The manager of a plaster-manufacturing plant developed the following model to predict the demand for plaster using quarterly data for the last eight years (standard errors of the coefficients are given in parentheses):

PLAST = 5.131 + 0.0623 * BUILD - 1.212 * RATE + 0.0221 * GDP

(1.315) (0.0301) (0.662) (0.0048)

where

PLAST = quantity of plaster boards in hundreds

BUILD = number of building permits issued

RATE = average variable mortgage interest rate (in per cent)

GDP = real GDP per capita in thousands of dollars

The manager believed that higher interest rates lead to lower demand for plaster boards, taking into account the number of permits issued and real GDP per capita, and wished to test this claim using a 5% level of significance.

1. State the direction of the alternative hypothesis used for this test. Type gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box.

2. Calculate the test statistic, report your answer correct to two decimal places.

3. Use the tables in the text to determine the critical value used to conduct the test. If there are two critical values, state only the positive value.

4. Is the null hypothesis rejected for this test? Type yes or no.

5. Hence, on the basis of this test, does the manager's claim appear to be valid? Type yes or no.