Question

The government of state X is interested in increasing worker ability at manufacturing firms. To do so, it implemented a policy in 1987 that offered a random group of firms in the state a grant to train its workers. You collect the following data on 100 firms in the state that received the grant: the number of defective products produced at the firm after the training and the number of defective products produced at the firm before the training. The table below shows the average number of defective products produced at the firms that received the training grant, before and after the policy was implemented.

Do you reject the null hypothesis that the policy had no effect on the number of defective products against the alternative that the policy did have an effect at a 5% significance level? Show your work! The standard errors for each coefficient are shown in parenthesis below the ꞵ’s.

Year Average Number of Defective Products 1986 (before the policy) 1988 (after the policy) 100 80 |defective products = Bo + BxAfter (25.0) (10.0) X

Answer 1

We assume that the variable "After" in the regression equation is 1 for after the policy and is 0 for before the policy.

defective products = $\beta_0$ + x After

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For before the policy,

100 = $\beta_0$ + x 0

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=> $\beta_0$ = 100

For after the policy,

80 = $\beta_0$ + x 1

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=> $\beta_0$ + = 80

31

=> 100 + = 80

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=> = 80 - 100 = -20

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Thus, the regression equation is,

defective products = 100 - 20 x After

The hypothesis are,

H0: = 0

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H1:
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$\ne$ 0

Test statistic, t = Coeff / Std error = -20 / 10 = -2

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Degree of freedom, df = n - 2 = 100 - 2 = 98

For two tailed test,

P-value = 2 * P(t < -2, df = 98) =  0.0483

Since p-value is less than 0.05 significance level, we reject null hypothesis H0 and conclude that there is significant evidence that
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$\ne$ 0 and the policy had significant effect on the number of defective products.