Question

Q.1. ) Low-carbohydrate diet A study plans to have a sample of obese adults follow a proposed low-carbohydrate diet for three months. The diet imposes limited eating of starches (such as bread and pasta) and sweets, but otherwise no limit on calorie intake. Consider the hypothesis, The population mean of the values of weight change (= weight at start of study - weight at end of study) is a positive number.

• a. Is this a null or an alternative hypothesis? Explain your reasoning.

• b. Define a relevant parameter and express the hypothesis that the diet has no effect in terms of that parameter.Is it a null or alternative hypothesis?

• Q.2.) Examples of hypotheses Give an example of a null hypothesis and an alternative hypothesis about a (a) population proportion and (b) population mean.

Answer 1

Solution :

1(a) The null hypothesis is always represented as hypothesis of no difference. And any hypothesis which is complementary to the null hypothesis is known as alternative hypothesis.

Here it is hypothesized that the population mean of the values of weight change (= weight at start of study - weight at end of study) is a positive number. It means it is hypothesized that, there is a difference in mean weight before and after the study.

Hence, this is a alternative hypothesis.

1(b) The suitable parameter would be mean of the differences of the weights before the study and after the study. We would represent this parameter with μ_{​​​​​​d}.

The hypothesis would be expressed as follows :

Hypothesis : μ_{​​​​​​d} = 0

Since, this is a hypothesis of no difference, therefore this is a null hypothesis.