**Answer:**

(a) <em>**H₀**</em>**: **<em>**p**</em>**₁ ≤ **<em>**p**</em>**₂** vs. <em>**Hₐ**</em>**: **<em>**p**</em>**₁ > **<em>**p**</em>**₂**.

(b) The point estimate of the proportion of wells drilled in 2005 that were dry is **0.202**.

(c) The point estimate of the proportion of wells drilled in 2012 that were dry is **0.111**.

(d) The <em>p</em>-value of the test is **0.017**.

The wells drilled in 2005 were **more likely **to be dry than wells drilled in 2012.

**Step-by-step explanation:**

The data provided for the wells drilled in 2005 and 2012 are as follows:

** 2005 2012**

**Wells drilled** 119 162

**Dry Wells** 24 18

(**a**)

The hypothesis to test whether the wells drilled in 2005 were more likely to be dry than wells drilled in 2012 are defined as follows:

<em>**H₀**</em>**: **The wells drilled in 2005 were not more likely to be dry than wells drilled in 2012, i.e. <em>**p**</em>**₁ ≤ **<em>**p**</em>**₂**.

<em>**Hₐ**</em>**: **The wells drilled in 2005 were more likely to be dry than wells drilled in 2012, i.e. <em>**p**</em>**₁ > **<em>**p**</em>**₂**.

(**b**)

A point estimate of a parameter (population) is a distinct value used for the estimation the parameter (population). For instance, the sample mean is a point-estimate of the population mean μ.

Similarly the point estimate of population proportion <em>**p**</em> is, .

It is computed using the formula:

Compute the point estimate of the proportion of wells drilled in 2005 that were dry as follows:

Thus, the point estimate of the proportion of wells drilled in 2005 that were dry is **0.202**.

(**c**)

Compute the point estimate of the proportion of wells drilled in 2012 that were dry as follows:

Thus, the point estimate of the proportion of wells drilled in 2012 that were dry is **0.111**.

(**d**)

A <em>z</em> - test for two proportions will be used to perform the test.

The test statistic is defined as:

Compute the value of standard error as follows:

Compute the test statistic value as follows:

Compute the <em>p</em>-value of the test as follows:

*Use a <em>z</em>-table for the probability.

Thus, the <em>p</em>-value of the test is **0.017**.

The significance level of the test is <em>**α**</em>** = 0.025**.

The <em>p</em>-value = 0.017 < <em>α</em> = 0.025.

As the <em>p</em>-value is less than the significance level the null hypothesis will be rejected at 2.5% level of significance.

<u>**Conclusion:**</u>

As the null hypothesis is rejected it can b concluded that the wells drilled in 2005 were more likely to be dry than wells drilled in 2012.