Question

Use the Sign Test. If software is needed, please use Excel. I only have Excel and a TI-30X calculator.

Use the Sign Test. If software is needed, please use Excel. I only have Excel and a TI-30X calculator.

Appendix B Data Sets. In Exercises 13-16, refer to the indicated data set in Appendix B and use the sign test for the claim about the median of a population. 13. Earthquake Magnitudes Refer to Data Set 21 "Earthquakes" in Appendix B for the earthquake magnitudes. Use a 0.01 significance level to test the claim that the median is equal to 2.00. Data Set 21: Earthquakes MAGNITUDE is magnitude measured on the Richter scale and DEPTH is depth in km. The magnitude and depth both describe the source of the earthquake. The data are from the Southern California Data are from 600 matched pairs (first five rows shown here) of magnitude/depth measurements randomly selected from 10,594 earthquakes recorded in one year from a location in southern California. Only earthquakes with a magnitude of at least 1.00 are used Earthquake Data Center. MAGNITUDE DEPTH 2.45 0.7 3.62 6.0 3.06 7.0 3.30 5.4 1.09 0.5

Answer 1

We will set up the null hypothesis that

H₀: No of positive signs are equal to negative signs.
H₁: No of positive signs are not equal to negative signs.

Magnitude	Depth	Difference	Signs
2.45	0.7	1.75	+
3.62	6	-2.38	-
3.06	7	-3.94	-
3.3	5.4	-2.1	-
1.09	0.3	0.79	+

Out of 5 trials 2 are positive and 3 are  negative signs. The null hypothesis is that there are an equal number of signs (i.e. 50/50). Therefore, the test is a simple binomial experiment with a 0.5 chance of the sign being negative and 0.5 of it being positive (assuming the null hypothesis is true).

The p.value is obtained as follow

r(n-r) P p

r(n-r) P p

P.Value --

P Value - 0,5

Since P.value = 0.5 which is greater then 0.05 hence we will accept null hypothesis and  conclude that no of positive signs are equal to negative signs.