Question

It is known that cooking rice in limited water (all the water is absorbed by the kernels) increases the concentration of arsenic above what existed in the raw rice.  Can cooking rice in excess water (after the rice kernels are soft, the excess liquid is drained off) reduce the arsenic concentration? Five batches of rice were obtained. For each batch, the arsenic concentration was measured before cooking and again after cooking with excess water.

The appropriate hypotheses are

	A.	H0: μraw = μcooked versus Ha: μraw ≠ μcooked
	B.	H0: μraw = μcooked versus Ha: μraw < μcooked
	C.	H0: μraw = μcooked versus Ha: μraw > μcooked
	D.	H0: μraw < μcooked versus Ha: μraw > μcooked

Answer 1

Answer 2

The appropriate hypotheses for this scenario are:

A. H0: μraw = μcooked versus Ha: μraw ≠ μcooked

Explanation: In hypothesis testing, we have a null hypothesis (H0) and an alternative hypothesis (Ha). The null hypothesis usually represents the status quo or the default assumption, while the alternative hypothesis represents what we are trying to investigate or find evidence for.

In this case, the null hypothesis (H0) states that there is no difference in the mean arsenic concentration between raw rice and rice cooked with excess water. The symbol μraw represents the population mean of arsenic concentration in raw rice, and μcooked represents the population mean of arsenic concentration in rice cooked with excess water.

The alternative hypothesis (Ha) is a two-tailed hypothesis (indicated by "≠"), which means we are testing whether there is any difference in the mean arsenic concentration between raw rice and rice cooked with excess water, without specifying the direction of the difference. The alternative hypothesis allows for the possibility that the arsenic concentration could be either higher or lower in the cooked rice compared to the raw rice.

By choosing A. H0: μraw = μcooked versus Ha: μraw ≠ μcooked, we are testing whether the cooking method (excess water) has any effect on the mean arsenic concentration in rice, without assuming a specific direction for the difference.