Question

A local authority is going to study the relationship between the size of household and the daily plastic usage consumed by them. The results of a sampling given below in Table 5 indicate some values of X (weight o plastic usage) and Y (the size of household).

Table 5: Weight of plastic usage (X) and size of household (Y)

X	0.27	1.41	2.19	2.83	2.19	1.81	0.85	3.05
Y	2	3	3	6	4	2	1	5

i) From the above sampling, find the value of correlation coefficient r.

ii) Using the same sample data set above, conduct the hypothesis testing to know whether variable X and Y are really correlates using 95% confidence level.

iii) Find out if the decision in (ii) may change if you increase the confidence level to 99%.

Answer 1

Answer (i) r = 0.8424

Explanation:

The coefficient of correlation, r is given as:

  

  

Answer (ii)

Null Hypothesis, Ho:

Alternative Hypothesis, Ha:

Test - statistics: Under Ho,

  

p- value : P[ |t6| > 3.83 ] = 0.0087

Conclusion: Since, p-value = 0.0087 < 0.05 so we reject the null hypothesis and conclude i.e. x and y are correlated.

Answer (iii) For , p-value is still less than 0.01 so we reject Ho and conclude . The decision won't change.