Help with Writing null & alternative Hypotheses

[adamwitt]

Homework Statement

After extensive investigation, a researcher has found that the mean travel
time for mice through one particular maze is 29.0 seconds. She believes
that the mice will move faster through the maze when subjected to a loud
noise. In order to assess this, the researcher has run 17 mice separately
through the same maze, in the presence of such a noise, and recorded the
times taken. These produced a sample mean travel time of ¯x = 27.84 and a
sample standard deviation of s = 1.73 . (You may assume that the population
distribution is N(μ, σ2).)
(i) State the relevant null and alternative hypotheses, in terms of a suitable
parameter, in order to answer the question: Is there enough evidence to
suggest that the mean travel time is less than 29 seconds?

The Attempt at a Solution

I'm not sure if this is correct, could you please give me pointers on anything that I have missed?

H0: The number of samples n is sufficiently large enough to suggest that the sample mean ¯x accurately reflects the mean travel time when a loud noise is present.

H1: The number of samples n is not large enough to accurately suggest that the sample mean ¯x accurately reflects the mean travel time when a loud noise is present.



any pointers? I'm not very good at this, cheers.

 

[HallsofIvy]

You seem to be completely misunderstanding what a "hypothesis" is. The null hypothesis and alternate hypothesis have nothing to do with the number of samples.
A researcher always determines the null and alternate hypotheses before deciding how many samples to use.

"She believes that the mice will move faster through the maze when subjected to a loud noise." Her "null hypothesis", then, is "the mean time required to run the maze with a loud noise is NOT less than the mean time without the loud noise".

The number of trials determines whether or not the data is sufficient to support the null or alternate hypotheses.