Question

The annual maximum flow data for two different periods of record for Genesee River at Rochester, NY, are given below. Determine whether there is homogeneity in the sequence of data of two periods, at the 2.5% level of significance.

Year                  Discharge (m3/s)

Year                  Discharge (m3/s)

1948                           21,600 1949                           16,400 1950                           33,100 1951                           20,200 1952                           17,700 1953                           17,100 1954                           17,500 1955                           19,100 1956                           24,300 1957                           17,000 1958                           14,900 1959                           17,700 1960                           25,800

2001                           20,300 2002                           23,300 2003                           13,800 2004                           28,200 2005                           19,400 2006                           18,200 2007                           16,300 2008                            18,000 2009                           20,000 2010                           17,800 2011                           18,400 2012                           11,500 2013                           21,000 2014                           14,900

Answer 1

ANS -

STEP-1 State the hypotheses

I​n the test of homogeneity, the null hypothesis says that the distribution of a categorical response variable is the same in each population.

• H₀: Both the sequence of data for two periods are same.
• H_a: Both the sequence of data for two periods are not same.

Step 2 : Significance Level = 0.25

Step 3 Performing chi square test in SPSS software

Calculate Expected Frequencies and chi square statistics with the help of SPSS software

Step 4.: Test Statistic of chi square=2886400, p-value = 0.000

Step 5 : Conclusion

Since p-value = 0.000 ≤ 0.25, we reject the null hypothesis.

Step 6 : State conclusion in words

At 0.25 level of significance, there exists enough evidence to conclude that we reject the null hypothesis hence there is not homogeneity in the sequence of data of two periods, at the 2.5% level of significance.

NOTE -

• Chi-square test that is the test for homogeneity. This test determines if two or more populations (or subgroups of a population) have the same distribution of a single categorical variable.
• Homogeneous means the same in structure or composition. This test gets its name from the null hypothesis, where we claim that the distribution of the responses are the same (homogeneous) across groups.