A newspaper states that a family in Parramatta, on average, produces 5 kilograms of organic garbage per week.A public health officer feels that the figure is too high. The population standard deviation of the amount of organic garbage is known to be 2 kilograms.

A random sample of 10 families is chosen and the number of kilograms of organic garbage produced by these 10 families has been recorded and are as follows

2.8, 4.2, 4.0, 4.6, 2.5, 3.4, 3.2, 3.6, 5.3, 5.1

Can we conclude that public health officer is correct? Test using a level of significance of 0.05.