1) The Galileo Orbiter gathered data about Jupiter and it’s moons. In particular
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Question
1) The Galileo Orbiter gathered data about Jupiter and it’s moons. In particular, magnetometer data from Jupiter’s moon Ganymede was provided to investigators at two universities. They used the same set of data to each test the null hypothesis that no internal magnetic field existed against the alternative hypothesis that the internal magnetic field was different from zero.
After analyzing the data, investigator A concluded that Ganymede had an internal magnetic field that was different than zero, while investigator B concluded that there was no internal magnetic field.
Which of the following is NOT a valid reason why they obtained opposite results.
Investigator A used a z-statistic, whereas investigator B used a t-statistic.
Because of the volume of data available, both investigators selected a random sample of data on which to base their study. Investigator A drew a sample that was substantially smaller than the sample drawn by Investigator B.
Investigator B chose a significance level that was smaller than that selected by Investigator A.
Investigator A performed a one-tailed test to test the alternative hypothesis that the internal magnetic field was different from zero, whereas Investigator B performed a two-tailed test to test the alternative hypothesis that the magnetic field was different from zero.
Rather than be satisfied that there was a magnetic field if it was shown significantly greater than zero, Investigator B wanted a more rigorous test. He decided to conclude a magnetic field existed only if he could demonstrate that the magnetic field was significantly different than some positive number.
Investigator A used a z-statistic, whereas investigator B used a t-statistic.
Because of the volume of data available, both investigators selected a random sample of data on which to base their study. Investigator A drew a sample that was substantially smaller than the sample drawn by Investigator B.
Investigator B chose a significance level that was smaller than that selected by Investigator A.
Investigator A performed a one-tailed test to test the alternative hypothesis that the internal magnetic field was different from zero, whereas Investigator B performed a two-tailed test to test the alternative hypothesis that the magnetic field was different from zero.
Rather than be satisfied that there was a magnetic field if it was shown significantly greater than zero, Investigator B wanted a more rigorous test. He decided to conclude a magnetic field existed only if he could demonstrate that the magnetic field was significantly different than some positive number.
Explanation / Answer
1st point and 2nd point are not valid.
1st point:- Z-test is used when the sample size is large and population variance is known, whereas t-test is used when the sample size is small (<30) and population variance is unknown. Here since no information is given regarding variance and sample size, so there is no sufficient information that indicates why they obtained opposite results.
2nd point:- Choosing a sample of a small or large size does not reflect which hypothesis is true, since for any kind of test (one-sided or two-sided) the truth of null hypothesis is determined by how far the value of the test statistic lies from 0. But this is not determined by the sample size.
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