 percent were in favor. How would you test the hypothesis that support for the blue law is higher outside Drumlintown than in the city?
Two-sample difference of proportions
29. The people in Great Britain seem less interested in joining the European Union when compared to many other European countries. By contrast, a recent referendum in Germany showed 71 percent of their voters favored joining the Union. Using recent information from a sample of British voters, how would you discover if the percentage of British favoring the Union is significantly lower than the percentage of Germans who share this attitude? Is this a one-tailed or two-tailed test?
One-sample difference of proportions, one-tailed
32. Suppose an urban planner in San Francisco, California, wants to determine if residents in rental units differ from residents in owner-occupied units with regard to the percentage favoring city rent control legislation. If random samples of residents are taken from both types of residents, what statistical test should be used?
Two-sample difference of proportations
33. Transportation planners in Minneapolis, Minnesota, are concerned about the effect of weather on the ridership levels of public transit. The feeling is that days with “bad” weather conditions (cold and snow) tend to attract more riders than “good” weather days. Given daily ridership data from local bus routes, and knowing the overall population variability in these rates, how could the difference in ridership levels be statistically validated?
Two-sample difference of means—Z
48. A random sample of residents whose homes are on the flood plain of the Mississippi River are surveyed regarding their attitudes toward various flood management policies. After a flood has occurred, the same set of residents is surveyed again about these issues. What test should be used to determine if attitudes regarding flood management policies have changed?
Matched-pairs t
50. A 2006 survey of winter guests at Tamarac Lodge showed that 28 percent of the respondents did not ski during their visit. A consultant expects that a significantly higher percentage of visitors to Tamarac Lodge this upcoming winter will not ski. How can she test this hypothesis? Is this a one-tailed or two-tailed test?
One-sample difference of proportions, one-tailed
51. In previous years, the overall average travel time for a boat trip down the Colorado River through Grand Canyon National Park was six days. Because of river congestion and overuse, park personnel think the trip might take longer now. How can they determine if boat trips now take longer?
One-sample difference of means—Z or t
53. A glaciologist studying temperature variation in Antarctica has proposed that temperatures are significantly warmer today than 300 years ago. Using 100 test sites around the continent, he has (1) measured the average temperature over the last year, and (2) estimated the temperature at those sites 300 years ago from the chemical composition of ice bores. How would he test for warming over this time period?
Matched-pairs t
55. An economic geographer is studying the spatial patterns of income in Melbourne, Australia, and it is known that the average family income is $38,346. A sample survey of 15 Melbourne families reveals an average of $40,480. How can the geographer test to see if the sample of 15 families is representative of Melborne?
One-sample difference of means—t
56. A cartographer is studying the relative effectiveness of different types of maps. The same map is produced by computer in two ways: color and black-and-white. A random sample of 15 people is selected to answer a set of interpretive questions from the color map, and another random sample of 15 people is selected to answer the same set of questions from the black-and-white map. The score for each participant is recorded. How would the cartographer test the hypothesis that higher map interpretation scores occur when the color map is used? Is this a one-tailed or two-tailed test?
Two-sample difference of means—t, one-tailed
64. A demographer for the Ontario provincial government is looking at both the number of migrants moving into economic development areas and the number of migrants leaving the same sample set of areas. How can she test the number of in-migrants and the number of out-migrants for statistically significant differences?
Matched-pairs t
70. An hydrologist is studying the volume of material carried by two rivers (expressed in grams of solid material per liter of water). One river drains an agricultural area, while the other drains a forested area. To test for differences in volume of material carried, 12 random water samples are taken from both rivers (one sample a week through the summer months). What test should be used? Is this a one-tailed or two-tailed test?
Two-sample difference of means—t, two-tailed
75. A British political geographer wants to determine if the Labour party candidate for Parliament has a similar level of support among the voting population in two neighboring towns. The proportion of a random sample of voters in each town favoring the candidate is recorded. How can one test if the difference in support for the candidate between the two towns is significant?
Two-sample difference of proportions
79. An urban geographer is examining citizens’ attitudes toward growth in a rapidly expanding suburban area. The research design is set up to survey a random sample of 230 people at two different times. People’s attitudes toward growth will first be measured before construction of a major new regional shopping mall; then the same people will be resurveyed after the mall has been open about six months. How can the geographer test whether respondents’ attitudes toward growth have changed significantly?
Matched-pairs t
89. From a representative sample of British voters, how would a political geographer determine if the percentage of voters supporting conversion to the Euro differs significantly by gender?
Two-sample difference of proportions
90. Rates of tuberculosis infection appear higher in those neighborhoods of Lagos, Nigeria, that have lower levels of industrial pollution. The World Health Organization (WHO) planner in the area argues this finding appears contrary to expectation. If she takes samples from a set of “more polluted” and “less polluted” neighborhoods, how can she test to see if tuberculosis infection rates differ?
Two-sample difference of proportions
92. A sample of residents is surveyed to determine the number of miles traveled per week for reasons not related to work. A year later, following large increases in gasoline prices, the same individuals are surveyed a second time to monitor changes in their discretionary travel behavior. How could researchers test whether the change in gasoline price led to decreased automobile use?
Matched-pairs t
97. Suppose the average age of New Zealand residents is 29.6 year. The planning director of Wellington wants to determine if the city has a typical age profile, with a mean age similar to the national average. If information is collected from a sample of 80 Wellington residents, what test should he use?
One-sample difference of means—z
110. The resource manager at a ski resort in the Catskill Mountains thinks that weather conditions in New York City on the Fridays before a weekend have a psychological and behavioral impact on winter skiers traveling to the resort. Specifically, she thinks if it is a “warm” Friday, there will be fewer skiers, and if it is a “cold” Friday, there will be more skiers, regardless of the actual conditions on the slopes. How could she see if her perception is correct, using data from the “twelve critical weekends” last winter?
Two-sample difference of means—t
130. Experts studying the rate of inflation for European states suspect a pattern. They feel that countries occupied by Germany during World War II have a higher rate of inflation than those not occupied by the Third Reich. How could they test this hypothesis? Is this a one-tailed or two-tailed test?
Two-sample difference of means—t or z, one-tailed
146. A planner records the level of noise 200 yards behind a noise barrier running along an interstate highway at 12;00 noon each day for 4 months. The noise barrier is 10 yards off the highway. She also records the level of noise over the same period of time 210 yards away from the same highway, but in an adjacent area not protected by the noise barrier. Using a sample or samples from these two data sets, how would she test whether there is a significant difference in the percentage of days that exceed an acceptable noise level?
Two-sample difference of proportions