For the following conjecture, determine what would the null and alternative hypotheses be.

Question

Conjecture: The average pulse of male marathon runners is less than 70 beats per minute.

a)

b)

c)

d)

e)

f)

The null hypothesis is
[ Select ]

The alternative hypothesis is
[ Select ]

Answer 1

To formulate the null and alternative hypotheses for the given conjecture, we can define them as follows:

Let \( \mu \) represent the average pulse of male marathon runners.

• The null hypothesis (H0) typically states that there is no effect or no difference, and it is often a statement of equality. In this case, it would suggest that the average pulse is at least 70 beats per minute.

• The alternative hypothesis (H1) expresses the claim that we are trying to find evidence for, which in this case states that the average pulse is less than 70 beats per minute.

Therefore, we can articulate the hypotheses as:

a) Null hypothesis (H0): \( \mu \geq 70 \)

b) Alternative hypothesis (H1): \( \mu < 70 \)

So to summarize:

• The null hypothesis is \( \mu \geq 70 \).
• The alternative hypothesis is \( \mu < 70 \).