2 The total of the individual weights of garbage discarded b

2. The total of the individual weights of garbage discarded by 52 households in one week have a mean of 20.443 lb. Assume that the standard deviation of the weights is 10.458 lb. Use a 0.05 significance level to test the claim that the population of households has a mean less than 30 lb. Which is the maximum amount that can be handled by the current waste removal system.

What are the test hypothesis?

Calculate the appropriate test statistic. Justify your choice.

Find the p-value for the test statistic.

Do you reject or fail to reject the null hypothesis? Why?

Solution

Mean = 20.443 lbs

Standard Deviation = 10.458 lbs

n = 52

X =30 lb

Maximum amount that can be handled by the current waste removal system. = Mean + (z*SD)/sqrt(n)

=20.443 + 1.96 *10.458/sqrt(52)

= 23.28 Answer

Test Hypothesis:

Null Hypothesis : H0 : Mean < 30

Alternate Hypothesis : H1 : Mean >= 30

z = (X- Mean)/(SD/sqrt(n))

= (30 - 20.443 ) / (10.458/sqrt(52))

= 6.5898 Answer

P-value ~ 1

Since, 1> 0.05

Failed to reject null hypothesis