3) An experiment is conducted to examine susceptibility of root stocks of a vari

Question

3) An experiment is conducted to examine susceptibility of root stocks of a variety of lemon trees to a specific larvae. The researchers are concerned that susceptibility can exceed the threshold of 10 units per plant (the units here are long-transformed numbers of larvae per plant). Forty randomly selected plants from the studied planation were examined for larvae susceptibility. The sample mean for larvae susceptibility was equal to 10.5 and the standard deviation was equal to 3.8 Assuming that the sample standard deviation can be used as an approxi test to determine if larvae susceptibility of the planation exceeds 10 unit threshold (use a-0.05). Report the results in the table below: a. mation of the pop ulation standard deviation, conduct a statistical State HO State Ha Za Conclusion: art3 b. Determine the p-value for the test you conducted in part a. (Use Table 1) c. In part a. you conducted a one-tailed test. If you were conducting a 2 tailed test, would you expect the p-value for it would be higher or lower than what you currently have in part b.? d. Calculate what the p-value would be for a 2-tailed test

Explanation / Answer

Solution:-

3)

a)

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

Null hypothesis: u < 10
Alternative hypothesis: u > 10

Note that these hypotheses constitute a one-tailed test.  

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

Analyze sample data. Using sample data, we compute the standard error (SE), z statistic test statistic (z).

SE = s / sqrt(n)

S.E = 0.60083

z = (x - u) / SE

z = 0.832

zcritical = + 1.645

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a z statistic test statistic of 0.832.

b)

Thus the P-value in this analysis is 0.203.

Interpret results. Since the P-value (0.203) is greater than the significance level (0.05), we have to accept the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that larvea susceptibility of plantation exceeds 10 units threshold.

c) The p-value for the two tailed test would be higher than what we have currently in part b.

d) Thus the P-value in this analysis is 0.406.

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