Question

A local council is concerned about the amount of general household waste going to landfill. In 2018, the amount was an average of 10.42 kg per household per week. In 2019, the council introduced a series of initiatives to reduce this amount. A researcher at the local council wants to know if the average amount of general household waste going to landfill has changed since these initiatives were introduced. The researcher conducted a study in which the amount of general household waste per week was measured for a sample of 40 randomly selected households. The sample mean was 9.51 kg and the sample standard deviation was 2.33 kg. Research Question: Is the average amount of general household waste going to landfill equal to 10.42 kg per household per week, following these waste reduction initiatives? Perform an appropriate hypothesis test to answer the research question above. Hypothesis Test

Answer 1

To determine if the average amount of waste has changed, a one-sample t-test is used. The null hypothesis (H0) is that the mean waste is not different from 10.42 kg. After calculating the t-statistic, it's compared with the critical value to decide if the null hypothesis should be rejected or not.

Step-by-step explanation:

To assess whether the average amount of general household waste going to landfill has changed from 10.42 kg per household per week, we use a one-sample t-test. The null hypothesis (H0) is that the average waste per household per week is still 10.42 kg, while the alternative hypothesis (Ha) is that the average has changed (is not equal to 10.42 kg).

Step 1: State the hypotheses.

H0: μ = 10.42 (The average waste is 10.42 kg per week)

Ha: μ ≠ 10.42 (The average waste is not 10.42 kg per week)

Step 2: Calculate the test statistic.

t = (sample mean - population mean) / (sample standard deviation/√n)

t = ( 9.51 kg - 10.42 kg ) / ( 2.33 kg/√40 )

Perform the calculation to obtain the t-statistic.

Step 3: Determine the critical t-value for a 95% confidence level (usually 1.96 for large samples, but this will depend on the degrees of freedom and the exact level of significance chosen).

Step 4: Compare the t-statistic with the critical t-value to determine whether to reject or fail to reject the null hypothesis.

Note that for this test, we would need to look up the exact critical t-value based on the degrees of freedom (n-1), which is 40-1=39 for our example.

If the absolute value of the t-statistic is greater than the critical value, we reject the null hypothesis, suggesting that the waste reduction initiatives may have had an effect. If the t-statistic is within the range of the critical value, we fail to reject the null hypothesis, meaning there isn't enough evidence to suggest a change.