Question

In a question involving a hypothesis test having the population mean as the target parameter, you are given the sample size, n, the assumed population mean, the significance of the test, alpha, whether it is a right-tailed, left-tailed, or two-tailed test, and the result of the test (reject or do not reject the null hypothesis.)

Show how you can use this information to find bounds on the sample itself. You may put in simple values for the information given if your prefer that to working directly with the formulas.

Suppose you were also given the P-value. Show how to obtain the test statistic from this, and the sample mean itself.

Answer 1

Here, we have to show that how we can use given information for the formation of bounds on the sample itself.

We are given a sample size n for sample data, so we can find out a degrees of freedom df for this scenario.

df = n – 1

We are given a p-value, so we can find out the value for test statistic t by using t-table. [Do reverse as you find p-value.]

After finding the t test statistic find the corresponding bounds by using the following formulas:

Lower bound = X₀ = Xbar – t_c*[S/sqrt(n)]

Upper bound = X₁ = Xbar + t_c*[S/sqrt(n)]

Where, t_c is the critical t value which will be depends upon what significance level you use for finding the bounds. Also, S is sample standard deviation and n is the sample size.

If you don’t given a value for sample mean Xbar and you have other information, then in this case you can solve above two equations alternatively and find the value for sample mean or Xbar.