Question

In a rural area only about 39% of the wells that are drilled find adequate water at a depth of 100 feet or less. A local man claims to be able to find water by​ dowsing, that​ is, using a forked stick to indicate where the well should be drilled. You check with 66 of his customers and find that 35 have wells less than 100 feet deep. Answer the questions below.

​(a) Write appropriate hypotheses.

Upper H 0 :H0:	The percentage of successful wells drilled by the dowser (1) ______________
Upper H Subscript Upper A Baseline :HA:	The percentage of successful wells drilled by the dowser (2) _______________

​(b) Check the necessary assumptions and conditions.

The independence assumption is (3)______________

The randomization condition is (4)___________________

The​ 10% condition is (5)______________________

The​ success/failure condition is (6)_______________

​(c) Perform the mechanics of the test. What is the​ P-value?

​P-value =__________________ ​(Round to three decimal places as​ needed.)

​(d) Explain carefully what the​ P-value means in this context.

A. If his dowsing has a better success rate as standard drilling​ methods, the​ P-value is the probability of seeing results as good as those of the​ dowser, or​ better, because of natural sampling variation.

B. If his dowsing has a worse success rate as standard drilling​ methods, the​ P-value is the probability of seeing results as bad as those of the​ dowser, or​ worse, because of natural sampling variation.

C. If his dowsing has the same success rate as standard drilling​ methods, the​ P-value is the probability of seeing results as good as those of the​ dowser, or​ better, because of natural sampling variation.

​(e) What is your​ conclusion? (Consider a​ P-value of around​ 5% to represent strong​ evidence.)

A.We can reject the null hypothesis. There is evidence to suggest that the dowser has a success rate higher than 39%.

B.We can reject the null hypothesis. There is is not evidence to suggest that the dowser has a success rate higher than 39%.

C.We fail to reject the null hypothesis. There is not evidence to suggest that the dowser has a success rate higher than 39%.

(1)

is less than 39%.

is not equal to 39%.

is equal to 39%.

is greater than 39%.

(2)

is less than 39%.

is equal to 39%.

is not equal to 39%.

is greater than 39%.

(3)

not satisfied.

satisfied.

(4)

not satisfied.

satisfied.

(5)

satisfied.

not satisfied.

(6)

not satisfied.

satisfied.

Answer 1

a) Hypotheses Formulation:

Null hypothesis	The percentage of successful wells drilled by the dowser : 39% of the wells that are drilled find adequate water at a depth of 100 feet or less. i.e p = 0.39
Alternative hypotheiss	Greater than 39% of the wells that are drilled find adequate water at a depth of 100 feet or less. i.e p > 0.39

(b) conditions (3), (4), (5), (6)

(c)

We need to find evidence to support his claim. So: define

P=P( find water at a depth <100 fts via dowsing)

Test and CI for One Proportion

Method

p: event proportion

Exact method is used for this analysis.

Descriptive Statistics

N	Event	Sample p	95% Lower Bound for p
66	35	0.530303	0.422274

Test

Null hypothesis	H₀: p = 0.39
Alternative hypothesis	H₁: p > 0.39

P-Value

0.014

(d) C. If his dowsing has the same success rate as standard drilling​ methods, the​ P-value is the probability of seeing results as good as those of the​ dowser, or​ better, because of natural sampling variation.

(e) A. We can reject the null hypothesis. There is evidence to suggest that the dowser has a success rate higher than 39%.