Testing Hypotheses: Two Sample Tests

In 1992, a survey of 50 municipal hospitals revealed an average occupancy rate of 73.6 percent, and the sample standard deviation was 18.2 percent. Another survey of 75 municipal hospitals in 1995 found an average occupancy rate of 68.9 percent, and the sample standard deviation was 19.7 percent. At α = 0.10, can we conclude that the average occupancy rate changed signifi cantly during the 3 years between surveys?

General Cereals has just concluded a new advertising campaign for Fruit Crunch, its allnatural breakfast cereal with nuts, grains, and dried fruits. To test the effectiveness of the campaign, brand manager Alan Neebe surveyed 11 customers before the campaign and another 11 customers after the campaign. Given are the customers’ reported weekly consumption (in ounces) of Fruit Crunch:Before 14 5 18 18 30 10 8 26 13 29 24 After 23 14 13 29 33 11 12 25 21 26 34 (a) At α = 0.05, can Alan conclude that the campaign has succeeded in increasing demand for Fruit Crunch? (b) Given Alan’s initial survey before the campaign, can you suggest a better sampling procedure for him to follow after the campaign?

Ben & Jerry's Homemade, inc. is an unconventional manufacturer of super-premium ice cream known for adventurous flavors such as chocolate Chip Cookie Dough.

Students Against Drunk Driving has targeted seat-belt usage as a positive step to reduce accidents and injuries. Before a major campaign at one high school, 44 percent of 150 drivers entering the school parking lot were using their seat belts. After the seat-belt awareness program, the proportion using seat belts had risen to 52 percent in a sample of 200 vehicles. At a 0.04 signifi cance level, can the students conclude that their campaign was effective?

Allen Distributing Company hypothesizes that a phone call is more effective than a letter in speeding up collection of slow accounts. Two groups of slow accounts were contacted, one by each method, and the length of time between mailing the letter or making the call and the receipt of payment was recorded: Method Used Days to Collection Letter 10 8 9 11 11 14 10 Phone call 7 4 54869 (a) At α = 0.025, should Allen conclude that slow accounts are collected more quickly with calls than with letters? (b) Can Allen conclude that slow accounts respond more quickly to calls?

A buffered aspirin recently lost some of its market share to a new competitor. The competitor advertised that its brand enters the bloodstream faster than the buffered aspirin does and, as a result, it relieves pain sooner. The buffered-aspirin company would like to prove that there is no signifi cant difference between the two products and, hence, that the competitor’s claim is false. As a preliminary test, 9 subjects were given buffered aspirin once a day for 3 weeks. For another 3 weeks, the same subjects were given the competitive product. For each medication, the average number of minutes it took to reach each subject’s bloodstream was recorded: Subject 123456789 Buffered aspirin 16.5 25.5 23.0 14.5 28.0 10.0 21.5 18.5 15.5 Competitor 12.0 20.5 25.0 16.5 24.0 11.5 17.0 15.0 13.0 At α = 0.10, is there any signifi cant difference in the times the two medications take to reach the bloodstream?

Consider the data at the top of page 500. In the first three months of 1993, sales of luxury cary cars that were imported increased.

A chemist developing insect repellents wishes to know whether a newly developed formula gives greater protection from insect bites than that given by the leading product on the market. In an experiment, 14 volunteers each had one arm sprayed with the old product and the other sprayed with the new formula. Then each subject placed his arms into two chambers fi lled with equal numbers of mosquitoes, gnats, and other biting insects. The numbers of bites received on each arm follow. At α = 0.01, should the chemist conclude that the new formula is, indeed, more effective than the current market leader? Subject 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Old formula 525436242 65713 New formula 315114425 23312

Long Distance Carrier is trying to see the effect of offering “1 month free” with a monthly fi xed fee of $10.95, versus an offer of a low monthly fee $8.75 with no free month. To test which might be more attractive to consumers, Long Distance runs a brief market test: 12 phone reps make calls using one approach, and 10 use the other. The following number of customers agreed to switch from their present carrier to LDC: Offer Number of Switches 1 month free 118 115 122 99 106 125 102 100 92 103 113 129 Low monthly fee 115 126 113 110 135 102 124 137 108 128 Test at a signifi cance level of 10 percent whether there are signifi cant productivity differences with the two offers.

Is the perceived level of responsibility for an action related to the severity of its consequences? That question was the basis of a study of responsibility in which the subjects read a description of an accident on an interstate high-way. The consequences, in terms of cost and injury, were described as either very minor or serious. A questionnaire was used to rate the degree of responsibility that the subjects believed should be placed on the main fi gure in the story. Below are the ratings for both the mild-consequences and the severe-consequences groups. High ratings correspond to higher responsibility attributed to the main fi gure. If a 0.025 signifi cance level was used, did the study conclude that severe consequences lead to a greater attribution of responsibility?

Page 5 of 7

Start
Prev
1
2
3
4
5
6
7
Next
End

Latest Articles