Chapter 10.2, Problem 48E

a.

To determine

To find: The appropriate t statistic for the provided test.

Answer to Problem 48E

Two sample t statistic.

Explanation of Solution

Given:

The test statistic (t) is -1.05.

Two groups of birds have been compared in the first group.

There are 7 pairs and 6 pairs of birds in the first and second group respectively

Here, in this case the sample size in both groups is different which implies that the data is not paired. Since, the sample size is different and less than 30. Thus, the appropriate t statistic for the provided test is two sample t-statistic.

b.

To determine

To explain: The way in which the value of the test statistic is leading the quoted conclusion.

Answer to Problem 48E

The confidence interval is (413.62, 634.64).

Explanation of Solution

Calculation:

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:{\mu }_1={\mu }_2\\ H_a:{\mu }_1\ne {\mu }_2\end{array}$

The degree of freedom can be calculated as:

  $\begin{array}{c}df=\min \left(n_1-1,n_2-1\right)\\ =\min \left(7-1,6-1\right)\\ =5\end{array}$

The p-value is:

  $\begin{array}{c}p-value=2\times P\left(t>-1.05|\right)\\ =0.342\end{array}$

Here, p-value is greater than the significance level. The null hypothesis is not rejected. Thus, there is insufficient evidence to support the quoted conclusion.