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In general:

One proportion: one-sample $z$test/interval

Two proportions: two-sample $z$test/interval

One means: one-sample $t$test/interval

Two means: two-sample $t$test/interval or paired $t$test/interval

Use a test if you want to test for a difference, equality, increase or decrease. Use an interval if you want to estimate an interval in which the true value lies.

The two-sample t test for a population mean the difference

because we are interested in testing the means of two samples.

There are three conditions for the test: Random, Normal, Independent

Random: Satisfied, because the samples are given to be random samples.

Normal: Satisfied, because the histograms of the samples do not show strong skewness or outliers.

Independent: Satisfied, because the sample size is less than $10\%$of the population size.

Thus we note that all three conditions have been satisfied.

$H_0:{\mathrm{μ}}_1={\mathrm{μ}}_2$

$H_a:{\mathrm{μ}}_1<{\mathrm{μ}}_2$

$P=0.058=5.8\%$

The $P$-value is the probability of obtaining the value of the test statistic, or a value more extreme if the null hypothesis $H_0$is true.

This then means that if the population means are equal, then the probability of obtaining two samples with a difference as in the given two samples (or a more extreme difference) is localid="1650520353140" $5.8\%.$

$H_0:{\mathrm{μ}}_1={\mathrm{μ}}_2$

$H_a:{\mathrm{μ}}_1<{\mathrm{μ}}_2$

$P=0.058=5.8\%(\text{Exercise}13\mathrm{b})$

If the P-value is smaller than the significance level, reject the null hypothesis:

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

There is not sufficient evidence to support the claim that two-bedroom apartments rent for significantly more, on average than one-bedroom apartments.