Question

A random sample of 73 firms in an industrial area indicated that 12 of them had handled their industrial waste incorrectly for disposal. Test to see if the proportion of firms handling their industrial waste incorrectly for disposal is significantly lower than an assumed 20% overall. Use a 3% significance level.

Answer 1

Given that, n = 73 and x = 12

=> sample proportion = 12/73 = 0.1644

The null and alternative hypotheses are,

H0 : p = 0.20

Ha : p < 0.20

Test statistic is,

=> Test statistic = Z = -0.76

p-value = P(Z < -0.76) = 1 - P(Z < 0.76) = 1 - 0.7764 = 0.2236

=> p-value = 0.2236

Since, p-value is greater than 3% significance level, we fail to reject the null hypothesis (H0).

Conclusion : There is not sufficient evidence to conclude that the proportion of firms handling their industrial waste incorrectly for disposal is significantly lower than an assumed 20% overall.

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