This Question: 1 pt 4 of 10 (0 complete) This Quiz: 10 pts poss In a rural area

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This Question: 1 pt 4 of 10 (0 complete) This Quiz: 10 pts poss In a rural area only about 20% of the wells that are drilled find adequate water at a depth of 100 eet or less. A local man claims to be able to find water by dowsing that is using a orked stick to indicate where the well should be drilled. You check with 66 of his customers and find that 9 have wells less than 100 feet deep. Answer the questions below. (a) Write appropriate hypotheses. Ho The percentage of successful wells drilled by the dowser HA The percentage of successful wells drilled by the dowser (b) Check the necessary assumptions. The independence condition is The randomization condition is The 10% condition is The success/failure condition is (c) Compute the test statistic. 2Round to two decimal places as needed.) Find the P-value. P-valueRound to four decimal places as needed.) (d) Explain carefully what the P-value means in this context. 0 A If his dowsing has a better success rate as standard drilling methods, there is more than a 90.3% chance of seeing results as good as hose of the dowser, or better, by natural sampling vanation. ? B. his dowsing has a worse success rate as standard drilling methods, there is more than a 90.3% chance of seeing results as good as those of the dowser, or worse, by natural sampling variation. O 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, by natural sampling variation. (e) What is your conclusion? (Consider a P-value of around 5% to represent strong evidence.) O A. We fail to reject the null hypothesis. Tere is not evidence to suggest that the dowser has a success rate higher than 20%. 0 B. We can reject the null hypothesis. There is evidence to suggest that the dowser has a success rate higher than 20%. C. We fail to reject the null hypothesis. There is evidence to suggest that the dowser has a success rate higher than 20% Click to select your answer(s).

Explanation / Answer

Solution:-

a)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P < 0.20
Alternative hypothesis: P > 0.20

Note that these hypotheses constitute a two-tailed test.  

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).

S.D = sqrt[ P * ( 1 - P ) / n ]

S.D = 0.04924
z = (p - P) /S.D

z = - 1.29

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z-score is greater than -1.29.

Thus, the P-value = 0.901

Interpret results. Since the P-value (0.901) is greater than the significance level (0.05), we cannot reject the null hypothesis.

d) (B) If his dowsing has a worse success rate as standard drilling methods, there is more than a 90.3% chance of seeing results as good as those of the dowser, or worse, by natural sampling variation.

e) (A) We fail to reject the null hypothesis. There is not evidence to suggest that the dowser has a success rate higher than 20%.

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