A3. For each of the following situations give either the response "could happen" (CH) or the response "impossible" (I). For example, " = -19.4" gets the response CH while

x

"x - 1 = x + 1" would get the response I. In dealing with these situations, you should assume that the arithmetic is always done correctly.

______(a) In comparing before-and-after data on the performances of 37 mutual funds, the standard deviations were sbefore = 42.4 and safter = 47.2. The standard deviation of the "after minus before" difference was 12.4.

______(b) Martha had a sample of data in inches and tested the null

x x x 1 2 n , ,...,

hypothesis : = 10 inches against the alternative hypothesis

H0 H1

: 10 inches. Edna converted the data to centimeters by multiplying by 2.54 and tested : = 25.4 cm against : 25.4 cm. Martha

cmin H0 H1

accepted the null hypothesis while Edna (using the same ) rejected it.

______(c) In a single sample = 15.2 and s = 33.5.

x

______(d) In a very strong linear relationship, the correlation was found as r = 1.18.

______(e) A hypothesis test was done at the 5% level of significance, and was H0

rejected. With the same data, but using the 1% level of significance,

H0

was again rejected.

______(f) With a single sample of n = 22 values, the 95% confidence interval for was found as 85.0 6.2 and the null hypothesis : = 92 (tested

H0

against alternative : 92) was accepted at the 5% level of

significance.

H1

______(g) In a regression involving dependent variable Y and possible independent variables G, H, K, L, and M, the regression of Y on (G, H, L) had

= 53.2% and the regression of Y on (G, K, M) had = 56.4%.

R2 R2

______(h) In a regression involving dependent variable D and possible independent variables R, S, and V, the F statistic was significant at the 5% level while all three t statistics were non-significant at the 5% level.

______(i) For a regression with two independent variables, it was found that SSregr = 58,400 and SSerror = 245,800.

______(j) In a linear regression problem, AGE was used as one of the independent variables, even though AGE = 6 for every one of the data points (which were first-grade children). The estimated coefficient was found to be bAGE = 0.31.