Chapter 10, Problem 13PT

(a)

To determine

To explain: the suitable test and to demonstrate that the criteria for carrying out this test are fulfilled.

Explanation of Solution

One means:  t test / interval of one-sample

Two mean:  paired t-test / interval

One proportion: z test / interval one-sample

Two proportions: the z-test / interval of two samples

When there is required to test for a difference, equality, rise or decrease, use a test. If there is required to measure an interval in which the true value lies, use an interval. Two-sample t-test suggests difference for a population

The test has three requirements; Random, Normal, Independent,

Random: Satisfied, since random samples are given for the samples.

Normal: Satisfied, since the sample histograms do not display strong skewness or outliers.

(b)

To determine

To Explain: The P-value which will get from the part (a).

Answer to Problem 13PT

If the mean population is equal, the probability of obtaining two samples with a difference (or more extreme difference) as in the given two samples is 5.8 percent.

Explanation of Solution

Given:

  $\begin{array}{l}{H}_0:{\mu }_1={\mu }_2\\ H_1:{\mu }_1<{\mu }_2\\ P=0.058=5.8\%\end{array}$

If the null hypothesis is valid, the P-value is the possibility of receiving the value of the test statistic, or a value more extreme.

This then implies that if the population means are equal, then the likelihood of having two samples with a difference (or a more serious difference) as in the given two sample is 5.8 percent.

(c)

To determine

To Explain: the conclusion draws at 0.05 significance level.

Explanation of Solution

Given:

From the part (b)

  $\begin{array}{l}{H}_0:{\mu }_1={\mu }_2\\ H_1:{\mu }_1<{\mu }_2\\ P=0.058=5.8\%\end{array}$

If the P-value is less than the significance level, reject the null hypothesis.

  $P=0.058>0.05\Rightarrow \text{Fail to reject }{H}_0$

There is insufficient evidence to support the claim that, on average, two-bedroom apartments rent much more than one-bedroom apartments.