14.28 Can we trust this interval? Here are data on the percent change in the total mass (in tons) of wildlife in several West African game preserves in the years 1971 to 1999:'

1971 1972 1973 1974 1975 1976 1977 1978 2.9 3.1 -1.2 -1.1 -3.3 3.7 1.9 -0.3 1979 1980 1981 1982 1983 1984 1985 1986 -5.9 -7.9 -5.5 -7.2 -4.1 -8.6 -5.5 -0.7 1987 1988 1989 1990 1991 1992 1993 1994 -5.1 -7.1 -4.2 0.9 -6.1 -4.1 -4.8 -11.3 1995 1996 1997 1998 1999 -9.3 -10.7 -1.8 -7.4 -22.9 Software gives the 95% confidence interval for the mean an nual percent change as —6.66% to —2.55%. There are several reasons why we might not trust this interval.

(a) Examine the distribution of the data. What feature of the distribution throws doubt on the validity of statistical infer ence?

(b) Plot the percents against year. What trend do you see in this time series? Explain why a trend over time casts doubt on the condition that years 1971 to 1999 can be treated as an SRS from a larger population of years.