Question

Share with your peers the null and alternative hypotheses for a decision that is relevant to your life. This can be a personal item or something at work. Define the population parameter, the appropriate test statistic formula, and if the hypothesis test is left-tailed, right-tailed, or two-tailed. Be sure to set up your hypotheses, too. How did you decide on constructing these hypotheses? What level of significance would you use? Why?

The population parameters that you should use for this discussion are:

μ: the population mean

or

p: the population proportion

Answer 1

We all know that sleeping hours of a student varies very much. On expert opinion every student should get at least 8 hours of sleep everyday. So we decide to test whether school students get adequate sleep or not. We decide to use Population mean, , as our choice of parameter.

Let we have a sample of n students, and we have noted down their sleeping time for a day. We assume that the sleeping time follows a normal distribution.

Let us denote,

as the sleeping time of the i^th student.

as the population mean sleeping time(in hours) of a student.

as the hypothesised value of population mean.

as the population standard deviation.

as the mean of the sleeping time(in hours) of the sample of n student.

s as the sample standard deviation of the sample of n student.

• Our population parameter is mean sleeping time(in hours) of a student.
• Our test statistic is .

• Our alternate hypothesis is left tailed test, because we suspect students get less than adequate sleep. So it's rejection region lies only in the left side.

So, Our null hypothesis will be

H₀ : The sleeping time of a student is 8 hours.

and our alternate hypothesis will be,

H₁ : The sleeping time of a student is less than 8 hours.

Then we can write the null and alternative hypothesis as,

Under this null hypothesis,

• Our choice of level of significance is 0.05. This value is a standard level used in statistical tests. This signifies that for a large number of tests, approximately 95% of the time we will reach the same conclusion.

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