Technical Reports      https://en.wikipedia.org/wiki/Technical_report A technical report (also scientific report) is a document that describes the process, progress, or results of technical or scienti

STAT200 Introduction to Statistics Project 6

Given the data and information in the following examples, state which type of hypothesis test is appropriate, State the random variables, and the null hypothesis. The possible tests are Two Proportions Z-test, Two Sample Paired t-test, Two Sample Independent t-test, One Factor Analysis of Variance

Note: You don’t actually have to do the tests.

1. The Municipal Transit Authority wants to know if, on weekdays, more passengers ride the northbound blue line train towards the city center that departs at 8:15 a.m. or the one that departs at 8:30 a.m. The following sample statistics are assembled by the Transit Authority. Test at the 5% level of significance whether the data provide sufficient evidence to conclude that more passengers ride the 8:30 train.

2. Suppose chemical engineers wish to compare the fuel economy obtained by two different formulations of gasoline. They test various cars with each of the gasoline formulations and get the data below. Is there a difference in gas mileage obtained between the gasoline formulations? Test at the 5% level of significance.

Table 9.1 Fuel Economy of Pairs of Vehicles

3. The average of grade point averages (GPAs) of college courses in a specific major is a measure of difficulty of the major. An educator wishes to conduct a study to find out whether the difficulty levels of different majors are the same. For such a study, a random sample of major grade point averages (GPA) of 11 graduating seniors at a large university is selected for each of the four majors mathematics, English, education, and biology. The data are given in Table 11.17 "Difficulty Levels of College Majors". Test, at the 5% level of significance, whether the data contain sufficient evidence to conclude that there are differences among the average major GPAs of these four majors.

4. Randomly selected middle-aged people in both China and the United States were asked if they believed that adults have an obligation to financially support their aged parents. The results are summarized below. Test, at the 1% level of significance, whether the data provide sufficient evidence to conclude that there exists a cultural difference in attitude regarding this question.

5. A county environmental agency suspects that the fish in a particular polluted lake have elevated mercury level. To confirm that suspicion, five striped bass in that lake were caught and their tissues were tested for mercury. For the purpose of comparison, four striped bass in an unpolluted lake were also caught and tested. The fish tissue mercury levels in mg/kg are given below. Test, at the 5% level of significance, whether the data provide sufficient evidence to conclude that fish in the polluted lake have elevated levels of mercury in their tissue.

6. Voters in a particular city who identify themselves with one or the other of two political parties were randomly selected and asked if they favor a proposal to allow citizens with proper license to carry a concealed handgun in city parks. Test, at the 5% level of significance, the hypothesis that the proportion of all members of Party A who favor the proposal is less than the proportion of all members of Party B who do. The results are:

7. The owner of a professional football team believes that the league has become more offense oriented since five years ago. To check his belief, 32 randomly selected games from one year’s schedule were compared to 32 randomly selected games from the schedule five years later. Since more offense produces more offensive yards per game, the owner analyzed the following information on offensive yards per game (oypg). Test, at the 5% level of significance, whether the data on passing yards per game provide sufficient evidence to conclude that the passing offense has become more potent in recent years.

8. The Mozart effect refers to a boost of average performance on tests for elementary school students if the students listen to Mozart’s chamber music for a period of time immediately before the test. In order to attempt to test whether the Mozart effect actually exists, an elementary school teacher conducted an experiment by dividing her third-grade class of 15 students into three groups of 5. The first group was given an end-of-grade test without music; the second group listened to Mozart’s chamber music for 10 minutes; and the third groups listened to Mozart’s chamber music for 20 minutes before the test. Testing at the 10% level, is there sufficient evidence in the data to suggest that the Mozart effect exists? The scores of the 15 students are given below:

9. Eight golfers were asked to submit their latest scores on their favorite golf courses. These golfers were each given a set of newly designed clubs. After playing with the new clubs for a few months, the golfers were again asked to submit their latest scores on the same golf courses. The results are summarized below. Test, at the 1% level of significance, the hypothesis that on average golf scores are lower with the new clubs.

10. A genetic engineering company claims that it has developed a genetically modified tomato plant that yields on average more tomatoes than other varieties. A farmer wants to test the claim on a small scale before committing to a full-scale planting. Ten genetically modified tomato plants are grown from seeds along with ten other tomato plants. At the season’s end, the resulting yields in pound are recorded as below. Test, at the 1% level of significance, whether the data provide sufficient evidence to conclude that the mean yield of the genetically modified variety is greater than that for the standard variety.